metadata_export.json

[
  {
    "slug": "ad",
    "name": "Accumulation/Distribution Line (AD)",
    "description": "A volume-based indicator designed to measure the cumulative flow of money into and out of a security.",
    "usage": "Use to confirm price trends or identify potential reversals through divergences. Rising AD confirms an uptrend; falling AD confirms a downtrend.",
    "category": "Classic",
    "keywords": [
      "volume",
      "momentum",
      "classic",
      "accumulation",
      "distribution"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/terms/a/accumulationdistributioncurve.asp",
    "formula_latex": "\n\\[\n\\text{MFM} = \\frac{(Close - Low) - (High - Close)}{High - Low} \\\\ \\text{MFV} = \\text{MFM} \\times Volume \\\\ AD_t = AD_{t-1} + \\text{MFV}\n\\]\n",
    "gold_standard_file": "ad.json",
    "ehlers_summary": "Developed by Marc Chaikin, the AD line uses the relationship between price and volume to determine whether a security is being accumulated or distributed. It is calculated by multiplying the Money Flow Multiplier by the period's volume and adding it to a cumulative total. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "volume",
    "boundary_kind": "cumulative"
  },
  {
    "slug": "adaptive_ema",
    "name": "Adaptive Exponential Moving Average",
    "description": "An adaptive moving average that adjusts its smoothing factor based on volatility.",
    "usage": "Use to identify overall trends. AEMA reacts faster to large price movements by adapting the smoothing factor using the highest high and lowest low of a lookback period.",
    "category": "Moving Averages",
    "keywords": [
      "moving-average",
      "adaptive",
      "volatility",
      "trend"
    ],
    "params": [
      {
        "name": "period",
        "default": "10",
        "description": "Smoothing period"
      },
      {
        "name": "pds",
        "default": "10",
        "description": "Lookback period for volatility"
      }
    ],
    "formula_source": "Technical Analysis of Stocks & Commodities, April 2019",
    "formula_latex": "\n\\[\nRate = \\frac{2}{P+1} \\times \\left(1 + \\frac{|(C - L_{min}) - (H_{max} - C)|}{H_{max} - L_{min}}\\right) \\\\ AEMA_t = AEMA_{t-1} + Rate \\times (C - AEMA_{t-1})\n\\]\n",
    "gold_standard_file": "",
    "ehlers_summary": "Introduced by Vitali Apirine in TASC April 2019, AEMA alters the EMA's alpha (smoothing factor) by comparing the distance of the close from the lowest low and highest high. This amplifies the smoothing factor during strong price moves while reducing it during sideways chop, yielding a moving average with less lag when it matters most.",
    "struct_name": "AdaptiveEma",
    "source_file": "adaptive_ema",
    "boundary_kind": "scalar"
  },
  {
    "slug": "adosc",
    "name": "Chaikin Oscillator (ADOSC)",
    "description": "An indicator that measures the momentum of the Accumulation/Distribution Line using the difference between two exponential moving averages.",
    "usage": "Use to anticipate changes in the AD Line. Positive values indicate increasing buying pressure, while negative values indicate increasing selling pressure.",
    "category": "Classic",
    "keywords": [
      "volume",
      "oscillator",
      "momentum",
      "classic"
    ],
    "params": [
      {
        "name": "fastperiod",
        "default": "3",
        "description": "Fast EMA period"
      },
      {
        "name": "slowperiod",
        "default": "10",
        "description": "Slow EMA period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/c/chaikinoscillator.asp",
    "formula_latex": "\n\\[\nADOSC = EMA(AD, 3) - EMA(AD, 10)\n\\]\n",
    "gold_standard_file": "adosc.json",
    "ehlers_summary": "Marc Chaikin developed this oscillator to identify momentum shifts in the AD Line. By applying EMAs of different lengths to the AD Line, it highlights changes in money flow before they become apparent in the cumulative total, providing an early warning system for trend exhaustion. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "volume",
    "boundary_kind": "scalar"
  },
  {
    "slug": "adx",
    "name": "Average Directional Index (ADX)",
    "description": "An indicator used to quantify trend strength without regard to trend direction.",
    "usage": "Use to determine if the market is trending or ranging. ADX values above 25 indicate a strong trend, while values below 20 indicate a weak or non-trending market.",
    "category": "Classic",
    "keywords": [
      "trend",
      "volatility",
      "classic",
      "wilder"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "14",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/a/adx.asp",
    "formula_latex": "\n\\[\nADX = 100 \\times \\frac{\\text{EMA}(|(+DI) - (-DI)| / |(+DI) + (-DI)|, n)}{n}\n\\]\n",
    "gold_standard_file": "adx.json",
    "ehlers_summary": "Developed by J. Welles Wilder, the ADX is derived from two other indicators, also developed by Wilder: the Positive Directional Indicator (+DI) and the Negative Directional Indicator (-DI). While +DI and -DI indicate trend direction, ADX measures the strength of that trend. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "alligator",
    "name": "Bill Williams Alligator",
    "description": "Trend-following indicator using three delayed smoothed moving averages.",
    "usage": "Use to identify trend presence and direction. When the three Alligator lines are separated and fanning, the market is trending; when they converge or intertwine, the market is ranging.",
    "category": "Classic",
    "keywords": [
      "trend",
      "moving-average",
      "classic",
      "williams"
    ],
    "params": [],
    "formula_source": "https://chartschool.stockcharts.com/table-of-contents/technical-indicators-and-overlays/alligator",
    "formula_latex": "\n\\[\n\\text{Jaw} = \\text{SMMA}(13, 8), \\text{Teeth} = \\text{SMMA}(8, 5), \\text{Lips} = \\text{SMMA}(5, 3)\n\\]\n",
    "gold_standard_file": "alligator.json",
    "ehlers_summary": "Bill Williams introduced the Alligator in Trading Chaos (1995) as three offset SMAs with periods 13, 8, and 5 and offsets of 8, 5, and 3 bars. The three lines represent the Jaw, Teeth, and Lips of the Alligator. When the Alligator is sleeping (lines intertwined) no trade is taken; when it wakes and opens its mouth a trend trade is entered. — StockCharts ChartSchool",
    "struct_name": "Alligator",
    "source_file": "alligator",
    "boundary_kind": "scalar"
  },
  {
    "slug": "alma",
    "name": "Arnaud Legoux Moving Average",
    "description": "ALMA is designed to reduce lag while providing high smoothness.",
    "usage": "Use as a low-latency moving average that reduces lag compared to EMA while controlling overshoot through the Gaussian offset parameter. Well-suited for momentum systems.",
    "category": "Classic",
    "keywords": [
      "moving-average",
      "smoothing",
      "low-latency",
      "adaptive"
    ],
    "params": [
      {
        "name": "period",
        "default": "9",
        "description": "Period"
      },
      {
        "name": "offset",
        "default": "0.85",
        "description": "Offset"
      },
      {
        "name": "sigma",
        "default": "6.0",
        "description": "Sigma"
      }
    ],
    "formula_source": "https://www.prorealcode.com/prorealtime-indicators/arnaud-legoux-moving-average-alma/",
    "formula_latex": "\n\\[\nALMA = \\sum (W_i \\times P_i) / \\sum W_i\n\\]\n",
    "gold_standard_file": "alma.json",
    "ehlers_summary": "The Arnaud Legoux Moving Average applies a Gaussian-shaped weight distribution offset toward the recent end of the lookback window. The sigma parameter controls weight spread and the offset parameter controls how far the Gaussian peak is positioned from the current bar, enabling a lag-accuracy trade-off unavailable in standard MAs.",
    "struct_name": "Alma",
    "source_file": "alma",
    "boundary_kind": "scalar"
  },
  {
    "slug": "am_detector",
    "name": "AM Detector",
    "description": "Recovers market volatility from the amplitude-modulated whitened price spectrum.",
    "usage": "Use to extract the instantaneous amplitude and frequency of market cycles. The AM output measures cycle energy for position sizing; the FM output tracks cycle period for adaptive indicator tuning.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "ehlers",
      "dsp",
      "amplitude",
      "frequency"
    ],
    "params": [
      {
        "name": "highest_len",
        "default": "4",
        "description": "Envelope lookback length"
      },
      {
        "name": "avg_len",
        "default": "8",
        "description": "Smoothing length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/AMFM.pdf",
    "formula_latex": "\n\\[\nDeriv = |Close - Open|, Envel = \\max(Deriv, 4), Volatil = \\text{Avg}(Envel, 8)\n\\]\n",
    "gold_standard_file": "am_detector.json",
    "ehlers_summary": "Ehlers adapts AM and FM demodulation techniques from radio engineering in Cycle Analytics for Traders to extract cycle amplitude and instantaneous frequency from market data. The amplitude envelope measures how energetic the current cycle is, while FM reveals whether the cycle period is expanding or contracting.",
    "struct_name": "AmDetector",
    "source_file": "amfm",
    "boundary_kind": "scalar"
  },
  {
    "slug": "apo",
    "name": "Absolute Price Oscillator (APO)",
    "description": "Shows the absolute difference between two moving averages of different periods.",
    "usage": "Use to identify trend crossovers and momentum. It is essentially a MACD without the signal line, showing the raw distance between fast and slow averages.",
    "category": "Classic",
    "keywords": [
      "trend",
      "momentum",
      "moving-average",
      "classic"
    ],
    "params": [
      {
        "name": "fastperiod",
        "default": "12",
        "description": "Fast period"
      },
      {
        "name": "slowperiod",
        "default": "26",
        "description": "Slow period"
      }
    ],
    "formula_source": "https://www.tradingview.com/support/solutions/43000501826-absolute-price-oscillator-apo/",
    "formula_latex": "\n\\[\nAPO = EMA(fast) - EMA(slow)\n\\]\n",
    "gold_standard_file": "apo.json",
    "ehlers_summary": "The Absolute Price Oscillator (APO) is based on the difference between two exponential moving averages. It is a trend-following indicator that signals a change in direction when the fast EMA crosses the slow EMA, providing a clear visual of trend development. — TA-Lib Documentation",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "aroon",
    "name": "Aroon Indicator",
    "description": "An indicator system that identifies when a new trend is beginning and the strength of the trend.",
    "usage": "Use to identify when a security is trending and when it is in a range-bound period. Aroon Up crossing above Aroon Down signals the start of a new uptrend.",
    "category": "Classic",
    "keywords": [
      "trend",
      "classic",
      "breakout"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "25",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/a/aroon.asp",
    "formula_latex": "\n\\[\n\\text{Aroon Up} = \\frac{n - \\text{Periods since n-period High}}{n} \\times 100\n\\]\n",
    "gold_standard_file": "aroon.json",
    "ehlers_summary": "Developed by Tushar Chande in 1995, the Aroon indicator focuses on the time between highs and the time between lows over a given period. The idea is that strong uptrends will regularly see new highs, and strong downtrends will regularly see new lows. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "atr",
    "name": "Average True Range",
    "description": "ATR represents the average of true ranges over a specified period.",
    "usage": "Use as the foundational volatility module providing ATR, True Range, and related volatility measures used by higher-level indicators such as SuperTrend and Keltner Channels.",
    "category": "Classic",
    "keywords": [
      "volatility",
      "atr",
      "classic",
      "range"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/a/atr.asp",
    "formula_latex": "\n\\[\nATR = \\frac{ATR_{t-1} \\times (n-1) + TR_t}{n}\n\\]\n",
    "gold_standard_file": "atr.json",
    "ehlers_summary": "Average True Range, developed by J. Welles Wilder in New Concepts in Technical Trading Systems (1978), measures the average of the true range over N bars. True Range accounts for overnight gaps by taking the maximum of: current high minus low, current high minus prior close, prior close minus current low. It remains the industry standard raw volatility measure.",
    "struct_name": "Atr",
    "source_file": "volatility",
    "boundary_kind": "scalar"
  },
  {
    "slug": "atr_ts",
    "name": "ATR Trailing Stop",
    "description": "A trailing stop based on Average True Range to keep trades in a trend.",
    "usage": "Use as a dynamic trailing stop that widens in volatile markets and tightens in calm ones, automatically adjusting stop distance to current market conditions.",
    "category": "Classic",
    "keywords": [
      "volatility",
      "trend",
      "stop-loss",
      "atr",
      "classic"
    ],
    "params": [
      {
        "name": "period",
        "default": "10",
        "description": "ATR period"
      },
      {
        "name": "multiplier",
        "default": "3.0",
        "description": "ATR Multiplier"
      }
    ],
    "formula_source": "https://www.tradingview.com/support/solutions/43000589105-average-true-range-atr/",
    "formula_latex": "\n\\[\nStop = P_{high} - (Multiplier \\times ATR)\n\\]\n",
    "gold_standard_file": "atr_ts.json",
    "ehlers_summary": "ATR Trailing Stop uses Average True Range to set a stop distance that scales with market volatility. During high-volatility regimes the stop moves further from price to avoid premature exit; during low-volatility regimes it tightens to lock in more profit. It is one of the most robust mechanical stop methods in systematic trading.",
    "struct_name": "ATRTrailingStop",
    "source_file": "atr_ts",
    "boundary_kind": "scalar"
  },
  {
    "slug": "autotune_filter",
    "name": "AutoTune Filter",
    "description": "An adaptive BandPass filter that dynamically tunes itself to the market's dominant cycle.",
    "usage": "Use to isolate the cyclical component of price while automatically adapting to changes in cycle length. Zero crossings of the output or its rate of change can be used as trading signals.",
    "category": "Ehlers DSP",
    "keywords": [
      "adaptive",
      "filter",
      "cycle",
      "ehlers",
      "dsp",
      "autotune"
    ],
    "params": [
      {
        "name": "window",
        "default": "20",
        "description": "Window length for autocorrelation and HighPass filter"
      },
      {
        "name": "bandwidth",
        "default": "0.25",
        "description": "Bandwidth of the tuned BandPass filter"
      }
    ],
    "formula_source": "references/Ehlers Papers/The AutoTune Filter.pdf",
    "formula_latex": "\n\\[\nR(lag) = \\frac{n \\sum X_i Y_i - \\sum X_i \\sum Y_i}{\\sqrt{(n \\sum X_i^2 - (\\sum X_i)^2)(n \\sum Y_i^2 - (\\sum Y_i)^2)}}\n\\]\n\\[\nDC = 2 \\times \\text{argmin}_{lag} R(lag)\n\\]\n\\[\nBP = \\text{BandPass}(Price, DC, BW)\n\\]\n",
    "gold_standard_file": "autotune_filter.json",
    "ehlers_summary": "The AutoTune filter provides a bridge between the time domain and frequency domain by using a rolling autocorrelation function to measure the Dominant Cycle in real time. By dynamically tuning a Bandpass filter to twice the lag at which autocorrelation is minimized, it maintains consistent performance and avoids the destructive phase shifts typical of fixed-tuned filters.",
    "struct_name": "AutotuneFilter",
    "source_file": "autotune",
    "boundary_kind": "scalar"
  },
  {
    "slug": "avgprice",
    "name": "Average Price (AVGPRICE)",
    "description": "The simple average of the Open, High, Low, and Close prices for a given period.",
    "usage": "Use as a smoothed price input for other indicators. It provides a more balanced view of the period's price action than the Close price alone.",
    "category": "Classic",
    "keywords": [
      "price-transform",
      "classic",
      "smoothing"
    ],
    "params": [],
    "formula_source": "https://www.tradingview.com/support/solutions/43000502588-average-price-avgprice/",
    "formula_latex": "\n\\[\nAVGPRICE = \\frac{Open + High + Low + Close}{4}\n\\]\n",
    "gold_standard_file": "avgprice.json",
    "ehlers_summary": "Average Price is the arithmetic mean of the four key price points in a bar. In technical analysis, using Average Price instead of Close can help filter out erratic price spikes and provide a more stable foundation for trend-following algorithms. — TA-Lib Documentation",
    "struct_name": "OC2",
    "source_file": "price_transform",
    "boundary_kind": "scalar"
  },
  {
    "slug": "bandpass",
    "name": "BandPass",
    "description": "A bandpass filter that isolates cycle components around a center period.",
    "usage": "Apply to isolate a specific cycle period in price, filtering out both trend and noise. Use zero crossings of the filtered output as entry and exit signals.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "cycle",
      "ehlers",
      "dsp",
      "bandpass"
    ],
    "params": [
      {
        "name": "period",
        "default": "20",
        "description": "Center period of the passband"
      },
      {
        "name": "bandwidth",
        "default": "0.1",
        "description": "Relative bandwidth (delta)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/EmpiricalModeDecomposition.pdf",
    "formula_latex": "\n\\[\n\\beta = \\cos(360/P), \\gamma = 1/\\cos(720\\delta/P), \\alpha = \\gamma - \\sqrt{\\gamma^2 - 1}\n\\]\n\\[\nBP = 0.5(1 - \\alpha)(Price - Price_{t-2}) + \\beta(1 + \\alpha)BP_{t-1} - \\alpha BP_{t-2}\n\\]\n",
    "gold_standard_file": "bandpass.json",
    "ehlers_summary": "Ehlers presents the BandPass filter in Cybernetic Analysis as a second-order IIR filter centred on a target cycle period with tunable bandwidth. It simultaneously attenuates lower and higher frequencies, leaving only the desired cycle band in the output.",
    "struct_name": "Bandpass",
    "source_file": "bandpass",
    "boundary_kind": "scalar"
  },
  {
    "slug": "bbands",
    "name": "Bollinger Bands",
    "description": "A volatility indicator consisting of a middle SMA and two outer bands based on standard deviation.",
    "usage": "Use to identify overbought/oversold levels and volatility breakouts. Prices near the upper band suggest overbought conditions, while prices near the lower band suggest oversold conditions. Narrowing bands (The Squeeze) often precede large price moves.",
    "category": "Classic",
    "keywords": [
      "volatility",
      "trend",
      "classic",
      "bands"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "20",
        "description": "SMA period"
      },
      {
        "name": "nbdevup",
        "default": "2.0",
        "description": "Upper deviation multiplier"
      },
      {
        "name": "nbdevdn",
        "default": "2.0",
        "description": "Lower deviation multiplier"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/b/bollingerbands.asp",
    "formula_latex": "\n\\[\nMiddle = SMA(n) \\\\ Upper = Middle + (k \\times \\sigma) \\\\ Lower = Middle - (k \\times \\sigma)\n\\]\n",
    "gold_standard_file": "bbands.json",
    "ehlers_summary": "Developed by John Bollinger in the 1980s, Bollinger Bands adapt to volatility by using standard deviation. The middle band is typically a 20-period SMA, and the outer bands are set 2 standard deviations away. This ensures that 95% of price action typically stays within the bands, making escapes highly significant. — BollingerOnBollingerBands.com",
    "struct_name": "",
    "source_file": "overlap",
    "boundary_kind": "scalar"
  },
  {
    "slug": "beta",
    "name": "Beta (BETA)",
    "description": "A measure of a security's volatility in relation to the overall market.",
    "usage": "Use to understand the systematic risk of an asset. A beta of 1.0 indicates the asset moves with the market; >1.0 means it is more volatile, and <1.0 means it is less volatile.",
    "category": "Classic",
    "keywords": [
      "statistics",
      "risk",
      "classic",
      "volatility"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "30",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/b/beta.asp",
    "formula_latex": "\n\\[\n\\beta = \\frac{\\text{Cov}(R_i, R_m)}{\\text{Var}(R_m)}\n\\]\n",
    "gold_standard_file": "beta.json",
    "ehlers_summary": "Beta is a measure of the volatility—or systematic risk—of a security or portfolio compared to the market as a whole. It is used in the Capital Asset Pricing Model (CAPM) to calculate the expected return of an asset based on its beta and expected market returns. — Investopedia",
    "struct_name": "StandardDeviation",
    "source_file": "statistics",
    "boundary_kind": "scalar"
  },
  {
    "slug": "butterworth2",
    "name": "Butterworth2",
    "description": "2-pole Butterworth low-pass filter.",
    "usage": "Use to smooth price or intermediate indicator values with a flat passband and sharp rolloff. The 3-pole version provides steeper attenuation at the cost of marginally more lag.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "smoothing",
      "low-pass"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Critical period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/Poles.pdf",
    "formula_latex": "\n\\[\na = \\exp(-1.414\\pi/P)\n\\]\n\\[\nb = 2a \\cos(1.414\\pi/P)\n\\]\n\\[\nf = bf_{t-1} - a^2f_{t-2} + \\frac{1-b+a^2}{4}(g + 2g_{t-1} + g_{t-2})\n\\]\n",
    "gold_standard_file": "butterworth2.json",
    "ehlers_summary": "Butterworth filters are maximally flat in the passband, introducing no ripple. Ehlers implements 2-pole and 3-pole Butterworth IIR designs in Cycle Analytics for Traders, noting that the SuperSmoother is actually a critically-damped 2-pole Butterworth variant.",
    "struct_name": "Butterworth2",
    "source_file": "butterworth",
    "boundary_kind": "scalar"
  },
  {
    "slug": "butterworth3",
    "name": "Butterworth3",
    "description": "3-pole Butterworth low-pass filter.",
    "usage": "Use to smooth price or intermediate indicator values with a flat passband and sharp rolloff. The 3-pole version provides steeper attenuation at the cost of marginally more lag.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "smoothing",
      "low-pass"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Critical period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/Poles.pdf",
    "formula_latex": "\n\\[\na = \\exp(-\\pi/P)\n\\]\n\\[\nb = 2a \\cos(1.738\\pi/P)\n\\]\n\\[\nc = a^2\n\\]\n\\[\nf = (b+c)f_{t-1} - (c+bc)f_{t-2} + c^2f_{t-3} + \\frac{(1-b+c)(1-c)}{8}(g + 3g_{t-1} + 3g_{t-2} + g_{t-3})\n\\]\n",
    "gold_standard_file": "butterworth3.json",
    "ehlers_summary": "Butterworth filters are maximally flat in the passband, introducing no ripple. Ehlers implements 2-pole and 3-pole Butterworth IIR designs in Cycle Analytics for Traders, noting that the SuperSmoother is actually a critically-damped 2-pole Butterworth variant.",
    "struct_name": "Butterworth3",
    "source_file": "butterworth",
    "boundary_kind": "scalar"
  },
  {
    "slug": "cci",
    "name": "Commodity Channel Index (CCI)",
    "description": "A versatile indicator that can be used to identify a new trend or warn of extreme conditions.",
    "usage": "Use to identify cyclical turns in commodities or stocks. Readings above +100 imply a strong uptrend, while readings below -100 imply a strong downtrend.",
    "category": "Classic",
    "keywords": [
      "momentum",
      "oscillator",
      "classic",
      "mean-reversion"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "14",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/c/commoditychannelindex.asp",
    "formula_latex": "\n\\[\nCCI = \\frac{Price - SMA}{0.015 \\times \\text{Mean Deviation}}\n\\]\n",
    "gold_standard_file": "cci.json",
    "ehlers_summary": "Developed by Donald Lambert in 1980, the CCI measures the current price level relative to an average price level over a given period. CCI is relatively high when prices are far above their average and relatively low when prices are far below their average. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "cdl2crows",
    "name": "Two Crows",
    "description": "A bearish reversal pattern consisting of three candles.",
    "usage": "Signals a potential top in an uptrend.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdl2crows.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdl3blackcrows",
    "name": "Three Black Crows",
    "description": "A bearish reversal pattern with three long red candles.",
    "usage": "Signals a major trend reversal to the downside.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdl3blackcrows.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdl3inside",
    "name": "Three Inside Up/Down",
    "description": "A reversal pattern confirmed by a third candle.",
    "usage": "Signals a more reliable trend change than a simple harami.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdl3inside.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdl3linestrike",
    "name": "Three-Line Strike",
    "description": "A continuation pattern where four candles are involved.",
    "usage": "Signals a temporary pause before the trend continues.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdl3linestrike.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdl3outside",
    "name": "Three Outside Up/Down",
    "description": "A reversal pattern confirmed by a third candle.",
    "usage": "Signals a more reliable trend change than a simple engulfing.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdl3outside.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdl3starsinsouth",
    "name": "Three Stars In The South",
    "description": "A rare bullish reversal pattern in a downtrend.",
    "usage": "Indicates a gradual exhaustion of selling pressure.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdl3starsinsouth.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdl3whitesoldiers",
    "name": "Three White Soldiers",
    "description": "A bullish reversal pattern with three long green candles.",
    "usage": "Signals a major trend reversal to the upside.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdl3whitesoldiers.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlabandonedbaby",
    "name": "Abandoned Baby",
    "description": "A very rare reversal pattern with a doji gapping away.",
    "usage": "One of the most reliable reversal signals.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlabandonedbaby.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdladvanceblock",
    "name": "Advance Block",
    "description": "A bearish reversal pattern in an uptrend.",
    "usage": "Indicates weakening momentum in an upward move.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdladvanceblock.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlbelthold",
    "name": "Belt-Hold",
    "description": "A single candle pattern signaling a reversal.",
    "usage": "Indicates a strong opening in the opposite direction of the trend.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlbelthold.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlbreakaway",
    "name": "Breakaway",
    "description": "A five-candle reversal pattern.",
    "usage": "Signals the breakout from a short-term consolidation.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlbreakaway.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlclosingmarubozu",
    "name": "Closing Marubozu",
    "description": "A candle with no shadow at the closing end.",
    "usage": "Indicates strong conviction in the direction of the close.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlclosingmarubozu.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlconcealbabyswall",
    "name": "Concealed Baby Swallow",
    "description": "A rare bullish reversal pattern.",
    "usage": "Indicates a final 'flush out' before a reversal.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlconcealbabyswall.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlcounterattack",
    "name": "Counterattack",
    "description": "A reversal pattern where the second candle closes at the same level as the first.",
    "usage": "Signals a stalemate after a strong move.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlcounterattack.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdldarkcloudcover",
    "name": "Dark Cloud Cover",
    "description": "A bearish reversal pattern in an uptrend.",
    "usage": "Indicates a significant rejection of higher prices.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdldarkcloudcover.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdldoji",
    "name": "Doji",
    "description": "A candlestick pattern where the open and close are virtually equal.",
    "usage": "Indicates indecision between buyers and sellers.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdldoji.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdldojistar",
    "name": "Doji Star",
    "description": "A reversal pattern where a doji gaps away.",
    "usage": "Signals a potential shift in trend momentum.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdldojistar.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdldragonflydoji",
    "name": "Dragonfly Doji",
    "description": "A doji with a long lower shadow and no upper shadow.",
    "usage": "Signals a potential bullish reversal.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdldragonflydoji.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlengulfing",
    "name": "Engulfing",
    "description": "A pattern where a larger candle completely covers the previous smaller candle.",
    "usage": "Signals a strong shift in momentum.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlengulfing.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdleveningdojistar",
    "name": "Evening Doji Star",
    "description": "A bearish reversal pattern involving a doji.",
    "usage": "A highly reliable signal of a market top.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdleveningdojistar.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdleveningstar",
    "name": "Evening Star",
    "description": "A bearish reversal pattern with three candles.",
    "usage": "Signals a peak in an uptrend.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdleveningstar.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlgapsidesidewhite",
    "name": "Up/Down-Gap Side-By-Side White Lines",
    "description": "A continuation pattern involving gaps.",
    "usage": "Signals that the current trend is likely to continue.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlgapsidesidewhite.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlgravestonedoji",
    "name": "Gravestone Doji",
    "description": "A doji with a long upper shadow and no lower shadow.",
    "usage": "Signals a potential bearish reversal.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlgravestonedoji.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlhammer",
    "name": "Hammer",
    "description": "A bullish reversal pattern with a small body and long lower shadow.",
    "usage": "Signals a potential bottom after a downtrend.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlhammer.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlhangingman",
    "name": "Hanging Man",
    "description": "A bearish reversal pattern at the top of an uptrend.",
    "usage": "Signals a potential breakdown after a period of buying.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlhangingman.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlharami",
    "name": "Harami",
    "description": "A two-candle reversal pattern where the second is inside the first.",
    "usage": "Signals a potential trend exhaustion.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlharami.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlharamicross",
    "name": "Harami Cross",
    "description": "A harami where the second candle is a doji.",
    "usage": "A more reliable reversal signal than a standard harami.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlharamicross.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlhighwave",
    "name": "High-Wave Candle",
    "description": "A candle with very long shadows and a small body.",
    "usage": "Indicates extreme market confusion and volatility.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlhighwave.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlhikkake",
    "name": "Hikkake Pattern",
    "description": "A trap pattern used to identify false breakouts.",
    "usage": "Signals a move in the opposite direction of the trap.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlhikkake.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlhikkakemod",
    "name": "Modified Hikkake Pattern",
    "description": "A more conservative version of the Hikkake.",
    "usage": "Provides a higher probability signal.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlhikkakemod.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlhomingpigeon",
    "name": "Homing Pigeon",
    "description": "A bullish reversal pattern in a downtrend.",
    "usage": "Signals a potential bottom.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlhomingpigeon.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlidentical3crows",
    "name": "Identical Three Crows",
    "description": "A bearish reversal pattern with three identical candles.",
    "usage": "Signals a very strong trend change.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlidentical3crows.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlinneck",
    "name": "In-Neck Pattern",
    "description": "A bearish continuation pattern.",
    "usage": "Indicates that the downward move is not yet over.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlinneck.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlinvertedhammer",
    "name": "Inverted Hammer",
    "description": "A bullish reversal pattern at the bottom of a downtrend.",
    "usage": "Signals a potential move to the upside.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlinvertedhammer.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlkicking",
    "name": "Kicking",
    "description": "A two-candle reversal pattern involving a gap.",
    "usage": "Signals a violent shift in market sentiment.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlkicking.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlkickingbylength",
    "name": "Kicking - bull/bear determined by longer marubozu",
    "description": "A variation of the kicking pattern.",
    "usage": "Focuses on the relative strength of the marubozus.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlkickingbylength.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlladderbottom",
    "name": "Ladder Bottom",
    "description": "A five-candle bullish reversal pattern.",
    "usage": "Signals a major bottom after a steady decline.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlladderbottom.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdllongleggeddoji",
    "name": "Long-Legged Doji",
    "description": "A doji with long shadows on both sides.",
    "usage": "Indicates a significant struggle between bulls and bears.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdllongleggeddoji.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdllongline",
    "name": "Long Line Candle",
    "description": "A candle with an unusually long body.",
    "usage": "Indicates strong momentum in the direction of the candle.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdllongline.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlmarubozu",
    "name": "Marubozu",
    "description": "A candle with no shadows at either end.",
    "usage": "Indicates total dominance by one side for the entire period.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlmarubozu.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlmatchinglow",
    "name": "Matching Low",
    "description": "A bullish reversal pattern with two identical lows.",
    "usage": "Signals support at a specific price level.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlmatchinglow.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlmathold",
    "name": "Mat Hold",
    "description": "A bullish continuation pattern.",
    "usage": "Signals a strong trend that is likely to persist.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlmathold.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlmorningdojistar",
    "name": "Morning Doji Star",
    "description": "A bullish reversal pattern involving a doji.",
    "usage": "A highly reliable signal of a market bottom.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlmorningdojistar.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlmorningstar",
    "name": "Morning Star",
    "description": "A bullish reversal pattern with three candles.",
    "usage": "Signals a trough in a downtrend.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlmorningstar.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlonneck",
    "name": "On-Neck Pattern",
    "description": "A bearish continuation pattern.",
    "usage": "A weak signal that the downtrend will continue.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlonneck.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlpiercing",
    "name": "Piercing Pattern",
    "description": "A bullish reversal pattern in a downtrend.",
    "usage": "Indicates a significant entry of buyers.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlpiercing.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlrickshawman",
    "name": "Rickshaw Man",
    "description": "A long-legged doji where the body is in the center of the range.",
    "usage": "Indicates total equilibrium and indecision.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlrickshawman.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlrisefall3methods",
    "name": "Rising/Falling Three Methods",
    "description": "A strong continuation pattern.",
    "usage": "Signals a minor consolidation before the trend resumes.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlrisefall3methods.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlseparatinglines",
    "name": "Separating Lines",
    "description": "A continuation pattern where candles move in opposite directions.",
    "usage": "Signals trend persistence.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlseparatinglines.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlshootingstar",
    "name": "Shooting Star",
    "description": "A bearish reversal pattern at the top of an uptrend.",
    "usage": "Signals a potential move to the downside.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlshootingstar.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlshortline",
    "name": "Short Line Candle",
    "description": "A candle with a small body and small shadows.",
    "usage": "Indicates low volatility and consolidation.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlshortline.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlspinningtop",
    "name": "Spinning Top",
    "description": "A candle with a small body and long shadows.",
    "usage": "Indicates indecision after a strong move.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlspinningtop.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlstalledpattern",
    "name": "Stalled Pattern",
    "description": "A bearish reversal pattern in an uptrend.",
    "usage": "Indicates that the upward momentum is slowing down.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlstalledpattern.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlsticksandwich",
    "name": "Stick Sandwich",
    "description": "A reversal pattern with alternating candle colors.",
    "usage": "Signals a potential support or resistance level.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlsticksandwich.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdltakuri",
    "name": "Takuri",
    "description": "A dragonfly doji with an exceptionally long lower shadow.",
    "usage": "Indicates a very strong rejection of lower prices.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdltakuri.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdltasukigap",
    "name": "Tasuki Gap",
    "description": "A continuation pattern involving a gap.",
    "usage": "Signals trend strength.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdltasukigap.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlthrusting",
    "name": "Thrusting Pattern",
    "description": "A bearish continuation pattern.",
    "usage": "A weak signal of trend persistence.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlthrusting.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdltristar",
    "name": "Tristar Pattern",
    "description": "A rare reversal pattern consisting of three dojis.",
    "usage": "Signals an extreme shift in momentum.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdltristar.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlunique3river",
    "name": "Unique 3 River",
    "description": "A bullish reversal pattern.",
    "usage": "Signals a potential bottom.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlunique3river.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlupsidegap2crows",
    "name": "Upside Gap Two Crows",
    "description": "A bearish reversal pattern.",
    "usage": "Signals a potential top in an uptrend.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlupsidegap2crows.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cdlxsidegap3methods",
    "name": "Up/Down-Gap Three Methods",
    "description": "A continuation pattern.",
    "usage": "Signals that the trend is likely to continue after a gap.",
    "category": "Patterns",
    "keywords": [
      "pattern",
      "candlestick",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/articles/active-trading/062315/using-bullish-candlestick-patterns-buy-stocks.asp",
    "formula_latex": "\n\\text{Pattern Recognition Logic (TA-Lib Internal)}\n",
    "gold_standard_file": "cdlxsidegap3methods.json",
    "ehlers_summary": "Candlestick patterns were popularized in the West by Steve Nison in his 1991 book 'Japanese Candlestick Charting Techniques'. These patterns provide a visual representation of market psychology and the balance of power between buyers and sellers at key price levels.",
    "struct_name": "",
    "source_file": "pattern",
    "boundary_kind": "pattern"
  },
  {
    "slug": "cg",
    "name": "Center of Gravity Oscillator",
    "description": "The CG Oscillator identifies price turning points with essentially zero lag by calculating the balance point of prices.",
    "usage": "Use as a zero-lag momentum oscillator to detect cycle turning points. Crossovers of the trigger line provide high-accuracy entry and exit signals.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "momentum",
      "ehlers",
      "dsp",
      "zero-lag"
    ],
    "params": [
      {
        "name": "period",
        "default": "10",
        "description": "Observation window length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/TheCGOscillator.pdf",
    "formula_latex": "\n\\[\nCG = -\\frac{\\sum_{i=0}^{N-1} (i+1) \\times Price_i}{\\sum_{i=0}^{N-1} Price_i}\n\\]\n",
    "gold_standard_file": "cg.json",
    "ehlers_summary": "Ehlers introduces the Center of Gravity oscillator in Cybernetic Analysis (2004) as a near-zero-lag indicator. It computes the center of mass of a price series over a lookback window, producing an oscillator whose turning points lead price turns — a reversal of the usual indicator lag relationship.",
    "struct_name": "CenterOfGravity",
    "source_file": "cg",
    "boundary_kind": "scalar"
  },
  {
    "slug": "channel_cycle",
    "name": "ChannelCycle",
    "description": "Extracts cyclic components and a leading function using channel-normalized bandpass filtering.",
    "usage": "Use to estimate the dominant cycle period from the width of price channels. Useful as a simpler alternative to Hilbert Transform cycle measurement when computational resources are limited.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "ehlers",
      "dsp",
      "dominant-cycle"
    ],
    "params": [
      {
        "name": "period",
        "default": "20",
        "description": "Channel and Bandpass period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/InferringTradingStrategies.pdf",
    "formula_latex": "\n\\[\nDetrended = \\frac{Price - Low}{High - Low} - 0.5\n\\]\n\\[\nBP = \\text{Bandpass}(Detrended, Period)\n\\]\n\\[\nLeading = \\frac{BP - BP_{t-1}}{2\\pi/Period}\n\\]\n",
    "gold_standard_file": "channel_cycle.json",
    "ehlers_summary": "Ehlers estimates the dominant cycle period by tracking successive peaks and troughs of price. The distance between turning points approximates half the cycle period, and smoothing this measurement across recent bars gives a stable period estimate for use in adaptive indicators.",
    "struct_name": "ChannelCycle",
    "source_file": "channel_cycle",
    "boundary_kind": "scalar"
  },
  {
    "slug": "choppiness_index",
    "name": "Choppiness Index",
    "description": "Determines if the market is trending (low values) or ranging/choppy (high values).",
    "usage": "Use to determine whether a market is trending or choppy before selecting a trading strategy. Values above 61.8 indicate chop; values below 38.2 indicate a strong trend.",
    "category": "Modern",
    "keywords": [
      "volatility",
      "trend-strength",
      "classic",
      "range"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.tradingview.com/support/solutions/43000501980-choppiness-index-chop/",
    "formula_latex": "\n\\[\nCHOP = 100 \\times \\frac{\\log_{10}(\\sum_{i=1}^n ATR(1)_i / (\\max(H, n) - \\min(L, n)))}{\\log_{10}(n)}\n\\]\n",
    "gold_standard_file": "choppiness_index.json",
    "ehlers_summary": "The Choppiness Index, developed by E.W. Dreiss, measures how much of the total ATR-based range is consumed by the actual net price move over N bars. A value near 100 means price wandered back and forth using all available range without net progress (maximum chop); near 0 means a straight directional move with minimal retracement. — StockCharts ChartSchool",
    "struct_name": "ChoppinessIndex",
    "source_file": "choppiness_index",
    "boundary_kind": "scalar"
  },
  {
    "slug": "classic_laguerre",
    "name": "Classic Laguerre Filter",
    "description": "The original Laguerre filter from John Ehlers' 2002 'Time Warp' paper.",
    "usage": "Use when a smooth trend estimate with controllable lag using only 4 state variables is needed. Preferred over long EMAs when computational memory is constrained.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "smoothing",
      "laguerre"
    ],
    "params": [
      {
        "name": "gamma",
        "default": "0.8",
        "description": "Smoothing factor (0.0 to 1.0)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/TimeWarp.pdf",
    "formula_latex": "\n\\[\nL_0 = (1 - \\gamma) \\cdot Price + \\gamma \\cdot L_{0,t-1}\n\\]\n\\[\nL_1 = -\\gamma L_0 + L_{0,t-1} + \\gamma L_{1,t-1}\n\\]\n\\[\nL_2 = -\\gamma L_1 + L_{1,t-1} + \\gamma L_{2,t-1}\n\\]\n\\[\nL_3 = -\\gamma L_2 + L_{2,t-1} + \\gamma L_{3,t-1}\n\\]\n\\[\nFilt = \\frac{L_0 + 2L_1 + 2L_2 + L_3}{6}\n\\]\n",
    "gold_standard_file": "classic_laguerre.json",
    "ehlers_summary": "The Classic Laguerre Filter uses four first-order IIR sections sharing the same gamma coefficient. In Cybernetic Analysis (2004) Ehlers shows gamma maps directly to an effective period, making it highly tunable with minimal computation.",
    "struct_name": "ClassicLaguerre",
    "source_file": "classic_laguerre",
    "boundary_kind": "scalar"
  },
  {
    "slug": "cmo",
    "name": "Chande Momentum Oscillator (CMO)",
    "description": "An advanced momentum oscillator developed by Tushar Chande that measures the difference between up and down days.",
    "usage": "Use to identify extreme overbought and oversold conditions. CMO is more sensitive to price action than RSI as it uses unsmoothed data in its internal calculations.",
    "category": "Classic",
    "keywords": [
      "momentum",
      "oscillator",
      "classic",
      "overbought",
      "oversold"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "14",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/c/chandemomentumoscillator.asp",
    "formula_latex": "\n\\[\nCMO = 100 \\times \\frac{S_u - S_d}{S_u + S_d}\n\\]\n",
    "gold_standard_file": "cmo.json",
    "ehlers_summary": "Developed by Tushar Chande in 1994, the CMO is similar to the RSI but uses the net sum of up and down moves in both the numerator and denominator. This makes it more sensitive to price movements and useful for identifying short-term overextensions in the market. — The New Technical Trader",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "continuation_index",
    "name": "Continuation Index",
    "description": "An oscillator that identifies trend onset and exhaustion by comparing a fast UltimateSmoother with a Generalized Laguerre filter.",
    "usage": "Use to measure whether a price move is likely to continue or reverse based on cycle analysis. High index values suggest trend continuation; low values suggest an impending cycle turn.",
    "category": "Ehlers DSP",
    "keywords": [
      "trend",
      "momentum",
      "ehlers",
      "cycle"
    ],
    "params": [
      {
        "name": "gamma",
        "default": "0.8",
        "description": "Laguerre gamma parameter"
      },
      {
        "name": "order",
        "default": "8",
        "description": "Laguerre filter order"
      },
      {
        "name": "length",
        "default": "40",
        "description": "Base smoothing length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS%E2%80%99%20TIPS%20-%20SEPTEMBER%202025.html",
    "formula_latex": "\n\\[\nUS = UltimateSmoother(Close, Length/2)\n\\]\n\\[\nLG = Laguerre(Close, \\gamma, Order, Length)\n\\]\n\\[\nVariance = SMA(|US - LG|, Length)\n\\]\n\\[\nRef = 2 \\times (US - LG) / Variance\n\\]\n\\[\nCI = \\tanh(Ref)\n\\]\n",
    "gold_standard_file": "continuation_index.json",
    "ehlers_summary": "The Continuation Index measures the persistence of directional price movement relative to the dominant cycle. Ehlers derives it from the cycle phase velocity — when phase advances quickly in one direction, momentum is strong and continuation is likely; slow or reversing phase suggests the move is exhausting.",
    "struct_name": "ContinuationIndex",
    "source_file": "continuation_index",
    "boundary_kind": "scalar"
  },
  {
    "slug": "correl",
    "name": "Correlation Coefficient (CORREL)",
    "description": "A statistical measure that determines the degree to which two securities move in relation to each other.",
    "usage": "Use to measure the strength and direction of the linear relationship between two assets. Values range from -1.0 (inverse correlation) to +1.0 (perfect correlation).",
    "category": "Classic",
    "keywords": [
      "statistics",
      "correlation",
      "classic"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "30",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/c/correlationcoefficient.asp",
    "formula_latex": "\n\\[\n\\rho_{X,Y} = \\frac{\\text{cov}(X,Y)}{\\sigma_X \\sigma_Y}\n\\]\n",
    "gold_standard_file": "correl.json",
    "ehlers_summary": "The Pearson Correlation Coefficient measures the strength and direction of a linear relationship between two price series. It is a fundamental tool for pair trading and portfolio diversification, allowing traders to quantify how much of a security's movement is explained by another. — StockCharts ChartSchool",
    "struct_name": "StandardDeviation",
    "source_file": "statistics",
    "boundary_kind": "scalar"
  },
  {
    "slug": "correlation_cycle",
    "name": "CorrelationCycle",
    "description": "Determines cycle phase angle by correlating price with orthogonal sinusoids.",
    "usage": "Use to measure the dominant cycle period via autocorrelation in an amplitude-independent way. Prefer over DFT methods when price amplitude varies significantly across the measurement window.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "dominant-cycle",
      "ehlers",
      "dsp",
      "spectral"
    ],
    "params": [
      {
        "name": "period",
        "default": "20",
        "description": "Correlation wavelength"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/CORRELATION%20AS%20A%20CYCLE%20INDICATOR.pdf",
    "formula_latex": "\n\\[\nR = \\text{Corr}(Price, \\cos(2\\pi n/P)), I = \\text{Corr}(Price, -\\sin(2\\pi n/P))\n\\]\n\\[\n\\text{Angle} = 90 + \\arctan(R/I) \\text{ (with quadrant resolution)}\n\\]\n",
    "gold_standard_file": "correlation_cycle.json",
    "ehlers_summary": "Ehlers introduces Correlation Cycle measurement in Cycle Analytics for Traders (2013) as an improvement on DFT. By normalizing autocorrelation coefficients to unity variance, the resulting periodogram is independent of price amplitude variations, producing more consistent cycle period estimates.",
    "struct_name": "CorrelationCycle",
    "source_file": "correlation_cycle",
    "boundary_kind": "scalar"
  },
  {
    "slug": "correlation_trend",
    "name": "Correlation Trend",
    "description": "Calculates the Pearson correlation between price and a linear time ramp to identify trends.",
    "usage": "Use to confirm whether price is trending or cycling before applying directional strategies. High correlation indicates a strong trend; low correlation indicates a cycling market.",
    "category": "Ehlers DSP",
    "keywords": [
      "trend",
      "correlation",
      "ehlers",
      "statistics"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Correlation window length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/CORRELATION%20AS%20A%20TREND%20INDICATOR.pdf",
    "formula_latex": "\n\\[\nX_i = Price_{t-i}, Y_i = -i\n\\]\n\\[\nR = \\frac{n \\sum X_i Y_i - \\sum X_i \\sum Y_i}{\\sqrt{(n \\sum X_i^2 - (\\sum X_i)^2)(n \\sum Y_i^2 - (\\sum Y_i)^2)}}\n\\]\n",
    "gold_standard_file": "correlation_trend.json",
    "ehlers_summary": "In 'Correlation As A Trend Indicator' (2020), Ehlers uses the Pearson correlation coefficient between price and a linear ramp to identify trend strength. A coefficient near +1.0 indicates a consistent uptrend, while -1.0 indicates a consistent downtrend. Unlike standard moving averages, this approach is independent of price amplitude and focuses purely on the linearity of the move.",
    "struct_name": "CorrelationTrend",
    "source_file": "correlation_trend",
    "boundary_kind": "scalar"
  },
  {
    "slug": "cyber_cycle",
    "name": "Cyber Cycle",
    "description": "An oscillator introduced by John Ehlers that models the cyclical component of a time series using FIR smoothing.",
    "usage": "Use as a high-resolution short-term cycle oscillator to time entries and exits around cycle turns. Pair with a trend classifier to suppress signals in trending conditions.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "oscillator",
      "ehlers",
      "dsp"
    ],
    "params": [
      {
        "name": "length",
        "default": "14",
        "description": "Alpha smoothing length parameter"
      }
    ],
    "formula_source": "Cybernetic Analysis for Stocks and Futures, John Ehlers, 2004, Chapter 4",
    "formula_latex": "\n\\[\n\\alpha = \\frac{2}{\\text{Length} + 1}\n\\]\n\\[\n\\text{Smooth} = \\frac{X_t + 2X_{t-1} + 2X_{t-2} + X_{t-3}}{6}\n\\]\n\\[\nCC_t = \\left(1 - \\frac{\\alpha}{2}\\right)^2 (\\text{Smooth}_t - 2\\text{Smooth}_{t-1} + \\text{Smooth}_{t-2}) + 2(1 - \\alpha)CC_{t-1} - (1 - \\alpha)^2 CC_{t-2}\n\\]\n",
    "gold_standard_file": "cyber_cycle.json",
    "ehlers_summary": "Ehlers introduces the Cyber Cycle in Cybernetic Analysis (2004) as a bandpass-like filter isolating the short-term cyclical component. The trigger line is the Cyber Cycle delayed by one bar, creating a clean crossover signal without derivative noise.",
    "struct_name": "CyberCycle",
    "source_file": "cyber_cycle",
    "boundary_kind": "scalar"
  },
  {
    "slug": "cybernetic_oscillator",
    "name": "CyberneticOscillator",
    "description": "Combined HighPass and SuperSmoother filters normalized by RMS.",
    "usage": "Use as a generalized Ehlers cycle oscillator when you need a configurable bandpass response tuned to a specific dominant cycle period.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "ehlers",
      "dsp",
      "cycle",
      "momentum"
    ],
    "params": [
      {
        "name": "hp_length",
        "default": "30",
        "description": "HighPass filter length"
      },
      {
        "name": "lp_length",
        "default": "20",
        "description": "LowPass (SuperSmoother) length"
      },
      {
        "name": "rms_len",
        "default": "100",
        "description": "RMS normalization length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20JUNE%202025.html",
    "formula_latex": "\n\\[\nHP = HighPass(Price, HPLen)\n\\]\n\\[\nLP = SuperSmoother(HP, LPLen)\n\\]\n\\[\nRMS = \\sqrt{\\frac{1}{N} \\sum_{i=0}^{N-1} LP_{t-i}^2}\n\\]\n\\[\nCO = \\frac{LP}{RMS}\n\\]\n",
    "gold_standard_file": "cybernetic_oscillator.json",
    "ehlers_summary": "The Cybernetic Oscillator is derived from the bandpass filter framework in Ehlers Cybernetic Analysis for Stocks and Futures (2004). By tuning the filter center frequency to the measured dominant cycle period, it extracts only the cyclical component and presents it as an oscillator ranging above and below zero.",
    "struct_name": "CyberneticOscillator",
    "source_file": "cybernetic_oscillator",
    "boundary_kind": "scalar"
  },
  {
    "slug": "cycle_trend_analytics",
    "name": "Cycle/Trend Analytics",
    "description": "A set of oscillators (Price - SMA) with lengths from 5 to 30 used to visualize cycles and trends.",
    "usage": "Use to classify the current market mode as trending or cycling before selecting your strategy. Apply trend-following systems in trend mode and mean-reversion systems in cycle mode.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "trend",
      "ehlers",
      "classification",
      "adaptive"
    ],
    "params": [
      {
        "name": "min_length",
        "default": "5",
        "description": "Minimum SMA length"
      },
      {
        "name": "max_length",
        "default": "30",
        "description": "Maximum SMA length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’ TIPS - OCTOBER 2021.html",
    "formula_latex": "\n\\[\nOsc(L) = Price - SMA(Price, L) \\quad \\text{for } L \\in [min, max]\n\\]\n",
    "gold_standard_file": "cycle_trend_analytics.json",
    "ehlers_summary": "Ehlers presents Cycle/Trend Analytics in Cycle Analytics for Traders as a framework for determining the dominant market mode. By measuring the correlation between price and the best-fit dominant cycle, the indicator classifies market behavior, enabling traders to switch between trend and cycle trading strategies dynamically.",
    "struct_name": "CycleTrendAnalytics",
    "source_file": "cycle_trend_analytics",
    "boundary_kind": "scalar"
  },
  {
    "slug": "dema",
    "name": "Double Exponential Moving Average (DEMA)",
    "description": "A fast-acting moving average that reduces lag by using two exponential moving averages.",
    "usage": "Use as a replacement for EMA when faster signal generation is required without excessive noise. DEMA reacts more quickly to price changes than a standard EMA.",
    "category": "Classic",
    "keywords": [
      "moving-average",
      "smoothing",
      "lag-reduction",
      "classic"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "30",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/d/double-exponential-moving-average.asp",
    "formula_latex": "\n\\[\nDEMA = 2 \\times EMA - EMA(EMA)\n\\]\n",
    "gold_standard_file": "dema.json",
    "ehlers_summary": "Developed by Patrick Mulloy in 1994, DEMA provides a less-laggy alternative to traditional moving averages. It is calculated by taking a single EMA and then subtracting it from a double EMA of the same period. This effectively cancels out some of the lag inherent in the EMA calculation. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "overlap",
    "boundary_kind": "scalar"
  },
  {
    "slug": "dmh",
    "name": "DMH",
    "description": "An improved Directional Movement indicator using Hann windowing for smoother signals and reduced lag.",
    "usage": "Use as a momentum oscillator with high-pass filtering to isolate cyclical momentum while removing the trend bias that corrupts standard momentum indicators.",
    "category": "Ehlers DSP",
    "keywords": [
      "momentum",
      "oscillator",
      "ehlers",
      "high-pass",
      "dsp"
    ],
    "params": [
      {
        "name": "length",
        "default": "14",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/implemented/TRADERS%E2%80%99%20TIPS%20-%20DECEMBER%202021.html",
    "formula_latex": "\n\\[\n\\text{PlusDM} = \\text{High} - \\text{High}_{t-1} \\text{ if } > (\\text{Low}_{t-1} - \\text{Low}) \\text{ and } > 0, \\text{ else } 0\n\\]\n\\[\n\\text{MinusDM} = \\text{Low}_{t-1} - \\text{Low} \\text{ if } > (\\text{High} - \\text{High}_{t-1}) \\text{ and } > 0, \\text{ else } 0\n\\]\n\\[\n\\text{EMA} = \\frac{1}{L}(\\text{PlusDM} - \\text{MinusDM}) + (1 - \\frac{1}{L})\\text{EMA}_{t-1}\n\\]\n\\[\n\\text{DMH} = \\frac{\\sum_{i=1}^{L} w_i \\text{EMA}_{t-i+1}}{\\sum_{i=1}^{L} w_i}, \\text{ where } w_i = 1 - \\cos\\left(\\frac{2\\pi i}{L+1}\\right)\n\\]\n",
    "gold_standard_file": "dmh.json",
    "ehlers_summary": "Ehlers constructs the DMH by applying a high-pass filter to the momentum calculation, removing the low-frequency trend component that causes conventional momentum to drift. The result is a zero-centered momentum oscillator that oscillates cleanly around the cycle midpoint.",
    "struct_name": "Dmh",
    "source_file": "dmh",
    "boundary_kind": "scalar"
  },
  {
    "slug": "donchian",
    "name": "Donchian Channels",
    "description": "Donchian Channels are volatility indicators formed by taking the highest high and the lowest low of the last N periods.",
    "usage": "Use for breakout trading systems: a close above the N-period high signals a long entry; below the N-period low signals a short entry. The Turtle Traders famously used 20 and 55-day Donchian channels.",
    "category": "Classic",
    "keywords": [
      "breakout",
      "volatility",
      "trend",
      "classic",
      "support-resistance"
    ],
    "params": [
      {
        "name": "period",
        "default": "20",
        "description": "Channel period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/d/donchianchannels.asp",
    "formula_latex": "\n\\[\nUC = \\max(H_{t-n \\dots t}) \\\\ LC = \\min(L_{t-n \\dots t})\n\\]\n",
    "gold_standard_file": "donchian.json",
    "ehlers_summary": "Developed by Richard Donchian in the 1970s, Donchian Channels plot the highest high and lowest low over N bars. They define the current trading range and signal breakouts when price escapes the channel. The Turtle Trading system of Richard Dennis built its entire entry and exit logic on 20 and 55-day Donchian channels. — TurtleTrader.com",
    "struct_name": "Donchian",
    "source_file": "donchian",
    "boundary_kind": "scalar"
  },
  {
    "slug": "dsma",
    "name": "DSMA",
    "description": "Deviation Scaled Moving Average adapts to price variations using standard deviation scaled oscillators.",
    "usage": "Use as a highly adaptive moving average that tracks price closely during trends and large moves but provides heavy filtering during consolidation. Ideal for trend-following entries and trailing stops.",
    "category": "Ehlers DSP",
    "keywords": [
      "moving-average",
      "adaptive",
      "ehlers",
      "dsp",
      "dominant-cycle"
    ],
    "params": [
      {
        "name": "period",
        "default": "40",
        "description": "Critical period for smoothing and RMS calculation"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/DEVIATION%20SCALED%20MOVING%20AVERAGE.pdf",
    "formula_latex": "\n\\[\nZeros = Close - Close_{t-2}\n\\]\n\\[\nFilt = c_1 \\frac{Zeros + Zeros_{t-1}}{2} + c_2 Filt_{t-1} + c_3 Filt_{t-2}\n\\]\n\\[\nRMS = \\sqrt{\\frac{1}{P} \\sum_{i=0}^{P-1} Filt_{t-i}^2}\n\\]\n\\[\n\\alpha = \\min\\left(1.0, \\left| \\frac{Filt}{RMS} \\right| \\frac{5}{P}\\right)\n\\]\n\\[\nDSMA = \\alpha \\cdot Close + (1 - \\alpha) \\cdot DSMA_{t-1}\n\\]\n",
    "gold_standard_file": "dsma.json",
    "ehlers_summary": "In 'The Deviation-Scaled Moving Average' (2018), Ehlers introduces an adaptive EMA where the alpha (smoothing factor) is dynamically adjusted based on a deviation-scaled oscillator. By scaling the SuperSmoother-filtered momentum by its RMS, the indicator becomes reactive to significant price deviations while remaining smooth during low-volatility periods.",
    "struct_name": "Dsma",
    "source_file": "dsma",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ehlers_autocorrelation",
    "name": "Ehlers Autocorrelation",
    "description": "Computes Pearson correlation of smoothed price with its lags to identify market structure.",
    "usage": "Use to generate an autocorrelation periodogram showing which cycle periods are currently dominant. Visualise as a heatmap to track cycle period shifts over time.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "spectral",
      "ehlers",
      "dsp",
      "dominant-cycle"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Correlation window length"
      },
      {
        "name": "num_lags",
        "default": "100",
        "description": "Number of lags to compute"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’ TIPS - FEBRUARY 2025.html",
    "formula_latex": "\n\\[\n\\rho(lag) = \\frac{N \\sum X Y - \\sum X \\sum Y}{\\sqrt{(N \\sum X^2 - (\\sum X)^2)(N \\sum Y^2 - (\\sum Y)^2)}}\n\\]\n",
    "gold_standard_file": "ehlers_autocorrelation.json",
    "ehlers_summary": "Ehlers introduces autocorrelation-based cycle measurement in Cycle Analytics for Traders (2013) as a more robust alternative to DFT. By computing autocorrelation of Roofing-filtered price at each lag, then applying a spectral DFT to the lag series, he obtains a periodogram insensitive to amplitude variations.",
    "struct_name": "EhlersAutocorrelation",
    "source_file": "ehlers_autocorrelation",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ehlers_filter",
    "name": "Ehlers Filter",
    "description": "A non-linear FIR filter using distance coefficients to adapt to price transitions while maintaining smoothness.",
    "usage": "Use as a configurable digital filter from Ehlers DSP toolkit when you need a specific frequency response not covered by the standard smoother or Butterworth designs.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "smoothing"
    ],
    "params": [
      {
        "name": "length",
        "default": "15",
        "description": "Filter window length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/EhlersFilters.pdf",
    "formula_latex": "\n\\[\nC_i = \\sum_{j=1}^{L-1} (Price_{t-i} - Price_{t-i-j})^2\n\\]\n\\[\nFilt = \\frac{\\sum_{i=0}^{L-1} C_i Price_{t-i}}{\\sum_{i=0}^{L-1} C_i}\n\\]\n",
    "gold_standard_file": "ehlers_filter.json",
    "ehlers_summary": "The Ehlers Filter is a generalized IIR filter design drawn from Ehlers digital signal processing framework for markets. Its coefficients can be tuned to approximate different filter types (lowpass, highpass, bandpass), making it a flexible building block for custom indicator pipelines.",
    "struct_name": "EhlersFilter",
    "source_file": "ehlers_filter",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ehlers_loops",
    "name": "Ehlers Loops",
    "description": "Converts price and volume into normalized standard deviation units for scatter plot analysis.",
    "usage": "Use to visualize cycle dynamics in phase-space by plotting the indicator value against its derivative. Loop patterns reveal cycle turns before they appear in the price chart.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "phase",
      "ehlers",
      "dsp",
      "visualization"
    ],
    "params": [
      {
        "name": "lp_period",
        "default": "20",
        "description": "Low-pass filter period (SuperSmoother)"
      },
      {
        "name": "hp_period",
        "default": "125",
        "description": "High-pass filter period (Butterworth)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20JUNE%202022.html",
    "formula_latex": "\n\\[\nHP = c_1 (Price - 2 Price_{t-1} + Price_{t-2}) + c_2 HP_{t-1} + c_3 HP_{t-2}\n\\]\n\\[\nSS = s_1 \\frac{HP + HP_{t-1}}{2} + s_2 SS_{t-1} + s_3 SS_{t-2}\n\\]\n\\[\nMS = \\alpha SS^2 + (1 - \\alpha) MS_{t-1}\n\\]\n\\[\nRMS = \\frac{SS}{\\sqrt{MS}}\n\\]\n",
    "gold_standard_file": "ehlers_loops.json",
    "ehlers_summary": "Ehlers describes phase-space loops in Cybernetic Analysis as a powerful visualization technique where an indicator is plotted against its first derivative. In cycle mode the path traces elliptical loops; in trend mode the path collapses to a line, enabling visual market mode identification.",
    "struct_name": "EhlersLoops",
    "source_file": "ehlers_loops",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ehlers_stochastic",
    "name": "Ehlers Stochastic",
    "description": "A Stochastic oscillator applied to the output of a Roofing Filter to eliminate Spectral Dilation.",
    "usage": "Use as a cycle-aware stochastic oscillator that adapts its lookback window to the current dominant cycle period rather than using a fixed period.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "stochastic",
      "ehlers",
      "cycle",
      "adaptive"
    ],
    "params": [
      {
        "name": "hp_period",
        "default": "48",
        "description": "HighPass critical period"
      },
      {
        "name": "ss_period",
        "default": "10",
        "description": "SuperSmoother critical period"
      },
      {
        "name": "stoch_period",
        "default": "20",
        "description": "Stochastic lookback period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/Anticipating Turning Points.pdf",
    "formula_latex": "\n\\[\nRoof = RoofingFilter(HP, SS)\n\\]\n\\[\nStoch = 100 \\times \\frac{Roof - \\min(Roof, L)}{\\max(Roof, L) - \\min(Roof, L)}\n\\]\n",
    "gold_standard_file": "ehlers_stochastic.json",
    "ehlers_summary": "Ehlers computes the stochastic oscillator using the measured dominant cycle period as the lookback window. This adaptive approach ensures the stochastic spans exactly one full market cycle, making overbought and oversold conditions consistently meaningful.",
    "struct_name": "EhlersStochastic",
    "source_file": "ehlers_stochastic",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ehlers_ultimate_oscillator",
    "name": "EhlersUltimateOscillator",
    "description": "A highly responsive oscillator created from the difference of two highpass filters, normalized by RMS.",
    "usage": "Use as a multi-scale momentum oscillator that combines signals from multiple cycle-aware timeframes to reduce false signals from any single period.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "ehlers",
      "dsp",
      "momentum",
      "adaptive"
    ],
    "params": [
      {
        "name": "band_edge",
        "default": "20",
        "description": "Critical period (shorter period)"
      },
      {
        "name": "bandwidth",
        "default": "2.0",
        "description": "Multiplier for the longer period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20APRIL%202025.html",
    "formula_latex": "\n\\[\nHP_1 = \\text{HighPass}(Price, BandEdge \\cdot Bandwidth)\n\\]\n\\[\nHP_2 = \\text{HighPass}(Price, BandEdge)\n\\]\n\\[\nSignal = HP_1 - HP_2\n\\]\n\\[\nUO = \\frac{Signal}{RMS(Signal, 100)}\n\\]\n",
    "gold_standard_file": "ehlers_ultimate_oscillator.json",
    "ehlers_summary": "Ehlers Ultimate Oscillator combines the outputs of multiple cycle-synchronized oscillators operating at different dominant cycle harmonics. By averaging across scales, it reduces the likelihood of false signals that occur when any single oscillator is temporarily misaligned with the market cycle.",
    "struct_name": "EhlersUltimateOscillator",
    "source_file": "ehlers_ultimate_oscillator",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ema",
    "name": "Exponential Moving Average",
    "description": "The Exponential Moving Average gives more weight to recent prices.",
    "usage": "Use as the foundational smoothing module providing SMA, EMA, WMA, and SMMA implementations that power higher-level indicators across the library.",
    "category": "Classic",
    "keywords": [
      "moving-average",
      "smoothing",
      "classic",
      "ema"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/e/ema.asp",
    "formula_latex": "\n\\[\nEMA = P_t \\times \\alpha + EMA_{t-1} \\times (1 - \\alpha)\n\\]\n",
    "gold_standard_file": "ema.json",
    "ehlers_summary": "The core smoothing algorithms — SMA, EMA, WMA — are the building blocks of nearly all technical indicators. EMA applies exponential decay weighting (alpha = 2/(n+1)), SMA applies uniform weighting over N bars, and WMA applies linearly increasing weights emphasizing more recent bars.",
    "struct_name": "Ema",
    "source_file": "smoothing",
    "boundary_kind": "scalar"
  },
  {
    "slug": "emd",
    "name": "EMD",
    "description": "Empirical Mode Decomposition separates cycles from trends using bandpass filtering and identifies market modes via adaptive thresholds.",
    "usage": "Use to decompose price into Intrinsic Mode Functions to separate cycles of different periods without any a priori period assumption. Useful for multi-timescale analysis.",
    "category": "Ehlers DSP",
    "keywords": [
      "decomposition",
      "cycle",
      "spectral",
      "dsp"
    ],
    "params": [
      {
        "name": "period",
        "default": "20",
        "description": "Bandpass center period"
      },
      {
        "name": "delta",
        "default": "0.5",
        "description": "Bandwidth half-width"
      },
      {
        "name": "fraction",
        "default": "0.1",
        "description": "Threshold multiplier for peaks/valleys"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/EmpiricalModeDecomposition.pdf",
    "formula_latex": "\n\\[\n\\beta = \\cos\\left(\\frac{360}{P}\\right), \\gamma = \\frac{1}{\\cos\\left(\\frac{720\\delta}{P}\\right)}, \\alpha = \\gamma - \\sqrt{\\gamma^2 - 1}\n\\]\n\\[\nBP = 0.5(1 - \\alpha)(Price - Price_{t-2}) + \\beta(1 + \\alpha)BP_{t-1} - \\alpha BP_{t-2}\n\\]\n\\[\nMean = \\text{SMA}(BP, 2P)\n\\]\n\\[\nThreshold = \\text{Fraction} \\cdot \\text{SMA}(\\text{Peak/Valley}, 50)\n\\]\n",
    "gold_standard_file": "emd.json",
    "ehlers_summary": "Empirical Mode Decomposition is a data-driven method developed by Huang et al. (1998) that decomposes a signal into Intrinsic Mode Functions by iteratively sifting local extrema. Unlike Fourier methods, it requires no predetermined basis functions, making it adaptive to non-stationary market data.",
    "struct_name": "Emd",
    "source_file": "emd",
    "boundary_kind": "scalar"
  },
  {
    "slug": "fisher",
    "name": "Fisher Transform",
    "description": "Converts inputs to a nearly Gaussian probability distribution, creating sharp peaks at turning points.",
    "usage": "Apply to normalized prices or oscillators to sharpen turning-point signals. The near-Gaussian output makes extreme values statistically significant and easy to trade.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "ehlers",
      "normalization",
      "momentum"
    ],
    "params": [],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/UsingTheFisherTransform.pdf",
    "formula_latex": "\n\\[\nFish(x) = 0.5 \\times \\ln\\left(\\frac{1 + x}{1 - x}\\right) = \\text{atanh}(x)\n\\]\n",
    "gold_standard_file": "fisher.json",
    "ehlers_summary": "Ehlers introduces the Fisher Transform in Cybernetic Analysis (2004) to convert any bounded indicator into a Gaussian normal distribution. Values beyond ±1.5 signal statistically significant price extremes, sharper than raw oscillators.",
    "struct_name": "Fisher",
    "source_file": "fisher",
    "boundary_kind": "scalar"
  },
  {
    "slug": "fisher_high_pass",
    "name": "FisherHighPass",
    "description": "Fisher Transform applied to normalized HighPass filtered prices.",
    "usage": "Use to isolate high-frequency momentum from the cyclical component of price after trend removal. Provides a purer momentum signal than standard Fisher Transform applied to raw price.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "ehlers",
      "dsp",
      "high-pass",
      "momentum"
    ],
    "params": [
      {
        "name": "hp_len",
        "default": "20",
        "description": "HighPass filter length"
      },
      {
        "name": "norm_len",
        "default": "20",
        "description": "Normalization lookback period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/InferringTradingStrategies.pdf",
    "formula_latex": "\n\\[\nHP = \\text{HighPass}(Price, hp\\_len)\n\\]\n\\[\nN = 2 \\cdot \\frac{HP - Low(HP, norm\\_len)}{High(HP, norm\\_len) - Low(HP, norm\\_len)} - 1\n\\]\n\\[\nS = \\frac{N + N_{t-1} + N_{t-2}}{3}\n\\]\n\\[\nFisher = 0.5 \\cdot \\ln\\left(\\frac{1+S}{1-S}\\right)\n\\]\n",
    "gold_standard_file": "fisher_high_pass.json",
    "ehlers_summary": "FisherHighPass applies the Fisher Transform to the high-pass filtered price rather than raw price. By first removing the low-frequency trend component with a high-pass filter, the resulting Fisher output captures only the cycle-domain momentum, producing an oscillator that is unaffected by the prevailing trend direction.",
    "struct_name": "FisherHighPass",
    "source_file": "fisher_high_pass",
    "boundary_kind": "scalar"
  },
  {
    "slug": "fm_demodulator",
    "name": "FM Demodulator",
    "description": "Extracts market timing information by demodulating the frequency-modulated price spectrum.",
    "usage": "Use to extract the instantaneous amplitude and frequency of market cycles. The AM output measures cycle energy for position sizing; the FM output tracks cycle period for adaptive indicator tuning.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "ehlers",
      "dsp",
      "amplitude",
      "frequency"
    ],
    "params": [
      {
        "name": "period",
        "default": "30",
        "description": "SuperSmoother period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/AMFM.pdf",
    "formula_latex": "\n\\[\nDeriv = Close - Open, HL = \\text{Clip}(10 \\times Deriv, -1, 1)\n\\]\n\\[\nSS = c_1 \\frac{HL + HL_{t-1}}{2} + c_2 SS_{t-1} + c_3 SS_{t-2}\n\\]\n",
    "gold_standard_file": "fm_demodulator.json",
    "ehlers_summary": "Ehlers adapts AM and FM demodulation techniques from radio engineering in Cycle Analytics for Traders to extract cycle amplitude and instantaneous frequency from market data. The amplitude envelope measures how energetic the current cycle is, while FM reveals whether the cycle period is expanding or contracting.",
    "struct_name": "FmDemodulator",
    "source_file": "amfm",
    "boundary_kind": "scalar"
  },
  {
    "slug": "fourier_dominant_cycle",
    "name": "FourierDominantCycle",
    "description": "Dominant cycle period estimation using resolution-enhanced DFT and center of gravity.",
    "usage": "Use to compute the dominant market cycle period via DFT. Feed the output period into adaptive indicators like DSMA or Ehlers Stochastic to make them cycle-synchronized.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "spectral",
      "ehlers",
      "dsp",
      "dominant-cycle",
      "fourier"
    ],
    "params": [
      {
        "name": "window_len",
        "default": "50",
        "description": "DFT window length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/FourierTransformForTraders.pdf",
    "formula_latex": "\n\\[\nHP = \\text{HighPass}(Price, 40)\n\\]\n\\[\nCleaned = \\frac{HP + 2HP_{t-1} + 3HP_{t-2} + 3HP_{t-3} + 2HP_{t-4} + HP_{t-5}}{12}\n\\]\n\\[\nPwr(P) = \\left(\\sum_{n=0}^{W-1} Cleaned_{t-n} \\cos\\left(\\frac{2\\pi n}{P}\\right)\\right)^2 + \\left(\\sum_{n=0}^{W-1} Cleaned_{t-n} \\sin\\left(\\frac{2\\pi n}{P}\\right)\\right)^2\n\\]\n\\[\nDB(P) = \\min\\left(20, -10 \\log_{10}\\left(\\frac{0.01}{1 - 0.99 \\frac{Pwr(P)}{\\max(Pwr)}}\\right)\\right)\n\\]\n\\[\nDC = \\frac{\\sum_{P=8}^{50} P \\cdot (3 - DB(P)) \\text{ where } DB(P) < 3}{\\sum (3 - DB(P))}\n\\]\n",
    "gold_standard_file": "fourier_dominant_cycle.json",
    "ehlers_summary": "Ehlers implements a Discrete Fourier Transform cycle measurement in Cybernetic Analysis using a Hann-windowed data segment. The DFT computes power across periods from 6 to 50 bars, and the peak power identifies the dominant cycle period driving price movement.",
    "struct_name": "FourierDominantCycle",
    "source_file": "fourier_transform",
    "boundary_kind": "scalar"
  },
  {
    "slug": "fourier_series_model",
    "name": "FourierSeriesModel",
    "description": "Synthesized market model using fundamental and harmonic frequency components.",
    "usage": "Use to model price as a sum of sine wave harmonics for short-term prediction. Most effective in clearly cyclical markets; combine with a cycle mode detector to disable it in trends.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "spectral",
      "ehlers",
      "prediction",
      "fourier"
    ],
    "params": [
      {
        "name": "fundamental",
        "default": "20",
        "description": "Fundamental cycle period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/FOURIER%20SERIES%20MODEL%20OF%20THE%20MARKET.pdf",
    "formula_latex": "\n\\[\nBP_k = \\text{BandPass}(Price, Fundamental/k)\n\\]\n\\[\nQ_k = \\frac{Fundamental}{2\\pi} (BP_{k} - BP_{k,t-1})\n\\]\n\\[\nP_k = \\sum_{n=0}^{F-1} (BP_{k,t-n}^2 + Q_{k,t-n}^2)\n\\]\n\\[\nWave = BP_1 + \\sqrt{P_2/P_1}BP_2 + \\sqrt{P_3/P_1}BP_3\n\\]\n",
    "gold_standard_file": "fourier_series_model.json",
    "ehlers_summary": "The Fourier Series Model fits harmonically related sine waves to recent price history using least-squares coefficients. Ehlers shows that projecting this model one bar forward gives a price forecast useful for anticipatory entry timing at predicted cycle turns.",
    "struct_name": "FourierSeriesModel",
    "source_file": "fourier_series",
    "boundary_kind": "scalar"
  },
  {
    "slug": "frac_diff",
    "name": "Fractional Differentiation",
    "description": "Applies Prado-style fractional differencing to preserve memory while reducing non-stationarity in price series.",
    "usage": "Use as an ML feature primitive on log-prices or returns. Lower d (e.g. 0.3–0.5) retains more memory than integer differencing while improving stationarity for tree models and neural nets.",
    "category": "ML Features",
    "keywords": [
      "ml",
      "stationarity",
      "prado",
      "feature-engineering",
      "fractional"
    ],
    "params": [
      {
        "name": "d",
        "default": "0.4",
        "description": "Fractional differentiation order (0 = identity, 1 = full integer diff)"
      },
      {
        "name": "threshold",
        "default": "1e-5",
        "description": "Truncate weights when |w_k| falls below this value"
      }
    ],
    "formula_source": "https://www.wiley.com/en-us/Advances+in+Financial+Machine+Learning-p-9781119482086",
    "formula_latex": "\n\\[\nw_0 = 1,\\quad w_k = -w_{k-1}\\frac{d - k + 1}{k},\\quad\n\\tilde{X}_t = \\sum_{k=0}^{K} w_k X_{t-k}\n\\]\n",
    "gold_standard_file": "frac_diff.json",
    "ehlers_summary": "",
    "struct_name": "FracDiff",
    "source_file": "frac_diff",
    "boundary_kind": "scalar"
  },
  {
    "slug": "fractals",
    "name": "Bill Williams Fractals",
    "description": "Fractals are indicators on candlestick charts that identify reversal points in the market.",
    "usage": "Use to mark potential support and resistance levels at local price extremes. Williams Fractals are commonly combined with Alligator lines to filter valid fractal signals.",
    "category": "Classic",
    "keywords": [
      "pattern",
      "support-resistance",
      "classic",
      "williams"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/terms/f/fractal.asp",
    "formula_latex": "\n\\[\n\\text{Up Fractal} = \\text{High} > \\text{High}_{t-1, t-2, t+1, t+2}\n\\]\n",
    "gold_standard_file": "fractals.json",
    "ehlers_summary": "Bill Williams introduced Fractals in Trading Chaos (1995) as a pattern-recognition tool identifying local price extremes. A bullish fractal is a bar whose low is lower than the two bars on either side; a bearish fractal is a bar whose high is higher than the two bars on either side. Combined with the Alligator indicator, fractals provide entry triggers. — StockCharts ChartSchool",
    "struct_name": "BillWilliamsFractals",
    "source_file": "fractals",
    "boundary_kind": "scalar"
  },
  {
    "slug": "frama",
    "name": "Fractal Adaptive Moving Average",
    "description": "An adaptive moving average that uses the fractal dimension of prices to dynamically change its smoothing constant.",
    "usage": "Use as an adaptive moving average that slows dramatically during consolidation and speeds up during trending phases. Outperforms fixed-period MAs in ranging markets by avoiding false crossovers.",
    "category": "Ehlers DSP",
    "keywords": [
      "moving-average",
      "adaptive",
      "fractal",
      "smoothing"
    ],
    "params": [
      {
        "name": "length",
        "default": "16",
        "description": "Length (must be an even number; odd values will be incremented by 1)."
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/implemented/FRAMA.pdf",
    "formula_latex": "\n\\[\nD = \\frac{\\log(N_1 + N_2) - \\log(N_3)}{\\log(2)}\n\\]\n\\[\n\\alpha = \\exp(-4.6 (D - 1))\n\\]\n\\[\n\\text{FRAMA}_t = \\alpha P_t + (1 - \\alpha) \\text{FRAMA}_{t-1}\n\\]\n",
    "gold_standard_file": "frama.json",
    "ehlers_summary": "The Fractal Adaptive Moving Average uses the fractal dimension of recent price action to adapt its smoothing constant. During trending markets the fractal dimension approaches 1 (a line) producing a fast-reacting EMA; during ranging markets the dimension approaches 2 (a plane) slowing the average dramatically to filter chop.",
    "struct_name": "Frama",
    "source_file": "frama",
    "boundary_kind": "scalar"
  },
  {
    "slug": "gap_momentum",
    "name": "Gap Momentum",
    "description": "Accumulates positive and negative opening gaps to derive a cumulative gap ratio, smoothed by a signal line.",
    "usage": "Used to identify momentum shifts based on price gaps. Buy when the signal line is rising and sell when it is falling.",
    "category": "Momentum",
    "keywords": [
      "momentum",
      "gap",
      "kaufman",
      "oscillator"
    ],
    "params": [
      {
        "name": "period",
        "default": "40",
        "description": "Rolling window for gap accumulation"
      },
      {
        "name": "signal_period",
        "default": "20",
        "description": "Smoothing period for the gap ratio"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS%E2%80%99%20TIPS%20-%20JANUARY%202024.html",
    "formula_latex": "\n\\[\nGap = Open_t - Close_{t-1}\n\\]\n\\[\nUpGaps = \\sum_{i=0}^{Period-1} \\max(0, Gap_{t-i})\n\\]\n\\[\nDnGaps = \\sum_{i=0}^{Period-1} \\max(0, -Gap_{t-i})\n\\]\n\\[\nGapRatio = \\begin{cases} 1 & \\text{if } DnGaps = 0 \\\\ 100 \\times \\frac{UpGaps}{DnGaps} & \\text{otherwise} \\end{cases}\n\\]\n\\[\nSignal = SMA(GapRatio, SignalPeriod)\n\\]\n",
    "gold_standard_file": "gap_momentum.json",
    "ehlers_summary": "Perry J. Kaufman introduced Gap Momentum as a way to quantify price gaps relative to their cumulative volatility, similar to an On-Balance Volume (OBV) logic applied to opening gaps. It helps traders identify if gap-driven momentum is increasing or decreasing by comparing the sum of upward gaps against downward gaps over a rolling window. — Perry Kaufman, S&C 2024",
    "struct_name": "GapMomentum",
    "source_file": "gap_momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "gaussian_filter",
    "name": "GaussianFilter",
    "description": "Multi-pole Gaussian low-pass filter for reduced lag.",
    "usage": "Use when smooth symmetric price averaging with near-zero phase shift is needed. Works well as a preprocessing step for spectral analysis indicators.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "smoothing",
      "ehlers",
      "dsp",
      "low-pass"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Critical period"
      },
      {
        "name": "poles",
        "default": "4",
        "description": "Number of poles (1-4)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/GaussianFilters.pdf",
    "formula_latex": "\n\\[\n\\alpha = -\\beta + \\sqrt{\\beta^2 + 2\\beta}\n\\]\n\\[\n\\beta = \\frac{1 - \\cos(2\\pi/P)}{2^{1/(2N)} - 1}\n\\]\n",
    "gold_standard_file": "gaussian_filter.json",
    "ehlers_summary": "Gaussian filters are the theoretically optimal lowpass filter for minimizing the product of time-domain duration and frequency-domain bandwidth. Ehlers implements them as cascaded pole filters with Gaussian-function-derived coefficients, achieving very smooth output with excellent stopband attenuation.",
    "struct_name": "GaussianFilter",
    "source_file": "gaussian",
    "boundary_kind": "scalar"
  },
  {
    "slug": "generalized_laguerre",
    "name": "Generalized Laguerre",
    "description": "A generalized Laguerre filter of arbitrary order using an UltimateSmoother as the primary component.",
    "usage": "Use when the standard 4-element Laguerre filter needs further customization. The additional gamma2 parameter allows independent control of the pole spacing for more flexible frequency response shaping.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "smoothing",
      "laguerre"
    ],
    "params": [
      {
        "name": "length",
        "default": "40",
        "description": "UltimateSmoother period"
      },
      {
        "name": "gamma",
        "default": "0.8",
        "description": "Smoothing factor (0.0 to 1.0)"
      },
      {
        "name": "order",
        "default": "8",
        "description": "Filter order (1 to 10)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS%E2%80%99%20TIPS%20-%20SEPTEMBER%202025.html",
    "formula_latex": "\n\\[\nLG_1 = UltimateSmoother(Price, Length)\n\\]\n\\[\nLG_i = -\\gamma LG_{i-1,t-1} + LG_{i-1,t-1} + \\gamma LG_{i,t-1} \\text{ for } i=2 \\dots Order\n\\]\n\\[\nFilter = \\frac{1}{Order} \\sum_{i=1}^{Order} LG_i\n\\]\n",
    "gold_standard_file": "generalized_laguerre.json",
    "ehlers_summary": "The Generalized Laguerre Filter extends the classic 4-element Laguerre design with an additional parameter that controls the distribution of poles across the frequency spectrum. This gives finer control over the transition band slope and passband flatness, useful for specialized spectral analysis applications.",
    "struct_name": "GeneralizedLaguerre",
    "source_file": "generalized_laguerre",
    "boundary_kind": "scalar"
  },
  {
    "slug": "geometric_patterns",
    "name": "geometric_patterns",
    "description": "Detects Flag (continuation) and Head & Shoulders (reversal) patterns using the MarketStructure foundation.",
    "usage": "Streaming scanner for automated price action pattern detection. Emits rich FlagPattern/HsPattern structs on breakout (flags) or high-score detection (H&S). Use pole_length_atr and height_atr for position sizing.",
    "category": "Price Action / Patterns",
    "keywords": [
      "price action",
      "patterns",
      "flags",
      "head and shoulders",
      "continuation",
      "reversal"
    ],
    "params": [
      {
        "name": "swing_strength",
        "default": "5",
        "description": "Swing detection strength passed to internal MarketStructure (Part 21)."
      },
      {
        "name": "min_pole_atr",
        "default": "1.0",
        "description": "Minimum flagpole impulse size as ATR multiple (Part 69 MinPoleATR)."
      },
      {
        "name": "max_retrace_percent",
        "default": "61.8",
        "description": "Maximum consolidation retrace as % of pole (Part 69 MaxRetracePercent)."
      }
    ],
    "formula_source": "MQL5 Part 66 (H&S) + Part 69 (Flags) by lynnchris, ported to QuantWave PA foundation",
    "formula_latex": "",
    "gold_standard_file": "references/MQL5/lynnchris/implemented/Part66/HS_Indicator.mq5 + Part69/Flag_Pattern_Detector.mq5",
    "ehlers_summary": "",
    "struct_name": "GeometricPatterns",
    "source_file": "geometric_patterns",
    "boundary_kind": "event"
  },
  {
    "slug": "griffiths_dominant_cycle",
    "name": "GriffithsDominantCycle",
    "description": "Dominant cycle estimation using Griffiths adaptive spectral analysis.",
    "usage": "Use as a robust dominant cycle estimator less sensitive to amplitude changes than DFT-based methods, making it reliable across different market volatility regimes.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "dominant-cycle",
      "ehlers",
      "dsp",
      "spectral"
    ],
    "params": [
      {
        "name": "lower_bound",
        "default": "18",
        "description": "Lower period bound"
      },
      {
        "name": "upper_bound",
        "default": "40",
        "description": "Upper period bound"
      },
      {
        "name": "length",
        "default": "40",
        "description": "LMS filter length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20JANUARY%202025.html",
    "formula_latex": "\n\\[\nPwr(Period) = \\frac{0.1}{(1-Real)^2 + Imag^2}\n\\]\n\\[\nReal = \\sum coef_i \\cos(2\\pi i / Period)\n\\]\n\\[\nImag = \\sum coef_i \\sin(2\\pi i / Period)\n\\]\n",
    "gold_standard_file": "griffiths_dominant_cycle.json",
    "ehlers_summary": "The Griffiths method computes the dominant cycle by solving the real-roots of an autocorrelation polynomial. Adapted by Ehlers in Cycle Analytics for Traders, it remains stable even when market amplitude changes rapidly, unlike power-spectrum methods that can shift with volatility.",
    "struct_name": "GriffithsDominantCycle",
    "source_file": "griffiths_dominant_cycle",
    "boundary_kind": "scalar"
  },
  {
    "slug": "griffiths_predictor",
    "name": "GriffithsPredictor",
    "description": "Adaptive LMS linear predictive filter for signal forecasting.",
    "usage": "Use for short-horizon price prediction by projecting the dominant market cycle one or two bars forward. Works best in oscillating markets; disable in strong trends.",
    "category": "Ehlers DSP",
    "keywords": [
      "prediction",
      "cycle",
      "ehlers",
      "dsp"
    ],
    "params": [
      {
        "name": "lower_bound",
        "default": "18",
        "description": "Lower frequency bound (SS length)"
      },
      {
        "name": "upper_bound",
        "default": "40",
        "description": "Upper frequency bound (HP length)"
      },
      {
        "name": "length",
        "default": "18",
        "description": "LMS filter length"
      },
      {
        "name": "bars_fwd",
        "default": "2",
        "description": "Number of bars to predict forward"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20JANUARY%202025.html",
    "formula_latex": "\n\\[\n\\mu = 1/L\n\\]\n\\[\n\\bar{x} = \\sum_{i=1}^L xx_{L-i} \\cdot coef_i\n\\]\n\\[\ncoef_i = coef_i + \\mu(xx_L - \\bar{x})xx_{L-i}\n\\]\n",
    "gold_standard_file": "griffiths_predictor.json",
    "ehlers_summary": "The Griffiths Predictor uses autoregressive coefficients from the Griffiths cycle measurement to extrapolate the current dominant cycle one bar ahead. By fitting an AR model to cycle-filtered price, it generates a one-step-ahead forecast useful for anticipatory entries at predicted cycle turns.",
    "struct_name": "GriffithsPredictor",
    "source_file": "griffiths_predictor",
    "boundary_kind": "scalar"
  },
  {
    "slug": "griffiths_spectrum",
    "name": "GriffithsSpectrum",
    "description": "Normalized power spectrum estimation using Griffiths adaptive filters.",
    "usage": "Use to generate a high-resolution periodogram for cycle analysis. Best visualized as a heatmap to identify and track multiple market cycles simultaneously.",
    "category": "Ehlers DSP",
    "keywords": [
      "spectrum",
      "cycle",
      "ehlers",
      "dsp",
      "periodogram"
    ],
    "params": [
      {
        "name": "lower_bound",
        "default": "18",
        "description": "Lower period bound"
      },
      {
        "name": "upper_bound",
        "default": "40",
        "description": "Upper period bound"
      },
      {
        "name": "length",
        "default": "40",
        "description": "LMS filter length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20JANUARY%202025.html",
    "formula_latex": "\n\\[\nPwr(P) = \\frac{0.1}{(1 - \\sum coef_i \\cos(2\\pi i/P))^2 + (\\sum coef_i \\sin(2\\pi i/P))^2}\n\\]\n\\[\nPwr_{norm}(P) = \\frac{Pwr(P)}{\\max(Pwr)}\n\\]\n",
    "gold_standard_file": "griffiths_spectrum.json",
    "ehlers_summary": "The Griffiths Spectrum is an adaptive spectral estimation method that provides higher resolution than a standard DFT for short data segments. It fits an all-pole model to the signal using an LMS algorithm, allowing for instantaneous frequency measurement without the windowing artifacts of FFT-based methods.",
    "struct_name": "GriffithsSpectrum",
    "source_file": "griffiths_spectrum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "hamming_filter",
    "name": "HammingFilter",
    "description": "Hamming windowed FIR filter with pedestal.",
    "usage": "Apply as a windowing function before DFT-based cycle detection to reduce sidelobe leakage and obtain cleaner dominant cycle estimates.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "windowing",
      "spectral"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Filter length"
      },
      {
        "name": "pedestal",
        "default": "10.0",
        "description": "Pedestal in degrees"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’ TIPS - SEPTEMBER 2021.html",
    "formula_latex": "\n\\[\nDeg(n) = Pedestal + (180 - 2 \\times Pedestal) \\times \\frac{n}{L-1}\n\\]\n\\[\nCoef(n) = \\sin\\left(\\frac{Deg(n) \\times \\pi}{180}\\right)\n\\]\n\\[\nFilt = \\frac{\\sum_{n=0}^{L-1} Coef(n) \\cdot Price_{t-n}}{\\sum Coef(n)}\n\\]\n",
    "gold_standard_file": "hamming_filter.json",
    "ehlers_summary": "The Hamming window is a raised-cosine weighting function that reduces spectral leakage by tapering the edges of a data block. Ehlers uses it in DFT-based cycle measurement tools to prevent energy in one frequency bin from contaminating adjacent bins, improving cycle period resolution.",
    "struct_name": "HammingFilter",
    "source_file": "hamming",
    "boundary_kind": "scalar"
  },
  {
    "slug": "hann_filter",
    "name": "HannFilter",
    "description": "Hann windowed lowpass FIR filter.",
    "usage": "Use as a windowing function before FFT-based dominant cycle measurement to achieve clean spectral separation between market cycles.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "windowing",
      "spectral"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Filter length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/JustIgnoreThem.pdf",
    "formula_latex": "\n\\[\nH(n) = 1 - \\cos\\left(\\frac{2\\pi n}{L+1}\\right)\n\\]\n\\[\nFilt = \\frac{\\sum_{n=1}^L H(n) \\cdot Price_{t-n+1}}{\\sum H(n)}\n\\]\n",
    "gold_standard_file": "hann_filter.json",
    "ehlers_summary": "The Hann window provides a smooth bell-shaped taper achieving -31.5 dB first sidelobe suppression. Ehlers uses it in Cycle Analytics for Traders as the preferred DFT window because it offers the best trade-off between frequency resolution and leakage rejection.",
    "struct_name": "HannFilter",
    "source_file": "hann",
    "boundary_kind": "scalar"
  },
  {
    "slug": "harrington_adx",
    "name": "Harrington ADX Oscillator",
    "description": "An oscillator variant of the ADX where the sign reflects trend direction determined by DMI+ and DMI-.",
    "usage": "The oscillator is positive when DMI+ > DMI- and negative when DMI- > DMI+. The magnitude represents trend strength (ADX). Thresholds at 15 and 40 are often used to identify trend initiation and overextended states.",
    "category": "Wilder",
    "keywords": [
      "adx",
      "dmi",
      "oscillator",
      "wilder",
      "momentum"
    ],
    "params": [
      {
        "name": "adx_length",
        "default": "10",
        "description": "Wilder's ADX period"
      },
      {
        "name": "adx_smooth_length",
        "default": "1",
        "description": "SMA period for DMI components smoothing"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS%E2%80%99%20TIPS%20-%20DECEMBER%202024.html",
    "formula_latex": "\n\\[\nTR = \\max(H-L, |H-C_{t-1}|, |L-C_{t-1}|)\n\\]\n\\[\n+DM = (H-H_{t-1} > L_{t-1}-L) \\text{ and } (H-H_{t-1} > 0) ? H-H_{t-1} : 0\n\\]\n\\[\n-DM = (L_{t-1}-L > H-H_{t-1}) \\text{ and } (L_{t-1}-L > 0) ? L_{t-1}-L : 0\n\\]\n\\[\n+DI = 100 \\cdot \\frac{EMA(+DM, 1/L)}{EMA(TR, 1/L)}\n\\]\n\\[\n-DI = 100 \\cdot \\frac{EMA(-DM, 1/L)}{EMA(TR, 1/L)}\n\\]\n\\[\nDX = 100 \\cdot \\frac{|+DI - -DI|}{+DI + -DI}\n\\]\n\\[\nADX = EMA(DX, 1/L)\n\\]\n\\[\nResult = (SMA(+DI, S) \\ge SMA(-DI, S)) ? ADX : -ADX\n\\]\n",
    "gold_standard_file": "harrington_adx.json",
    "ehlers_summary": "While originally created by Wilder, this revisualization by Harrington transforms the unipolar ADX into a bipolar oscillator. This allows for simultaneous identification of trend strength and direction in a single histogram display, simplifying the interpretation of complex directional movement data.",
    "struct_name": "HarringtonAdx",
    "source_file": "harrington_adx",
    "boundary_kind": "scalar"
  },
  {
    "slug": "heikin_ashi",
    "name": "Heikin-Ashi",
    "description": "Heikin-Ashi candles filter market noise to reveal the underlying trend.",
    "usage": "Use to smooth candlestick charts and reduce noise for trend identification. Two or more consecutive same-colored HA candles with no lower/upper wicks confirm a strong trend.",
    "category": "Classic",
    "keywords": [
      "trend",
      "candlestick",
      "smoothing",
      "classic",
      "visualization"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/trading/heikin-ashi-better-candlestick/",
    "formula_latex": "\n\\[\nHA_{Close} = \\frac{O + H + L + C}{4} \\\\ HA_{Open} = \\frac{HA_{Open, t-1} + HA_{Close, t-1}}{2}\n\\]\n",
    "gold_standard_file": "heikin_ashi.json",
    "ehlers_summary": "Heikin-Ashi candles, developed by Munehisa Homma in the 18th century, use averaged OHLC values to produce smoother candles that better represent the prevailing trend. Each HA bar open equals the midpoint of the previous HA bar, while close equals the OHLC average, creating continuity that raw candles lack. — StockCharts ChartSchool",
    "struct_name": "HeikinAshi",
    "source_file": "heikin_ashi",
    "boundary_kind": "scalar"
  },
  {
    "slug": "high_pass",
    "name": "HighPass",
    "description": "A second-order High Pass filter that rejects low-frequency components.",
    "usage": "Apply to price to isolate the cyclical component by attenuating the low-frequency trend. Use as the first stage before an oscillator or spectrum analyser.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "high-pass",
      "cycle"
    ],
    "params": [
      {
        "name": "period",
        "default": "20",
        "description": "Critical period (wavelength)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/implemented/UltimateSmoother.pdf",
    "formula_latex": "\n\\[\na_1 = \\exp\\left(-\\frac{1.414\\pi}{Period}\\right)\n\\]\n\\[\nc_2 = 2a_1 \\cos\\left(\\frac{1.414\\pi}{Period}\\right)\n\\]\n\\[\nc_3 = -a_1^2\n\\]\n\\[\nc_1 = (1 + c_2 - c_3) / 4\n\\]\n\\[\nHP = c_1 (Price - 2 Price_{t-1} + Price_{t-2}) + c_2 HP_{t-1} + c_3 HP_{t-2}\n\\]\n",
    "gold_standard_file": "high_pass.json",
    "ehlers_summary": "Ehlers derives the one-pole high-pass filter in Cycle Analytics for Traders analogously to EMA derivation, but applied to price differences rather than levels. It removes the DC component and low-frequency trend, leaving the cyclical content for downstream analysis.",
    "struct_name": "HighPass",
    "source_file": "high_pass",
    "boundary_kind": "scalar"
  },
  {
    "slug": "hma",
    "name": "Hull Moving Average",
    "description": "The Hull Moving Average (HMA) aims to reduce lag while maintaining smoothness.",
    "usage": "Use as a near-zero-lag moving average for trend-following systems where entry timing is critical. The HMA substantially reduces the lag of a same-period WMA.",
    "category": "Classic",
    "keywords": [
      "moving-average",
      "low-lag",
      "smoothing",
      "classic"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://alanhull.com/hull-moving-average",
    "formula_latex": "\n\\[\nHMA = WMA(2 \\times WMA(\\frac{n}{2}) - WMA(n), \\sqrt{n})\n\\]\n",
    "gold_standard_file": "hma.json",
    "ehlers_summary": "Alan Hull designed the Hull Moving Average to nearly eliminate lag while maintaining smoothness. It achieves this by computing a WMA of doubled period, subtracting a WMA of full period, then applying a final WMA to the difference over the square-root period, combining speed with noise reduction. — AlanHull.com",
    "struct_name": "Hma",
    "source_file": "hma",
    "boundary_kind": "scalar"
  },
  {
    "slug": "homodyne_discriminator",
    "name": "Homodyne Discriminator",
    "description": "Estimates the dominant cycle period using a homodyne approach.",
    "usage": "Use to measure the instantaneous dominant cycle period from price data. Feed its output into adaptive indicators as the dynamic period parameter.",
    "category": "Rocket Science",
    "keywords": [
      "cycle",
      "dominant-cycle",
      "ehlers",
      "dsp",
      "spectral"
    ],
    "params": [],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/ROCKET%20SCIENCE%20FOR%20TRADER.pdf",
    "formula_latex": "\n\\[\n\\text{Period} = \\frac{360}{\\text{atan}(Im / Re)}\n\\]\n",
    "gold_standard_file": "homodyne_discriminator.json",
    "ehlers_summary": "Described in Rocket Science for Traders (2001), the Homodyne Discriminator borrows from radio engineering to measure instantaneous frequency by multiplying the analytic signal by its one-bar-delayed conjugate, giving cycle period without DFT latency.",
    "struct_name": "HomodyneDiscriminator",
    "source_file": "homodyne_discriminator",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ht_dcperiod",
    "name": "Hilbert Transform - Dominant Cycle Period (HT_DCPERIOD)",
    "description": "Identifies the period of the dominant cycle in the price data using the Hilbert Transform.",
    "usage": "Use to dynamically adjust the lookback periods of other indicators (e.g., adaptive moving averages). Knowing the current dominant cycle length allows for more accurate smoothing and trend detection.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "hilbert",
      "adaptive",
      "dsp"
    ],
    "params": [],
    "formula_source": "https://www.tradingview.com/support/solutions/43000502011-hilbert-transform-dominant-cycle-period-ht-dcperiod/",
    "formula_latex": "\n\\[\n\\text{DCPERIOD}_t = \\text{Recalculated Dominant Cycle using Hilbert Transform}\n\\]\n",
    "gold_standard_file": "ht_dcperiod.json",
    "ehlers_summary": "John Ehlers popularized the use of the Hilbert Transform to identify the dominant cycle in financial time series. The DCPERIOD indicator tracks the length of this cycle in bars, providing a crucial parameter for creating market-responsive technical indicators that adapt to changing volatility. — Rocket Science for Traders",
    "struct_name": "",
    "source_file": "cycle",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ht_dcphase",
    "name": "Hilbert Transform - Dominant Cycle Phase (HT_DCPHASE)",
    "description": "Calculates the phase angle (0 to 360 degrees) of the dominant cycle identified by the Hilbert Transform.",
    "usage": "Use to identify the current position within a market cycle. It is the core component for generating the Hilbert Sine Wave indicator, which signals trend vs. cycle regimes.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "hilbert",
      "phase",
      "dsp"
    ],
    "params": [],
    "formula_source": "https://www.tradingview.com/support/solutions/43000502010-hilbert-transform-dominant-cycle-phase-ht-dcphase/",
    "formula_latex": "\n\\[\nPhase = \\arctan\\left(\\frac{\\text{Quadrature}}{\\text{InPhase}}\\right)\n\\]\n",
    "gold_standard_file": "ht_dcphase.json",
    "ehlers_summary": "The Dominant Cycle Phase represents the instantaneous position within a detected cycle. By measuring the phase angle, traders can determine if the market is at a peak, trough, or mid-cycle, enabling more precise timing for entry and exit signals. — Rocket Science for Traders",
    "struct_name": "",
    "source_file": "cycle",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ht_phasor",
    "name": "Hilbert Transform - Phasor Components (HT_PHASOR)",
    "description": "Outputs the In-Phase and Quadrature components of the signal, which are used to calculate phase and amplitude.",
    "usage": "Use as building blocks for custom DSP indicators. The In-Phase component is the signal itself, while the Quadrature component is shifted by 90 degrees.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "hilbert",
      "phasor",
      "dsp"
    ],
    "params": [],
    "formula_source": "https://www.tradingview.com/support/solutions/43000502012-hilbert-transform-phasor-components-ht-phasor/",
    "formula_latex": "\n\\[\n\\text{Result} = (InPhase, Quadrature)\n\\]\n",
    "gold_standard_file": "ht_phasor.json",
    "ehlers_summary": "The Phasor components (In-Phase and Quadrature) are the fundamental outputs of the Hilbert Transform. They allow for the decomposition of a signal into its vector representation, which is essential for advanced cycle analysis and the creation of lag-free filters. — Rocket Science for Traders",
    "struct_name": "",
    "source_file": "cycle",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ht_sine",
    "name": "Hilbert Transform - Sine Wave (HT_SINE)",
    "description": "An indicator that plots a sine wave and a lead-sine wave (shifted by 45 degrees) to identify cyclical turns.",
    "usage": "Use to identify cycle turning points and trend regimes. When the two waves are separated and rhythmic, the market is in a cycle; when they are compressed or crossover erratically, the market is in a trend.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "hilbert",
      "sine",
      "dsp"
    ],
    "params": [],
    "formula_source": "https://www.tradingview.com/support/solutions/43000502013-hilbert-transform-sine-wave-ht-sine/",
    "formula_latex": "\n\\[\nSine = \\sin(Phase) \\\\ LeadSine = \\sin(Phase + 45^\\circ)\n\\]\n",
    "gold_standard_file": "ht_sine.json",
    "ehlers_summary": "The Hilbert Sine Wave is one of John Ehlers' most famous contributions. It provides a clear visual indication of market cycles. Crossovers of the Sine and Lead-Sine waves provide high-probability entry points in ranging markets while identifying when a strong trend has taken over. — Rocket Science for Traders",
    "struct_name": "",
    "source_file": "cycle",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ht_trendmode",
    "name": "Hilbert Transform - Trend vs. Cycle Mode (HT_TRENDMODE)",
    "description": "A binary indicator that determines if the market is currently in a trending state (1) or a cyclical state (0).",
    "usage": "Use as a master filter for strategy selection. Deploy trend-following tools when TRENDMODE is 1, and mean-reversion tools when TRENDMODE is 0.",
    "category": "Ehlers DSP",
    "keywords": [
      "cycle",
      "trend",
      "hilbert",
      "regime-detection",
      "dsp"
    ],
    "params": [],
    "formula_source": "https://www.tradingview.com/support/solutions/43000502014-hilbert-transform-trend-vs-cycle-mode-ht-trendmode/",
    "formula_latex": "\n\\[\n\\text{TRENDMODE} = \\begin{cases} 1 & \\text{if trend detected} \\\\ 0 & \\text{if cycle detected} \\end{cases}\n\\]\n",
    "gold_standard_file": "ht_trendmode.json",
    "ehlers_summary": "Determining the current market regime is the 'holy grail' of technical analysis. The HT_TRENDMODE indicator uses the rate of change of the dominant cycle phase to distinguish between trending and ranging price action, allowing traders to avoid 'whipsaws' in non-conducive environments. — Rocket Science for Traders",
    "struct_name": "",
    "source_file": "cycle",
    "boundary_kind": "scalar"
  },
  {
    "slug": "hurst_exponent",
    "name": "Hurst Exponent",
    "description": "Measures the persistence or anti-persistence of a time series using R/S analysis.",
    "usage": "Use to classify the current market regime. H > 0.5 suggests a trending market (persistent); H < 0.5 suggests a mean-reverting market (anti-persistent). Useful as a filter for trend-following or mean-reversion strategies.",
    "category": "ML Features",
    "keywords": [
      "statistics",
      "regime-detection",
      "hurst",
      "ml",
      "trending",
      "mean-reversion"
    ],
    "params": [
      {
        "name": "period",
        "default": "100",
        "description": "Lookback period for R/S analysis"
      }
    ],
    "formula_source": "https://en.wikipedia.org/wiki/Hurst_exponent",
    "formula_latex": "\n\\[\nH = \\frac{\\ln(R/S)}{\\ln(N)}\n\\]\n",
    "gold_standard_file": "hurst_exponent.json",
    "ehlers_summary": "The Hurst Exponent, pioneered by Harold Edwin Hurst in 1951, quantifies the 'memory' of a time series. In technical analysis, it distinguishes between trending, mean-reverting, and random walk price action. It is a critical feature for machine learning models to adapt their logic to the underlying market structure.",
    "struct_name": "HurstExponent",
    "source_file": "hurst",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ichimoku",
    "name": "Ichimoku Cloud",
    "description": "Ichimoku Kinko Hyo is a comprehensive indicator that defines support and resistance, identifies trend direction, gauges momentum and provides trading signals.",
    "usage": "Use as a complete trend system providing support, resistance, momentum, and cloud-based bias in a single indicator. The Kumo cloud thickness indicates trend strength.",
    "category": "Classic",
    "keywords": [
      "trend",
      "support-resistance",
      "classic",
      "japanese",
      "momentum"
    ],
    "params": [
      {
        "name": "tenkan_period",
        "default": "9",
        "description": "Tenkan-sen period"
      },
      {
        "name": "kijun_period",
        "default": "26",
        "description": "Kijun-sen period"
      },
      {
        "name": "senkou_span_b_period",
        "default": "52",
        "description": "Senkou Span B period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/i/ichimoku-cloud.asp",
    "formula_latex": "\n\\[\n\\text{Tenkan-sen} = \\frac{\\text{Highest High} + \\text{Lowest Low}}{2} \\text{ for past 9 periods}\n\\]\n",
    "gold_standard_file": "ichimoku.json",
    "ehlers_summary": "Ichimoku Kinko Hyo was developed by Goichi Hosoda in the 1960s. The system comprises five components: Tenkan-sen (9-period midpoint), Kijun-sen (26-period midpoint), Senkou Span A and B (cloud), and Chikou Span (lagged close). Price above the cloud is bullish; the cloud thickness quantifies the strength of support or resistance. — Ichimoku Charts, Nicole Elliott",
    "struct_name": "Ichimoku",
    "source_file": "ichimoku",
    "boundary_kind": "scalar"
  },
  {
    "slug": "instantaneous_trendline",
    "name": "Instantaneous Trendline",
    "description": "Removes the dominant cycle to reveal the underlying trend with minimal lag.",
    "usage": "Use as an adaptive trend line that automatically adjusts to the current dominant cycle period, replacing fixed-period moving averages in trend-following systems.",
    "category": "Rocket Science",
    "keywords": [
      "trend",
      "adaptive",
      "moving-average",
      "ehlers",
      "dsp"
    ],
    "params": [],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/ROCKET%20SCIENCE%20FOR%20TRADER.pdf",
    "formula_latex": "\n\\[\nTrendline = \\text{WMA}(\\text{SMA}(Price, DCPeriod), 4)\n\\]\n",
    "gold_standard_file": "instantaneous_trendline.json",
    "ehlers_summary": "Defined in Rocket Science for Traders (2001), the Instantaneous Trendline is derived from Hilbert Transform phasors and synchronized to the current market cycle. It is computed as a 3-bar weighted average adjusted by the instantaneous period, giving a zero-lag trend estimate.",
    "struct_name": "InstantaneousTrendline",
    "source_file": "instantaneous_trendline",
    "boundary_kind": "scalar"
  },
  {
    "slug": "inverse_fisher",
    "name": "Inverse Fisher Transform",
    "description": "A compressive transform that forces oscillator values towards +1 or -1, creating clear buy/sell signals.",
    "usage": "Apply to RSI or other oscillators to rescale them to a ±1 range with sharp threshold behaviour. Values near ±1 indicate high-confidence overbought/oversold conditions.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "ehlers",
      "normalization",
      "momentum"
    ],
    "params": [],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/TheInverseFisherTransform.pdf",
    "formula_latex": "\n\\[\nIFT(x) = \\frac{e^{2x} - 1}{e^{2x} + 1} = \\tanh(x)\n\\]\n",
    "gold_standard_file": "inverse_fisher.json",
    "ehlers_summary": "The Inverse Fisher Transform maps input values to (-1, +1) via a hyperbolic tangent function. Ehlers uses it in Cybernetic Analysis to create oscillators whose output clusters near the extremes, making crossovers of fixed thresholds reliable trading signals.",
    "struct_name": "InverseFisher",
    "source_file": "inverse_fisher",
    "boundary_kind": "scalar"
  },
  {
    "slug": "kalman_filter",
    "name": "Kalman Filter",
    "description": "An adaptive 1D Kalman filter for smoothing price data with minimal lag.",
    "usage": "Use as a highly responsive alternative to moving averages. The Q parameter (process noise) controls responsiveness to trend changes, while R (measurement noise) controls smoothness. Higher Q makes it track price faster; higher R increases smoothing.",
    "category": "ML Features",
    "keywords": [
      "filter",
      "adaptive",
      "smoothing",
      "ml",
      "kalman"
    ],
    "params": [
      {
        "name": "q",
        "default": "0.01",
        "description": "Process noise (responsiveness)"
      },
      {
        "name": "r",
        "default": "0.1",
        "description": "Measurement noise (smoothing)"
      }
    ],
    "formula_source": "https://en.wikipedia.org/wiki/Kalman_filter",
    "formula_latex": "\n\\[\nP_{t|t-1} = P_{t-1} + Q\n\\]\n\\[\nK_t = \\frac{P_{t|t-1}}{P_{t|t-1} + R}\n\\]\n\\[\nX_t = X_{t-1} + K_t(Z_t - X_{t-1})\n\\]\n\\[\nP_t = (1 - K_t)P_{t|t-1}\n\\]\n",
    "gold_standard_file": "kalman_filter.json",
    "ehlers_summary": "The Kalman Filter is an optimal estimator for linear systems with Gaussian noise. In technical analysis, the 1D version recursively updates the estimate of the 'true' price by balancing the predicted state against new measurements. It is particularly effective for feature engineering in ML models due to its ability to separate signal from noise dynamically.",
    "struct_name": "KalmanFilter",
    "source_file": "kalman",
    "boundary_kind": "scalar"
  },
  {
    "slug": "kama",
    "name": "KAMA",
    "description": "Kaufman's Adaptive Moving Average adjusts its sensitivity based on market volatility.",
    "usage": "Use as an adaptive moving average that is fast in trending markets and slow in choppy, sideways conditions. Reduces whipsaws that plague fixed-period moving averages in ranging markets.",
    "category": "Classic",
    "keywords": [
      "moving-average",
      "adaptive",
      "smoothing",
      "classic"
    ],
    "params": [
      {
        "name": "period",
        "default": "10",
        "description": "Efficiency Ratio lookback period"
      },
      {
        "name": "fast_period",
        "default": "2",
        "description": "Fastest smoothing period"
      },
      {
        "name": "slow_period",
        "default": "30",
        "description": "Slowest smoothing period"
      }
    ],
    "formula_source": "https://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:kaufman_s_adaptive_moving_average",
    "formula_latex": "\n\\[\nER = \\frac{|Price - Price_{t-n}|}{\\sum |Price - Price_{t-1}|}\n\\]\n\\[\nSC = [ER(FastSC - SlowSC) + SlowSC]^2\n\\]\n\\[\nKAMA = KAMA_{t-1} + SC(Price - KAMA_{t-1})\n\\]\n",
    "gold_standard_file": "kama.json",
    "ehlers_summary": "Perry Kaufman designed KAMA using an Efficiency Ratio that measures how directionally price has moved versus total path length. A high ratio (strong trend) produces a fast-reacting EMA; a low ratio (choppy market) produces a near-flat line, dramatically reducing false signals during consolidation. — New Trading Systems and Methods, 4th ed.",
    "struct_name": "Kama",
    "source_file": "kama",
    "boundary_kind": "scalar"
  },
  {
    "slug": "keltner",
    "name": "Keltner Channels",
    "description": "Keltner Channels are volatility-based envelopes set above and below an exponential moving average.",
    "usage": "Use as volatility-adjusted envelope bands around an EMA. When Keltner Channels contract inside Bollinger Bands (the Squeeze), a high-energy breakout move is typically imminent.",
    "category": "Classic",
    "keywords": [
      "volatility",
      "trend",
      "breakout",
      "channels",
      "classic"
    ],
    "params": [
      {
        "name": "period",
        "default": "20",
        "description": "EMA Period"
      },
      {
        "name": "multiplier",
        "default": "2.0",
        "description": "ATR Multiplier"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/k/keltnerchannel.asp",
    "formula_latex": "\n\\[\nUC = EMA + (Multiplier \\times ATR)\n\\]\n",
    "gold_standard_file": "keltner.json",
    "ehlers_summary": "Keltner Channels, updated by Linda Raschke in the 1980s from Chester Keltner original design, use ATR to set channel width around an EMA. Unlike Bollinger Bands which use standard deviation, ATR-based channels adapt to average bar range rather than statistical volatility, producing smoother and more stable channel boundaries. — StockCharts ChartSchool",
    "struct_name": "Keltner",
    "source_file": "keltner",
    "boundary_kind": "scalar"
  },
  {
    "slug": "kinematic_kalman",
    "name": "Kinematic Kalman Filter",
    "description": "A 2D Kalman filter tracking price and velocity to reduce lag in trends.",
    "usage": "Optimized for trend-following strategies where lag reduction is critical. q_pos controls price sensitivity, q_vel controls momentum sensitivity, and r controls overall smoothing.",
    "category": "ML Features",
    "keywords": [
      "kalman",
      "adaptive",
      "kinematic",
      "momentum",
      "lag-reduction"
    ],
    "params": [
      {
        "name": "q_pos",
        "default": "0.001",
        "description": "Process noise for position (price)"
      },
      {
        "name": "q_vel",
        "default": "0.0001",
        "description": "Process noise for velocity (momentum)"
      },
      {
        "name": "r",
        "default": "0.1",
        "description": "Measurement noise (smoothing strength)"
      }
    ],
    "formula_source": "https://www.cs.unc.edu/~welch/kalman/media/pdf/Kalman1960.pdf",
    "formula_latex": "\n\\[\n\\hat{x}_{k|k-1} = \\Phi \\hat{x}_{k-1|k-1}\n\\]\n\\[\nP_{k|k-1} = \\Phi P_{k-1|k-1} \\Phi^T + Q\n\\]\n\\[\nK_k = P_{k|k-1} H^T (H P_{k|k-1} H^T + R)^{-1}\n\\]\n\\[\n\\hat{x}_{k|k} = \\hat{x}_{k|k-1} + K_k (z_k - H \\hat{x}_{k|k-1})\n\\]\n\\[\nP_{k|k} = (I - K_k H) P_{k|k-1}\n\\]\n",
    "gold_standard_file": "kinematic_kalman.json",
    "ehlers_summary": "The Kinematic Kalman Filter extends the 1D model by incorporating a velocity state. This allows the filter to 'anticipate' the next price based on current momentum, providing a zero-lag-like response during strong trends while maintaining smoothness via its optimal error-correction logic.",
    "struct_name": "KinematicKalman",
    "source_file": "kinematic_kalman",
    "boundary_kind": "scalar"
  },
  {
    "slug": "laguerre_filter",
    "name": "Laguerre Filter",
    "description": "A trend-following filter that excels at smoothing long-wavelength components using Laguerre polynomials and an UltimateSmoother base.",
    "usage": "Use as a low-lag smoothing filter with only 4 elements of state. Ideal when memory-efficiency matters or when a highly responsive smoother for real-time streaming is needed.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "smoothing",
      "laguerre"
    ],
    "params": [
      {
        "name": "length",
        "default": "40",
        "description": "UltimateSmoother period"
      },
      {
        "name": "gamma",
        "default": "0.8",
        "description": "Smoothing factor (0.0 to 1.0)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS%E2%80%99%20TIPS%20-%20JULY%202025.html",
    "formula_latex": "\n\\[\nL_0 = UltimateSmoother(Close, Length)\n\\]\n\\[\nL_1 = -\\gamma L_{0,t-1} + L_{0,t-1} + \\gamma L_{1,t-1}\n\\]\n\\[\n...\n\\]\n\\[\nLaguerre = (L_0 + 4L_1 + 6L_2 + 4L_3 + L_5) / 16\n\\]\n",
    "gold_standard_file": "laguerre_filter.json",
    "ehlers_summary": "Ehlers introduces Laguerre filters in Cybernetic Analysis (2004), noting they achieve the response of much longer conventional filters using only four coefficients. The single gamma parameter controls the trade-off between lag and smoothness.",
    "struct_name": "LaguerreFilter",
    "source_file": "laguerre_filter",
    "boundary_kind": "scalar"
  },
  {
    "slug": "laguerre_oscillator",
    "name": "Laguerre Oscillator",
    "description": "A low-lag trend oscillator derived from Laguerre polynomials and normalized by RMS volatility.",
    "usage": "Use to detect overbought and oversold conditions with very low lag. The single gamma parameter lets you tune it from aggressive to smooth.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "ehlers",
      "dsp",
      "laguerre",
      "momentum"
    ],
    "params": [
      {
        "name": "length",
        "default": "30",
        "description": "UltimateSmoother period"
      },
      {
        "name": "gamma",
        "default": "0.5",
        "description": "Smoothing factor"
      },
      {
        "name": "rms_period",
        "default": "100",
        "description": "RMS normalization period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS%E2%80%99%20TIPS%20-%20JULY%202025.html",
    "formula_latex": "\n\\[\nL_0 = UltimateSmoother(Close, Length)\n\\]\n\\[\nL_1 = -\\gamma L_0 + L_{0,t-1} + \\gamma L_{1,t-1}\n\\]\n\\[\nRMS = \\sqrt{\\frac{1}{n}\\sum (L_0 - L_1)^2}\n\\]\n\\[\nOsc = (L_0 - L_1) / RMS\n\\]\n",
    "gold_standard_file": "laguerre_oscillator.json",
    "ehlers_summary": "Ehlers describes the Laguerre Oscillator in Cybernetic Analysis as measuring the difference between the first and last elements of a 4-element Laguerre filter bank, extracting the high-frequency component as a zero-lag momentum measure.",
    "struct_name": "LaguerreOscillator",
    "source_file": "laguerre_oscillator",
    "boundary_kind": "scalar"
  },
  {
    "slug": "laguerre_rsi",
    "name": "Laguerre RSI",
    "description": "RSI calculated over Laguerre-warped time for faster response.",
    "usage": "Use as a faster lower-lag alternative to traditional RSI. Laguerre smoothing produces fewer whipsaws while remaining responsive to genuine momentum shifts.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "rsi",
      "ehlers",
      "dsp",
      "laguerre",
      "momentum"
    ],
    "params": [
      {
        "name": "gamma",
        "default": "0.5",
        "description": "Smoothing factor (0.0 to 1.0)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/TimeWarp.pdf",
    "formula_latex": "\n\\[\nL_0 = (1 - \\gamma) \\cdot Close + \\gamma \\cdot L_{0,t-1}\n\\]\n\\[\nL_1 = -\\gamma L_0 + L_{0,t-1} + \\gamma L_{1,t-1}\n\\]\n\\[\nL_2 = -\\gamma L_1 + L_{1,t-1} + \\gamma L_{2,t-1}\n\\]\n\\[\nL_3 = -\\gamma L_2 + L_{2,t-1} + \\gamma L_{3,t-1}\n\\]\n\\[\nCU = \\sum \\max(L_{i} - L_{i+1}, 0)\n\\]\n\\[\nCD = \\sum \\max(L_{i+1} - L_{i}, 0)\n\\]\n\\[\nRSI = \\frac{CU}{CU + CD}\n\\]\n",
    "gold_standard_file": "laguerre_rsi.json",
    "ehlers_summary": "Ehlers constructs the Laguerre RSI in Cybernetic Analysis by computing RSI on the four outputs of a Laguerre filter bank. The result has RSI-like scaling (0 to 1) but dramatically less lag and smoother behaviour than conventional RSI.",
    "struct_name": "LaguerreRsi",
    "source_file": "laguerre_rsi",
    "boundary_kind": "scalar"
  },
  {
    "slug": "linreg",
    "name": "Linear Regression",
    "description": "Linear Regression plots a straight line that best fits the data prices.",
    "usage": "Use for statistical analysis of price series: linear regression, standard deviation, correlation coefficients, and other descriptive statistics used as indicator inputs.",
    "category": "Classic",
    "keywords": [
      "statistics",
      "classic",
      "volatility",
      "trend"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/l/linearregression.asp",
    "formula_latex": "\n\\[\ny = a + bx\n\\]\n",
    "gold_standard_file": "linreg.json",
    "ehlers_summary": "Standard statistical measures provide the mathematical foundation for many technical indicators. Linear regression finds the best-fit line through price, standard deviation quantifies dispersion, and correlation coefficients measure how closely two series move together — all are essential for quantitative strategy construction.",
    "struct_name": "StandardDeviation",
    "source_file": "statistics",
    "boundary_kind": "scalar"
  },
  {
    "slug": "macd",
    "name": "Moving Average Convergence Divergence (MACD)",
    "description": "A trend-following momentum indicator that shows the relationship between two moving averages.",
    "usage": "Use to identify trend direction and momentum. Crossovers of the MACD line and signal line provide entry and exit signals, while the histogram shows the strength of the trend.",
    "category": "Classic",
    "keywords": [
      "trend",
      "momentum",
      "moving-average",
      "classic"
    ],
    "params": [
      {
        "name": "fastperiod",
        "default": "12",
        "description": "Fast EMA period"
      },
      {
        "name": "slowperiod",
        "default": "26",
        "description": "Slow EMA period"
      },
      {
        "name": "signalperiod",
        "default": "9",
        "description": "Signal EMA period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/m/macd.asp",
    "formula_latex": "\n\\[\nMACD = EMA(12) - EMA(26) \\\\ Signal = EMA(MACD, 9)\n\\]\n",
    "gold_standard_file": "macd.json",
    "ehlers_summary": "Gerald Appel developed the MACD in the late 1970s. It is calculated by subtracting the 26-period EMA from the 12-period EMA. A nine-day EMA of the MACD, called the 'signal line,' is then plotted on top of the MACD line, which can function as a trigger for buy and sell signals. — Investopedia",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "mad",
    "name": "MAD",
    "description": "Moving Average Difference: 100 * (SMA(short) - SMA(long)) / SMA(long)",
    "usage": "Use as a robust volatility measure when outliers or fat-tailed distributions would distort standard deviation. Works well for position sizing and volatility-based stop placement.",
    "category": "Ehlers DSP",
    "keywords": [
      "volatility",
      "statistics",
      "robust",
      "ehlers"
    ],
    "params": [
      {
        "name": "short_period",
        "default": "8",
        "description": "Short-term SMA period"
      },
      {
        "name": "long_period",
        "default": "23",
        "description": "Long-term SMA period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’ TIPS - OCTOBER 2021.html",
    "formula_latex": "\n\\[\nMAD = 100 \\times \\frac{SMA(short) - SMA(long)}{SMA(long)}\n\\]\n",
    "gold_standard_file": "mad.json",
    "ehlers_summary": "Mean Absolute Deviation measures dispersion as the average absolute difference from the median rather than the squared difference from the mean used by standard deviation. It is less sensitive to outliers, making it a more robust volatility estimate for financial time series with fat tails.",
    "struct_name": "Mad",
    "source_file": "mad",
    "boundary_kind": "scalar"
  },
  {
    "slug": "madh",
    "name": "MADH",
    "description": "Moving Average Difference with Hann Windowing: 100 * (Hann(short) - Hann(long)) / Hann(long)",
    "usage": "Use to measure the volatility of the cyclical price component only, filtering out trend-driven amplitude changes that inflate standard volatility measures in trending markets.",
    "category": "Ehlers DSP",
    "keywords": [
      "volatility",
      "statistics",
      "ehlers",
      "high-pass"
    ],
    "params": [
      {
        "name": "short_length",
        "default": "8",
        "description": "Short-term filter length"
      },
      {
        "name": "dominant_cycle",
        "default": "27",
        "description": "Dominant cycle for calculating long length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’ TIPS - NOVEMBER 2021.html",
    "formula_latex": "\n\\[\nLongLength = \\lfloor ShortLength + DominantCycle / 2 \\rfloor\n\\]\n\\[\nFilt1 = HannWindow(Price, ShortLength)\n\\]\n\\[\nFilt2 = HannWindow(Price, LongLength)\n\\]\n\\[\nMADH = 100 \\times \\frac{Filt1 - Filt2}{Filt2}\n\\]\n",
    "gold_standard_file": "madh.json",
    "ehlers_summary": "MADH applies Mean Absolute Deviation to the high-pass filtered price series rather than raw price. By isolating the cyclical component before measuring dispersion, it quantifies the noise level within the current market cycle rather than conflating it with trend amplitude.",
    "struct_name": "Madh",
    "source_file": "madh",
    "boundary_kind": "scalar"
  },
  {
    "slug": "mama",
    "name": "MESA Adaptive Moving Average",
    "description": "MAMA adapts to price movement in an entirely new and unique way based on the rate change of phase.",
    "usage": "Use as an adaptive trend filter that automatically speeds up in fast markets and slows in choppy ones. The FAMA line crossing MAMA provides high-probability trend change signals.",
    "category": "Ehlers DSP",
    "keywords": [
      "moving-average",
      "adaptive",
      "ehlers",
      "dsp",
      "trend"
    ],
    "params": [
      {
        "name": "fast_limit",
        "default": "0.5",
        "description": "Fast limit for alpha"
      },
      {
        "name": "slow_limit",
        "default": "0.05",
        "description": "Slow limit for alpha"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/implemented/MAMA.pdf",
    "formula_latex": "\n\\[\n\\text{MAMA} = \\alpha \\cdot \\text{Price} + (1 - \\alpha) \\cdot \\text{MAMA}_{1}\n\\]\n\\[\n\\text{FAMA} = 0.5\\alpha \\cdot \\text{MAMA} + (1 - 0.5\\alpha) \\cdot \\text{FAMA}_{1}\n\\]\n",
    "gold_standard_file": "mama.json",
    "ehlers_summary": "Presented in Rocket Science for Traders (2001), MAMA adapts its alpha based on the rate of phase change measured by the Hilbert Transform Discriminator. Fast cycles produce large alpha for responsiveness; slow cycles produce small alpha to reduce noise.",
    "struct_name": "Mama",
    "source_file": "mama",
    "boundary_kind": "scalar"
  },
  {
    "slug": "market_state",
    "name": "MarketState",
    "description": "Identifies trend vs cycle regimes using Correlation Cycle phase angle.",
    "usage": "Returns 1 for uptrend, -1 for downtrend, and 0 for cycle mode. Use to switch between trend-following and mean-reversion strategies.",
    "category": "Ehlers DSP",
    "keywords": [
      "trend",
      "cycle",
      "regime",
      "ehlers",
      "dsp"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Correlation wavelength"
      },
      {
        "name": "threshold",
        "default": "9.0",
        "description": "Angle rate of change threshold for trend detection"
      }
    ],
    "formula_source": "https://www.traders.com/Documentation/FEEDbk_docs/2020/06/TradersTips.html",
    "formula_latex": "\n\\[\n\\text{State} = \n\\begin{cases} \n1 & \\text{if } |\\Delta \\text{Angle}| < \\text{Threshold} \\text{ and Angle} \\geq 0 \\\\\n-1 & \\text{if } |\\Delta \\text{Angle}| < \\text{Threshold} \\text{ and Angle} < 0 \\\\\n0 & \\text{otherwise}\n\\end{cases}\n\\]\n",
    "gold_standard_file": "market_state.json",
    "ehlers_summary": "In 'Correlation As A Cycle Indicator' (2020), Ehlers defines a Market State variable based on the rate of change of the Correlation Cycle phase angle. When the angle changes slowly (less than 9 degrees per bar), the market is in a trend regime (positive angle for uptrend, negative for downtrend). Rapid angle changes indicate a cycle regime.",
    "struct_name": "MarketState",
    "source_file": "market_state",
    "boundary_kind": "scalar"
  },
  {
    "slug": "market_structure",
    "name": "Market Structure (Swings + BOS)",
    "description": "Adaptive swing detection with ATR-derived depth + bias tracking and confirmed Break of Structure flips (HH/HL/LL/LH). Foundation for geometric PA patterns (Flags, H&S) and S/R monitoring from the MQL5 lynnchris toolkit (Part 21).",
    "usage": "Use .ta.market_structure() or the Rust struct for rich PA events. Bias and flips feed position sizing, regime filters, and confluence with ML features / Ehlers regimes. Emit as Struct for backtester consumption.",
    "category": "Price Action",
    "keywords": [
      "price-action",
      "structure",
      "swing",
      "bos",
      "market-structure",
      "mql5"
    ],
    "params": [
      {
        "name": "swing_strength",
        "default": "3",
        "description": "Bar window radius for local extremum (depth). Part 21 derives this from ATR*mult; fixed here for streaming parity + immediate use (see source Flip_Detector.mq5:150)."
      }
    ],
    "formula_source": "https://www.mql5.com/en/articles/17891 (Part 21) + cross Part 66/69/67",
    "formula_latex": "\n\\text{depth} = \\max(1, \\lfloor \\text{ATR} \\times \\text{mult} \\times \\text{loosen} / \\text{point} \\rfloor)\n\\text{IsSwingHigh}(shift, depth) = \\forall i \\in [shift-depth, shift+depth], i \\ne shift: High_i \\le High_{shift}\n",
    "gold_standard_file": "",
    "ehlers_summary": "Not Ehlers DSP; classical PA structure from MQL5 series. See Part 21 for ATR-adaptive depth swings and confirmed flips only after bias (avoids premature signals).",
    "struct_name": "MarketStructure",
    "source_file": "market_structure",
    "boundary_kind": "event"
  },
  {
    "slug": "medprice",
    "name": "Median Price (MEDPRICE)",
    "description": "The midpoint between the High and Low prices for a given period.",
    "usage": "Use to identify the central tendency of a bar's range. It is the basis for many oscillators and trend-following indicators like the Bill Williams Alligator.",
    "category": "Classic",
    "keywords": [
      "price-transform",
      "classic",
      "midpoint"
    ],
    "params": [],
    "formula_source": "https://www.tradingview.com/support/solutions/43000502589-median-price-medprice/",
    "formula_latex": "\n\\[\nMEDPRICE = \\frac{High + Low}{2}\n\\]\n",
    "gold_standard_file": "medprice.json",
    "ehlers_summary": "Median Price represents the 50% retracement level of the current period's range. By focusing on the High-Low midpoint, it removes the 'bias' of the closing price, which can often be manipulated by end-of-day positioning. — TA-Lib Documentation",
    "struct_name": "OC2",
    "source_file": "price_transform",
    "boundary_kind": "scalar"
  },
  {
    "slug": "mesa_stochastic",
    "name": "MESA Stochastic",
    "description": "Standard Stochastic calculation applied to Roofing Filtered data, followed by SuperSmoothing.",
    "usage": "Use as a cycle-synchronized stochastic that automatically scales its lookback to the measured dominant cycle period for consistent overbought/oversold signals.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "stochastic",
      "ehlers",
      "cycle",
      "adaptive"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Stochastic lookback length"
      },
      {
        "name": "hp_period",
        "default": "48",
        "description": "HighPass critical period"
      },
      {
        "name": "ss_period",
        "default": "10",
        "description": "SuperSmoother critical period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/Anticipating%20Turning%20Points.pdf",
    "formula_latex": "\n\\[\nFilt = \\text{RoofingFilter}(Price, P_{hp}, P_{ss})\n\\]\n\\[\nStoc = \\frac{Filt - \\min(Filt, L)}{\\max(Filt, L) - \\min(Filt, L)}\n\\]\n\\[\nMESAStoch = \\text{SuperSmoother}(Stoc \\times 100, P_{ss})\n\\]\n",
    "gold_standard_file": "mesa_stochastic.json",
    "ehlers_summary": "The MESA Stochastic extends Ehlers adaptive stochastic concept by using the MESA-measured dominant cycle period as the lookback window. Unlike traditional stochastics with fixed periods, it adapts to the current market rhythm, keeping the oscillator calibrated to one full cycle at all times.",
    "struct_name": "MesaStochastic",
    "source_file": "mesa_stochastic",
    "boundary_kind": "scalar"
  },
  {
    "slug": "mfi",
    "name": "Money Flow Index (MFI)",
    "description": "A technical oscillator that uses price and volume data for identifying overbought or oversold signals.",
    "usage": "Use as a volume-weighted RSI. Divergences between MFI and price can signal potential reversals, especially when the MFI is in extreme territory (>80 or <20).",
    "category": "Classic",
    "keywords": [
      "momentum",
      "volume",
      "oscillator",
      "classic"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "14",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/m/mfi.asp",
    "formula_latex": "\n\\[\n\\text{Money Ratio} = \\frac{\\text{Positive Money Flow}}{\\text{Negative Money Flow}} \\\\ MFI = 100 - \\frac{100}{1 + \\text{Money Ratio}}\n\\]\n",
    "gold_standard_file": "mfi.json",
    "ehlers_summary": "The Money Flow Index (MFI) is a momentum indicator that measures the inflow and outflow of money into an asset over a specific period of time. It is related to the RSI but incorporates volume, whereas the RSI only considers price. — Investopedia",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "mom",
    "name": "Momentum (MOM)",
    "description": "A simple indicator that measures the amount that a security's price has changed over a given span of time.",
    "usage": "Use to measure the velocity of price changes. Positive values indicate an uptrend, while negative values indicate a downtrend.",
    "category": "Classic",
    "keywords": [
      "momentum",
      "classic",
      "trend"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "10",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/m/momentum.asp",
    "formula_latex": "\n\\[\nMOM = Price_t - Price_{t-n}\n\\]\n",
    "gold_standard_file": "mom.json",
    "ehlers_summary": "Momentum is one of the most basic and powerful concepts in technical analysis. It measures the rate of change of an asset's price, providing a clear indication of trend strength and potential exhaustion before the actual price reversal occurs. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "my_rsi",
    "name": "MyRSI",
    "description": "Ehlers' version of RSI that swings between -1 and +1.",
    "usage": "Use as Ehlers smoothed RSI variant that applies cycle-aware filtering to reduce whipsaws while maintaining RSI-style overbought/oversold interpretation.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "rsi",
      "ehlers",
      "momentum",
      "smoothing"
    ],
    "params": [
      {
        "name": "length",
        "default": "14",
        "description": "Smoothing length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/Noise%20Elimination%20Technology.pdf",
    "formula_latex": "\n\\[\nCU = \\sum_{i=0}^{length-1} \\max(0, Price_i - Price_{i+1})\n\\]\n\\[\nCD = \\sum_{i=0}^{length-1} \\max(0, Price_{i+1} - Price_i)\n\\]\n\\[\nMyRSI = \\frac{CU - CD}{CU + CD}\n\\]\n",
    "gold_standard_file": "my_rsi.json",
    "ehlers_summary": "Ehlers presents a smoothed RSI formulation that applies a Laguerre or SuperSmoother filter to the up/down ratio before computing the RSI index. This reduces the noise and oscillation of standard RSI without significantly increasing lag, producing more reliable overbought and oversold readings.",
    "struct_name": "MyRsi",
    "source_file": "my_rsi",
    "boundary_kind": "scalar"
  },
  {
    "slug": "natr",
    "name": "Normalized Average True Range (NATR)",
    "description": "A normalized version of ATR that represents volatility as a percentage of price.",
    "usage": "Use to compare volatility across different securities with varying price levels. NATR allows for normalized risk assessment and position sizing.",
    "category": "Classic",
    "keywords": [
      "volatility",
      "atr",
      "normalization",
      "classic"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "14",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://www.tradingtechnologies.com/help/x-study/technical-indicator-definitions/normalized-average-true-range-natr/",
    "formula_latex": "\n\\[\nNATR = \\frac{ATR(n)}{Close} \\times 100\n\\]\n",
    "gold_standard_file": "natr.json",
    "ehlers_summary": "Normalized ATR (NATR) was developed to allow traders to compare the volatility of high-priced stocks with low-priced stocks. By dividing the ATR by the closing price and multiplying by 100, the result is a percentage that can be used consistently across all assets. — TA-Lib Documentation",
    "struct_name": "TrueRange",
    "source_file": "volatility",
    "boundary_kind": "scalar"
  },
  {
    "slug": "noise_elimination",
    "name": "Noise Elimination Technology",
    "description": "Nonlinear noise removal using Kendall correlation against a straight line.",
    "usage": "Use as a pre-filter to remove spike noise from price or intermediate indicator data without introducing lag. Particularly useful when raw tick or 1-minute data is used.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "noise",
      "ehlers",
      "dsp",
      "smoothing"
    ],
    "params": [
      {
        "name": "length",
        "default": "14",
        "description": "Correlation length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/Noise%20Elimination%20Technology.pdf",
    "formula_latex": "\n\\[\nNum = \\sum_{i=1}^{N-1} \\sum_{j=0}^{i-1} -sgn(X_i - X_j)\n\\]\n\\[\nDenom = \\frac{N(N-1)}{2}\n\\]\n\\[\nNET = \\frac{Num}{Denom}\n\\]\n",
    "gold_standard_file": "noise_elimination.json",
    "ehlers_summary": "Ehlers Noise Elimination Technology (NET) is a nonlinear filter that removes isolated noise spikes while leaving genuine price moves intact. It works by comparing each bar to its neighbors and replacing outliers with interpolated values, achieving noise reduction without the lag of conventional smoothers.",
    "struct_name": "NoiseElimination",
    "source_file": "noise_elimination",
    "boundary_kind": "scalar"
  },
  {
    "slug": "obv",
    "name": "On-Balance Volume (OBV)",
    "description": "A momentum indicator that uses volume flow to predict changes in stock price.",
    "usage": "Use to identify accumulation by institutions. When price is flat but OBV is rising, a breakout to the upside is likely. Conversely, when price is flat but OBV is falling, a breakdown is likely.",
    "category": "Classic",
    "keywords": [
      "volume",
      "momentum",
      "classic",
      "accumulation",
      "distribution"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/terms/o/onbalancevolume.asp",
    "formula_latex": "\n\\[\nOBV_t = OBV_{t-1} + \\begin{cases} Volume & \\text{if } Close_t > Close_{t-1} \\\\ 0 & \\text{if } Close_t = Close_{t-1} \\\\ -Volume & \\text{if } Close_t < Close_{t-1} \\end{cases}\n\\]\n",
    "gold_standard_file": "obv.json",
    "ehlers_summary": "Introduced by Joe Granville in his 1963 book 'Granville's New Key to Stock Market Profits', OBV is one of the oldest and most respected volume indicators. It operates on the principle that volume precedes price, and that institutional money flow leaves a detectable trail in the volume data before the price move occurs. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "volume",
    "boundary_kind": "cumulative"
  },
  {
    "slug": "oc2",
    "name": "Open-Close Average (OC2)",
    "description": "A simple average of the Open and Close prices.",
    "usage": "Use to reduce noise in technical indicators. Based on John Ehlers' recent research, averaging the open and close can significantly improve signal-to-noise ratios in DSP-based indicators.",
    "category": "Ehlers DSP",
    "keywords": [
      "price-transform",
      "ehlers",
      "smoothing",
      "dsp"
    ],
    "params": [],
    "formula_source": "Every Little Bit Helps (John Ehlers, 2023)",
    "formula_latex": "\n\\[\nOC2 = \\frac{Open + Close}{2}\n\\]\n",
    "gold_standard_file": "oc2.json",
    "ehlers_summary": "In his 2023 paper 'Every Little Bit Helps', John Ehlers demonstrates that using the average of the Open and Close as an input can enhance the performance of various filters and oscillators by providing a cleaner signal with reduced aliasing. — John Ehlers",
    "struct_name": "Oc2",
    "source_file": "price_transform",
    "boundary_kind": "scalar"
  },
  {
    "slug": "oc_price_rsi",
    "name": "OCPriceRSI",
    "description": "RSI calculated using the average of Open and Close prices to reduce noise.",
    "usage": "Use to measure momentum on the open-to-close price differential rather than close-to-close, capturing intraday directional strength more directly.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "rsi",
      "ehlers",
      "momentum"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "RSI period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/EveryLittleBitHelps.pdf",
    "formula_latex": "\n\\[\nInput = \\frac{Open + Close}{2}\n\\]\n\\[\nRSI = \\text{Wilder's RSI}(Input, Period)\n\\]\n",
    "gold_standard_file": "oc_price_rsi.json",
    "ehlers_summary": "Ehlers computes this RSI variant on the difference between the open and close price of each bar rather than on the closing price series. The open-close differential captures the net directional pressure within each bar, producing a momentum oscillator more sensitive to intraday commitment than standard RSI.",
    "struct_name": "OcPriceRsi",
    "source_file": "oc_price_rsi",
    "boundary_kind": "scalar"
  },
  {
    "slug": "one_euro_filter",
    "name": "One Euro Filter",
    "description": "A speed-based adaptive low-pass filter that dynamically adjusts its smoothing coefficient.",
    "usage": "Use in real-time systems where you need low lag at high speeds and low noise at low speeds. The adaptive cutoff frequency makes it self-tuning for different signal velocities.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "smoothing",
      "adaptive",
      "real-time",
      "low-pass"
    ],
    "params": [
      {
        "name": "period_min",
        "default": "10",
        "description": "Minimum cutoff period"
      },
      {
        "name": "beta",
        "default": "0.2",
        "description": "Responsiveness factor"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20DECEMBER%202025.html",
    "formula_latex": "\n\\[\n\\alpha_{dx} = \\frac{2\\pi}{4\\pi + 10}\n\\]\n\\[\nSmoothedDX = \\alpha_{dx}(Price - Price_{t-1}) + (1 - \\alpha_{dx})SmoothedDX_{t-1}\n\\]\n\\[\nCutoff = PeriodMin + \\beta |SmoothedDX|\n\\]\n\\[\n\\alpha_3 = \\frac{2\\pi}{4\\pi + Cutoff}\n\\]\n\\[\nSmoothed = \\alpha_3 Price + (1 - \\alpha_3)Smoothed_{t-1}\n\\]\n",
    "gold_standard_file": "one_euro_filter.json",
    "ehlers_summary": "The One Euro Filter, developed by Casiez et al. (2012), is an adaptive lowpass filter that adjusts its cutoff frequency based on the signal derivative. When the signal changes quickly (high speed) the cutoff is raised to reduce lag; when it changes slowly the cutoff is lowered to reduce noise — automatically balancing the speed-accuracy trade-off.",
    "struct_name": "OneEuroFilter",
    "source_file": "one_euro_filter",
    "boundary_kind": "scalar"
  },
  {
    "slug": "pairs_rotation",
    "name": "PairsRotation",
    "description": "Relative rotation of two securities using normalized roofing filters.",
    "usage": "Use to detect and trade rotation between two correlated assets. When one asset leads and the other lags, the indicator signals a rotation trade opportunity.",
    "category": "Ehlers DSP",
    "keywords": [
      "pairs-trading",
      "rotation",
      "relative-strength",
      "ehlers"
    ],
    "params": [
      {
        "name": "hp_len",
        "default": "125",
        "description": "HighPass filter length"
      },
      {
        "name": "lp_len",
        "default": "20",
        "description": "LowPass (SuperSmoother) length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/PAIRS%20ROTATION.pdf",
    "formula_latex": "\n\\[\nFilt = SuperSmoother(HighPass(Price, HPLen), LPLen)\n\\]\n\\[\nMS = 0.0242 \\cdot Filt^2 + 0.9758 \\cdot MS_{t-1}\n\\]\n\\[\nNormalized = \\frac{Filt}{\\sqrt{MS}}\n\\]\n",
    "gold_standard_file": "pairs_rotation.json",
    "ehlers_summary": "Pairs Rotation analysis measures the relative cycle phase between two correlated assets. When one asset is at a cycle peak while its correlated partner is at a trough, a statistical rotation trade can be placed — long the laggard, short the leader — anticipating mean reversion of the spread.",
    "struct_name": "PairsRotation",
    "source_file": "pairs_rotation",
    "boundary_kind": "scalar"
  },
  {
    "slug": "phasor",
    "name": "Phasor",
    "description": "Extracts In-Phase (I) and Quadrature (Q) components using a Hilbert Transform.",
    "usage": "Use to measure the instantaneous phase and amplitude of the dominant market cycle. Phase crossings of key angles (90, 180 degrees) provide precise cycle turn timing signals.",
    "category": "Rocket Science",
    "keywords": [
      "cycle",
      "phase",
      "ehlers",
      "dsp",
      "dominant-cycle"
    ],
    "params": [],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/ROCKET%20SCIENCE%20FOR%20TRADER.pdf",
    "formula_latex": "\n\\[\nI = \\text{Detrender}_{t-3}\n\\]\n\\[\nQ = \\text{HilbertFIR}(\\text{Detrender}, \\text{Period})\n\\]\n",
    "gold_standard_file": "phasor.json",
    "ehlers_summary": "Ehlers borrows the concept of a phasor from electrical engineering to represent the amplitude and phase of a market cycle as a rotating vector. In Rocket Science for Traders (2001) he shows how measuring the instantaneous phasor angle gives more precise cycle timing than zero-crossing methods.",
    "struct_name": "Phasor",
    "source_file": "phasor",
    "boundary_kind": "scalar"
  },
  {
    "slug": "pivot_points",
    "name": "Pivot Points",
    "description": "Pivot Points are used to determine overall trend over different time frames.",
    "usage": "Use to identify key daily, weekly, or monthly support and resistance levels calculated from the prior session OHLC. Pivot levels are widely watched by floor traders and algorithms alike.",
    "category": "Classic",
    "keywords": [
      "support-resistance",
      "classic",
      "levels",
      "pattern"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/terms/p/pivotpoint.asp",
    "formula_latex": "\n\\[\nP = \\frac{H + L + C}{3}\n\\]\n",
    "gold_standard_file": "pivot_points.json",
    "ehlers_summary": "Traditional Pivot Points, widely used by floor traders, calculate a central pivot (P = (H+L+C)/3) plus support and resistance levels at fixed multiples of the prior session range. Because they are derived from universal OHLC data and widely published, they become self-fulfilling levels of institutional interest. — StockCharts ChartSchool",
    "struct_name": "PivotPoints",
    "source_file": "pivot_points",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ppo",
    "name": "Percentage Price Oscillator (PPO)",
    "description": "A momentum oscillator that measures the difference between two moving averages as a percentage of the larger moving average.",
    "usage": "Use to compare trend momentum across different securities with varying price levels. PPO is the percentage version of MACD.",
    "category": "Classic",
    "keywords": [
      "trend",
      "momentum",
      "moving-average",
      "classic",
      "normalization"
    ],
    "params": [
      {
        "name": "fastperiod",
        "default": "12",
        "description": "Fast period"
      },
      {
        "name": "slowperiod",
        "default": "26",
        "description": "Slow period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/p/ppo.asp",
    "formula_latex": "\n\\[\nPPO = \\frac{EMA(12) - EMA(26)}{EMA(26)} \\times 100\n\\]\n",
    "gold_standard_file": "ppo.json",
    "ehlers_summary": "The Percentage Price Oscillator (PPO) is identical to the MACD, except that it measures the difference between two moving averages as a percentage. This allows for comparison across different stocks regardless of their price, making it a superior tool for relative strength analysis. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "precision_trend_analysis",
    "name": "Precision Trend Analysis",
    "description": "Trend identification using the difference between two high-pass filters.",
    "usage": "Use as a high-precision trend indicator that applies DSP filtering to remove cycle noise before measuring trend direction, giving fewer but more reliable trend signals.",
    "category": "Ehlers DSP",
    "keywords": [
      "trend",
      "ehlers",
      "dsp",
      "filter"
    ],
    "params": [
      {
        "name": "length1",
        "default": "250",
        "description": "First HighPass filter period"
      },
      {
        "name": "length2",
        "default": "40",
        "description": "Second HighPass filter period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20SEPTEMBER%202024.html",
    "formula_latex": "\n\\[\nHP1 = HighPass(Price, Length1)\n\\]\n\\[\nHP2 = HighPass(Price, Length2)\n\\]\n\\[\nTrend = HP1 - HP2\n\\]\n\\[\nROC = \\frac{Length2}{6.28} \\cdot (Trend - Trend_{t-1})\n\\]\n",
    "gold_standard_file": "precision_trend.json",
    "ehlers_summary": "Ehlers Precision Trend analysis applies a roofing-filter style preprocessing to price before computing the trend indicator, removing the cyclical component that causes premature trend reversals in standard indicators. The result is a trend signal that changes state only when the genuine trend direction changes.",
    "struct_name": "PrecisionTrendAnalysis",
    "source_file": "precision_trend",
    "boundary_kind": "scalar"
  },
  {
    "slug": "projected_moving_average",
    "name": "Projected Moving Average",
    "description": "A lag-compensated moving average that uses linear regression slope to project the average forward.",
    "usage": "Use as a predictive moving average that uses linear regression projection to anticipate where price will be rather than where it has been, reducing effective lag.",
    "category": "Ehlers DSP",
    "keywords": [
      "moving-average",
      "prediction",
      "ehlers",
      "zero-lag"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Calculation length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20MARCH%202025.html",
    "formula_latex": "\n\\[\nSlope = -\\frac{n \\sum xy - \\sum x \\sum y}{n \\sum x^2 - (\\sum x)^2}\n\\]\n\\[\nPMA = SMA + Slope \\cdot \\frac{n}{2}\n\\]\n\\[\nPredict = PMA + 0.5 \\cdot (Slope - Slope_{t-2}) \\cdot n\n\\]\n",
    "gold_standard_file": "pma.json",
    "ehlers_summary": "The Projected Moving Average uses linear regression over the lookback window to project the best-fit line forward to the current bar. This predictive approach shifts the MA output toward the leading edge of price movement, achieving reduced lag compared to conventional MAs of the same period.",
    "struct_name": "ProjectedMovingAverage",
    "source_file": "pma",
    "boundary_kind": "scalar"
  },
  {
    "slug": "recursive_median",
    "name": "RecursiveMedian",
    "description": "EMA of a 5-bar median filter for smooth tracking with minimal jitter.",
    "usage": "Use to filter out extreme outliers and noise while maintaining trend sensitivity. Excellent as a baseline for other oscillators.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "median",
      "robust",
      "smoothing"
    ],
    "params": [
      {
        "name": "lp_period",
        "default": "12",
        "description": "Low-pass smoothing period"
      }
    ],
    "formula_source": "https://www.traders.com/Documentation/FEEDbk_docs/2018/03/TradersTips.html",
    "formula_latex": "\n\\[\n\\alpha = \\frac{\\cos(360/P) + \\sin(360/P) - 1}{\\cos(360/P)}\n\\]\n\\[\nRM_t = \\alpha \\cdot \\text{Median}(Price, 5)_t + (1 - \\alpha) \\cdot RM_{t-1}\n\\]\n",
    "gold_standard_file": "recursive_median.json",
    "ehlers_summary": "Standard filters like SMA or EMA are distorted by price spikes. The recursive median filter uses the median to reject outliers and an EMA to provide smoothness, offering a cleaner trend representation than standard moving averages.",
    "struct_name": "RecursiveMedian",
    "source_file": "recursive_median",
    "boundary_kind": "scalar"
  },
  {
    "slug": "recursive_median_oscillator",
    "name": "RecursiveMedianOscillator",
    "description": "Oscillator derived from the Recursive Median filter using a 2nd-order Highpass filter.",
    "usage": "Identify cyclic turning points with reduced lag and noise. The high-pass component removes the trend, leaving the cycle.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "ehlers",
      "dsp",
      "median",
      "cycle",
      "highpass"
    ],
    "params": [
      {
        "name": "lp_period",
        "default": "12",
        "description": "Low-pass smoothing period"
      },
      {
        "name": "hp_period",
        "default": "30",
        "description": "High-pass cutoff period"
      }
    ],
    "formula_source": "https://www.traders.com/Documentation/FEEDbk_docs/2018/03/TradersTips.html",
    "formula_latex": "\n\\[\n\\alpha_2 = \\frac{\\cos(0.707 \\cdot 360/HP) + \\sin(0.707 \\cdot 360/HP) - 1}{\\cos(0.707 \\cdot 360/HP)}\n\\]\n\\[\nRMO_t = (1-\\alpha_2/2)^2(RM_t - 2RM_{t-1} + RM_{t-2}) + 2(1-\\alpha_2)RMO_{t-1} - (1-\\alpha_2)^2RMO_{t-2}\n\\]\n",
    "gold_standard_file": "recursive_median_oscillator.json",
    "ehlers_summary": "By applying a 2nd-order Highpass filter to the Recursive Median output, we create an oscillator that is specifically tuned to the dominant cycle while remaining immune to the outlier spikes that would otherwise create false signals.",
    "struct_name": "RecursiveMedianOscillator",
    "source_file": "recursive_median",
    "boundary_kind": "scalar"
  },
  {
    "slug": "reflex",
    "name": "Reflex",
    "description": "A zero-lag averaging indicator designed to synchronize with the cycle component in price data.",
    "usage": "Use to identify cyclic reversals with minimal lag. It is more sensitive to significant reversals than standard moving averages.",
    "category": "Ehlers DSP",
    "keywords": [
      "zero-lag",
      "cycle",
      "ehlers",
      "dsp",
      "oscillator"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Assumed cycle period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/implemented/TRADERS’ TIPS - FEBRUARY 2020.html",
    "formula_latex": "\n\\[\nFilt = \\text{SuperSmoother}(Price, Length/2)\n\\]\n\\[\nSlope = \\frac{Filt_{t-Length} - Filt_t}{Length}\n\\]\n\\[\nSum = \\frac{1}{Length} \\sum_{n=1}^{Length} (Filt_t + n \\cdot Slope - Filt_{t-n})\n\\]\n\\[\nMS = 0.04 \\cdot Sum^2 + 0.96 \\cdot MS_{t-1}\n\\]\n\\[\nReflex = \\frac{Sum}{\\sqrt{MS}}\n\\]\n",
    "gold_standard_file": "reflex.json",
    "ehlers_summary": "Ehlers introduces Reflex as a way to reduce lag in averaging indicators by measuring the difference between the current SuperSmoother value and its historical values, adjusted for a linear slope. This 'reflexes' the indicator to show reversals as they happen rather than after the fact.",
    "struct_name": "Reflex",
    "source_file": "reflex",
    "boundary_kind": "scalar"
  },
  {
    "slug": "reverse_ema",
    "name": "Reverse EMA",
    "description": "A causal forward and backward EMA indicator that minimizes lag using a series of alignment filters.",
    "usage": "Use to identify trends or cycles with minimal lag. Higher alpha values (e.g., 0.3) isolate cycles, while lower values (e.g., 0.05) isolate trends.",
    "category": "Ehlers DSP",
    "keywords": [
      "ema",
      "lag",
      "ehlers",
      "oscillator",
      "zero-lag"
    ],
    "params": [
      {
        "name": "alpha",
        "default": "0.1",
        "description": "Smoothing factor (0.0 to 1.0)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS%E2%80%99%20TIPS%20-%20SEPTEMBER%202017.html",
    "formula_latex": "\n\\[\nEMA = \\alpha \\cdot Price + (1 - \\alpha) \\cdot EMA_{t-1}\n\\]\n\\[\nRE_1 = (1 - \\alpha) \\cdot EMA + EMA_{t-1}\n\\]\n\\[\nRE_i = (1 - \\alpha)^{2^{i-1}} \\cdot RE_{i-1} + RE_{i-1, t-1} \\text{ for } i=2..8\n\\]\n\\[\nWave = EMA - \\alpha \\cdot RE_8\n\\]\n",
    "gold_standard_file": "reverse_ema.json",
    "ehlers_summary": "Ehlers' Reverse EMA approximates a non-causal zero-lag filter by using a product series of Z-transform components. It achieves double smoothing at high frequencies and mitigates spectral dilation at low frequencies, providing a unique balance of smoothness and responsiveness.",
    "struct_name": "ReverseEma",
    "source_file": "reverse_ema",
    "boundary_kind": "scalar"
  },
  {
    "slug": "reversion_index",
    "name": "Reversion Index",
    "description": "A mean-reversion oscillator that normalizes price changes by their absolute magnitude and applies SuperSmoother filtering.",
    "usage": "Use to identify mean-reversion opportunities when price has deviated significantly from its cycle trend. High index values signal overextended moves ripe for reversal.",
    "category": "Ehlers DSP",
    "keywords": [
      "mean-reversion",
      "oscillator",
      "ehlers",
      "cycle"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Summation period (approx. half dominant cycle)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS%E2%80%99%20TIPS%20-%20JANUARY%202026.html",
    "formula_latex": "\n\\[\n\\Delta_t = \\text{Close}_t - \\text{Close}_{t-1}\n\\]\n\\[\n\\text{Ratio} = \\frac{\\sum_{i=0}^{L-1} \\Delta_{t-i}}{\\sum_{i=0}^{L-1} |\\Delta_{t-i}|}\n\\]\n\\[\n\\text{Smooth} = SuperSmoother(\\text{Ratio}, 8)\n\\]\n\\[\n\\text{Trigger} = SuperSmoother(\\text{Ratio}, 4)\n\\]\n",
    "gold_standard_file": "reversion_index.json",
    "ehlers_summary": "Ehlers Reversion Index measures how far price has deviated from its Instantaneous Trendline in units of cycle amplitude. Because it normalizes by the current cycle energy, the index provides consistent overbought/oversold thresholds regardless of the absolute price level or volatility regime.",
    "struct_name": "ReversionIndex",
    "source_file": "reversion_index",
    "boundary_kind": "scalar"
  },
  {
    "slug": "roc",
    "name": "Rate of Change (ROC)",
    "description": "A momentum-based technical indicator that measures the percentage change in price between the current price and the price n periods ago.",
    "usage": "Use to measure the speed at which price is changing. It is often used to identify overbought/oversold conditions and trend reversals.",
    "category": "Classic",
    "keywords": [
      "momentum",
      "classic",
      "oscillator"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "10",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/r/rateofchange.asp",
    "formula_latex": "\n\\[\nROC = \\frac{Price_t - Price_{t-n}}{Price_{t-n}} \\times 100\n\\]\n",
    "gold_standard_file": "roc.json",
    "ehlers_summary": "The Rate of Change (ROC) indicator is a pure momentum oscillator that measures the percentage change in price from one period to the next. It is highly effective at identifying the velocity of a move and anticipating when that velocity is slowing down. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "rocket_rsi",
    "name": "RocketRSI",
    "description": "Highly responsive RSI variant using SuperSmoother and Fisher Transform.",
    "usage": "Use for rapid cycle identification and reversal detection. The Fisher Transform converts the RSI distribution into a Gaussian-like distribution with sharp peaks at reversals.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "rsi",
      "ehlers",
      "dsp",
      "fisher",
      "momentum"
    ],
    "params": [
      {
        "name": "rsi_length",
        "default": "8",
        "description": "RSI calculation period"
      },
      {
        "name": "smooth_length",
        "default": "10",
        "description": "SuperSmoother filter period"
      }
    ],
    "formula_source": "https://www.traders.com/Documentation/FEEDbk_docs/2018/05/TradersTips.html",
    "formula_latex": "\n\\[\nMom = Price - Price_{t-(L-1)}\n\\]\n\\[\nFilt = \\text{SuperSmoother}(Mom, SL)\n\\]\n\\[\nMyRSI = \\frac{\\sum \\max(0, \\Delta Filt) - \\sum \\max(0, -\\Delta Filt)}{\\sum |\\Delta Filt|}\n\\]\n\\[\nRocketRSI = 0.5 \\cdot \\ln\\left(\\frac{1 + MyRSI}{1 - MyRSI}\\right)\n\\]\n",
    "gold_standard_file": "rocket_rsi.json",
    "ehlers_summary": "RocketRSI improves upon standard RSI by first smoothing the momentum with a SuperSmoother filter to eliminate high-frequency noise. The resulting RSI is then passed through a Fisher Transform to create clear, actionable signals at cyclical turning points.",
    "struct_name": "RocketRsi",
    "source_file": "rocket_rsi",
    "boundary_kind": "scalar"
  },
  {
    "slug": "roofing_filter",
    "name": "Roofing Filter",
    "description": "Combines a 2-pole HighPass filter and a SuperSmoother to isolate specific cyclic components.",
    "usage": "Apply before oscillators to remove both low-frequency trend drift and high-frequency noise, leaving only the tradable cycle band (roughly 10-48 bars).",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "cycle",
      "high-pass",
      "low-pass"
    ],
    "params": [
      {
        "name": "hp_period",
        "default": "48",
        "description": "HighPass critical period"
      },
      {
        "name": "ss_period",
        "default": "10",
        "description": "SuperSmoother critical period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/PredictiveIndicators.pdf",
    "formula_latex": "\n\\[\n\\alpha_1 = \\frac{\\cos(\\sqrt{2}\\pi/P_{hp}) + \\sin(\\sqrt{2}\\pi/P_{hp}) - 1}{\\cos(\\sqrt{2}\\pi/P_{hp})}\n\\]\n\\[\nHP = (1 - \\alpha_1/2)^2 (Price - 2 Price_{t-1} + Price_{t-2}) + 2(1 - \\alpha_1) HP_{t-1} - (1 - \\alpha_1)^2 HP_{t-2}\n\\]\n\\[\nFilt = c_1 \\frac{HP + HP_{t-1}}{2} + c_2 Filt_{t-1} + c_3 Filt_{t-2}\n\\]\n",
    "gold_standard_file": "roofing_filter.json",
    "ehlers_summary": "Introduced in Cycle Analytics for Traders (2013), the Roofing Filter first applies a high-pass filter to remove the dominant trend component, then a SuperSmoother to remove short-term noise. The result is a cycle-only signal with controlled bandwidth, ideal for use as input to oscillators and cycle indicators.",
    "struct_name": "RoofingFilter",
    "source_file": "roofing_filter",
    "boundary_kind": "scalar"
  },
  {
    "slug": "rsi",
    "name": "Relative Strength Index (RSI)",
    "description": "A momentum oscillator that measures the speed and change of price movements.",
    "usage": "Use to identify overbought (>70) and oversold (<30) conditions. RSI divergences against price often signal impending trend reversals.",
    "category": "Classic",
    "keywords": [
      "momentum",
      "oscillator",
      "overbought",
      "oversold",
      "classic"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "14",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/r/rsi.asp",
    "formula_latex": "\n\\[\nRS = \\frac{Average Gain}{Average Loss} \\\\ RSI = 100 - \\frac{100}{1 + RS}\n\\]\n",
    "gold_standard_file": "rsi.json",
    "ehlers_summary": "Developed by J. Welles Wilder in New Concepts in Technical Trading Systems (1978), the RSI compares the magnitude of recent gains to recent losses to determine overbought and oversold conditions of an asset. It remains the most widely used momentum oscillator in modern technical analysis.",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "rsih",
    "name": "RSIH",
    "description": "RSI enhanced with Hann windowing for superior smoothing and zero-centering.",
    "usage": "Use to measure momentum exclusively on the cyclical (high-pass filtered) component of price, eliminating the trend bias that makes standard RSI drift.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "rsi",
      "ehlers",
      "high-pass",
      "cycle"
    ],
    "params": [
      {
        "name": "length",
        "default": "14",
        "description": "RSI length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20JANUARY%202022.html",
    "formula_latex": "\n\\[\nCU = \\sum_{n=1}^L (1 - \\cos\\left(\\frac{2\\pi n}{L+1}\\right)) \\cdot \\max(0, Close_{t-n+1} - Close_{t-n})\n\\]\n\\[\nCD = \\sum_{n=1}^L (1 - \\cos\\left(\\frac{2\\pi n}{L+1}\\right)) \\cdot \\max(0, Close_{t-n} - Close_{t-n+1})\n\\]\n\\[\nRSIH = \\frac{CU - CD}{CU + CD}\n\\]\n",
    "gold_standard_file": "rsih.json",
    "ehlers_summary": "RSIH applies RSI computation to the high-pass filtered price rather than raw price. By removing the trend component first, the RSI calculation operates only on the cyclical content of the market, producing an oscillator that is centered around zero regardless of the prevailing trend direction.",
    "struct_name": "Rsih",
    "source_file": "rsih",
    "boundary_kind": "scalar"
  },
  {
    "slug": "sar",
    "name": "Parabolic SAR",
    "description": "A trend-following indicator used to determine price direction and potential reversals.",
    "usage": "Use for setting trailing stop losses and identifying trend reversals. Dots below price indicate an uptrend, while dots above price indicate a downtrend.",
    "category": "Classic",
    "keywords": [
      "trend",
      "classic",
      "stop-loss",
      "wilder"
    ],
    "params": [
      {
        "name": "acceleration",
        "default": "0.02",
        "description": "Acceleration factor"
      },
      {
        "name": "maximum",
        "default": "0.2",
        "description": "Maximum acceleration"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/p/parabolicindicator.asp",
    "formula_latex": "\n\\[\nSAR_{t+1} = SAR_t + AF \\times (EP - SAR_t)\n\\]\n",
    "gold_standard_file": "sar.json",
    "ehlers_summary": "Developed by J. Welles Wilder, the Parabolic Stop and Reverse (SAR) uses an acceleration factor that increases as the trend persists. This 'parabolic' nature allows the indicator to stay close to price action and provide timely exit signals when a trend exhausts. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "overlap",
    "boundary_kind": "scalar"
  },
  {
    "slug": "sdo",
    "name": "Stochastic Distance Oscillator",
    "description": "A momentum indicator based on the classic stochastic oscillator applied to price distances.",
    "usage": "Identify bull and bear trend changes through overbought (+40) and oversold (-40) levels. Suitable for both trending and ranging markets.",
    "category": "Momentum",
    "keywords": [
      "momentum",
      "stochastic",
      "oscillator",
      "apirine",
      "trend"
    ],
    "params": [
      {
        "name": "lookback_period",
        "default": "200",
        "description": "Range lookback for stochastic calculation"
      },
      {
        "name": "period",
        "default": "12",
        "description": "Distance calculation period"
      },
      {
        "name": "ema_pds",
        "default": "3",
        "description": "Smoothing EMA period"
      }
    ],
    "formula_source": "https://traders.com/Documentation/FEEDbk_docs/2023/06/TradersTips.html",
    "formula_latex": "\n\\[\nDist = |Price_t - Price_{t-n}|\n\\]\n\\[\nDVal = \\frac{Dist - \\min(Dist_{lookback})}{\\max(Dist_{lookback}) - \\min(Dist_{lookback})}\n\\]\n\\[\nDDVal = \\begin{cases} DVal & \\text{if } Price_t > Price_{t-n} \\\\ -DVal & \\text{if } Price_t < Price_{t-n} \\\\ 0 & \\text{otherwise} \\end{cases}\n\\]\n\\[\nSDO = EMA(DDVal, smoothing) \\times 100\n\\]\n",
    "gold_standard_file": "sdo.json",
    "ehlers_summary": "The Stochastic Distance Oscillator (SDO) by Vitali Apirine adapts the stochastic formula to measure the current price distance relative to its historical range. By smoothing this relative distance with an EMA, it provides a cleaner momentum signal that identifies potential trend reversals when crossing extreme thresholds.",
    "struct_name": "Sdo",
    "source_file": "sdo",
    "boundary_kind": "scalar"
  },
  {
    "slug": "simple_predictor",
    "name": "SimplePredictor",
    "description": "A fixed-coefficient 2-pole linear predictive filter.",
    "usage": "Use as a lightweight one-bar-ahead price predictor for cycle-mode markets. Its low computational cost makes it suitable for real-time streaming at high frequency.",
    "category": "Ehlers DSP",
    "keywords": [
      "prediction",
      "cycle",
      "ehlers",
      "dsp"
    ],
    "params": [
      {
        "name": "hp_len",
        "default": "15",
        "description": "HighPass filter length"
      },
      {
        "name": "lp_len",
        "default": "30",
        "description": "LowPass (SuperSmoother) length"
      },
      {
        "name": "q",
        "default": "0.35",
        "description": "Damping/Predictor coefficient"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20JANUARY%202025.html",
    "formula_latex": "\n\\[\nPredict = \\frac{Signal - 1.8Q \\cdot Signal_{t-1} + Q^2 \\cdot Signal_{t-2}}{1 - 1.8Q + Q^2}\n\\]\n",
    "gold_standard_file": "simple_predictor.json",
    "ehlers_summary": "Ehlers derives a Simple Predictor that extrapolates price one bar forward using only the current and prior bars weighted by the dominant cycle coefficient. Despite its simplicity it provides useful one-bar forecasts in cycling markets, demonstrating the predictive value of cycle measurement.",
    "struct_name": "SimplePredictor",
    "source_file": "simple_predictor",
    "boundary_kind": "scalar"
  },
  {
    "slug": "sine_wave",
    "name": "Sine Wave",
    "description": "Plots a sine wave and a lead-sine wave based on the cyclic phase of price movement.",
    "usage": "Use to confirm whether the market is in cycle or trend mode. When price follows the sine wave trade cycle reversals; when it diverges switch to trend-following.",
    "category": "Rocket Science",
    "keywords": [
      "cycle",
      "oscillator",
      "ehlers",
      "dsp",
      "phase"
    ],
    "params": [],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/ROCKET%20SCIENCE%20FOR%20TRADER.pdf",
    "formula_latex": "\n\\[\n\\text{Sine} = \\sin(\\text{Phase})\n\\]\n\\[\n\\text{LeadSine} = \\sin(\\text{Phase} + 45^\\circ)\n\\]\n",
    "gold_standard_file": "sine_wave.json",
    "ehlers_summary": "Introduced in Rocket Science for Traders, the Sine Wave Indicator plots the sine and cosine of measured instantaneous phase. In cycling markets price tracks the sine wave; in trending markets price breaks through the lead line signaling a mode change.",
    "struct_name": "SineWave",
    "source_file": "sine_wave",
    "boundary_kind": "scalar"
  },
  {
    "slug": "sma",
    "name": "Simple Moving Average",
    "description": "The Simple Moving Average calculates the unweighted mean of the previous N data points.",
    "usage": "Use as the foundational smoothing module providing SMA, EMA, WMA, and SMMA implementations that power higher-level indicators across the library.",
    "category": "Classic",
    "keywords": [
      "moving-average",
      "smoothing",
      "classic",
      "ema"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/s/sma.asp",
    "formula_latex": "\n\\[\nSMA = \\frac{1}{n} \\sum_{i=1}^{n} P_i\n\\]\n",
    "gold_standard_file": "sma.json",
    "ehlers_summary": "The core smoothing algorithms — SMA, EMA, WMA — are the building blocks of nearly all technical indicators. EMA applies exponential decay weighting (alpha = 2/(n+1)), SMA applies uniform weighting over N bars, and WMA applies linearly increasing weights emphasizing more recent bars.",
    "struct_name": "Sma",
    "source_file": "smoothing",
    "boundary_kind": "scalar"
  },
  {
    "slug": "sr_interaction_monitor",
    "name": "S/R Interaction Monitor (Part 67)",
    "description": "Real-time horizontal S/R monitoring with Approach/Touch/Breakout/Reversal/Retest detection. Auto levels from MarketStructure swings + dynamic user-provided levels. Rich event output designed for backtester and confluence (MQL5 Part 67 port).",
    "usage": "Use the Rust struct directly for streaming (add_user_level + next). Emits SRMonitorOutput with Vec<SRInteraction>. Ideal for event-driven backtesting and PA + regime filters. See also MarketStructure for the swing foundation.",
    "category": "Price Action",
    "keywords": [
      "price-action",
      "support-resistance",
      "sr-interaction",
      "breakout",
      "retest",
      "market-structure",
      "mql5",
      "part-67"
    ],
    "params": [
      {
        "name": "swing_strength",
        "default": "3",
        "description": "Depth for internal MarketStructure swing detection (Part 21)."
      },
      {
        "name": "touch_tolerance",
        "default": "0.5",
        "description": "Absolute price tolerance for Touch/Retest (Part 67 TouchTolerancePips scaled)."
      },
      {
        "name": "approach_zone",
        "default": "5.0",
        "description": "Outer Approach zone (Part 67 ApproachZonePips)."
      },
      {
        "name": "touch_tol_atr_mult",
        "default": "0.5",
        "description": "ATR-relative touch tolerance (use new_atr_relative)."
      },
      {
        "name": "approach_zone_atr_mult",
        "default": "2.0",
        "description": "ATR-relative approach zone (use new_atr_relative)."
      }
    ],
    "formula_source": "https://www.mql5.com/en/articles/21961 (SupportResistanceMonitor.mq5) + Part 21 market_structure foundation",
    "formula_latex": "\n\\text{side} = \\text{sign}(price - level)\\\\\n\\text{touch if } |level - [L,H]| \\le tol\\\\\n\\text{breakout if side flips}\\\\\n\\text{retest if post-breakout distance} \\le tol\n",
    "gold_standard_file": "",
    "ehlers_summary": "Classical price action (not DSP). Horizontal level state machine on top of adaptive swings.",
    "struct_name": "SrInteractionMonitor",
    "source_file": "sr_monitor",
    "boundary_kind": "event"
  },
  {
    "slug": "stc",
    "name": "Schaff Trend Cycle",
    "description": "A hybrid indicator that applies a double-smoothed stochastic to MACD for faster trend identification.",
    "usage": "Use as a faster trend-cycle momentum indicator. STC typically reaches overbought/oversold levels sooner than MACD while generating fewer false signals than a raw stochastic.",
    "category": "Modern",
    "keywords": [
      "trend",
      "momentum",
      "cycle",
      "oscillator",
      "classic"
    ],
    "params": [
      {
        "name": "cycle_period",
        "default": "10",
        "description": "Stochastic lookback period"
      },
      {
        "name": "fast_period",
        "default": "23",
        "description": "Fast EMA period for MACD"
      },
      {
        "name": "slow_period",
        "default": "50",
        "description": "Slow EMA period for MACD"
      }
    ],
    "formula_source": "https://www.investopedia.com/articles/forex/10/schaff-trend-cycle-indicator.asp",
    "formula_latex": "\n\\[\nMACD = EMA(23) - EMA(50)\n\\]\n\\[\nSTC = EMA(Stochastic(EMA(Stochastic(MACD, 10), 3), 10), 3)\n\\]\n",
    "gold_standard_file": "stc.json",
    "ehlers_summary": "The Schaff Trend Cycle, developed by Doug Schaff, applies the stochastic oscillator formula twice to MACD values rather than to price. This double stochastic smoothing produces faster, more defined overbought and oversold levels than MACD alone, while the cycle component reduces the lag of a conventional stochastic. — investopedia.com",
    "struct_name": "SchaffTrendCycle",
    "source_file": "stc",
    "boundary_kind": "scalar"
  },
  {
    "slug": "stddev",
    "name": "Standard Deviation",
    "description": "Standard Deviation is a statistical measure of market volatility.",
    "usage": "Use for statistical analysis of price series: linear regression, standard deviation, correlation coefficients, and other descriptive statistics used as indicator inputs.",
    "category": "Classic",
    "keywords": [
      "statistics",
      "classic",
      "volatility",
      "trend"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/s/standarddeviation.asp",
    "formula_latex": "\n\\[\n\\sigma = \\sqrt{ \\frac{\\sum (x_i - \\mu)^2}{N} }\n\\]\n",
    "gold_standard_file": "stddev.json",
    "ehlers_summary": "Standard statistical measures provide the mathematical foundation for many technical indicators. Linear regression finds the best-fit line through price, standard deviation quantifies dispersion, and correlation coefficients measure how closely two series move together — all are essential for quantitative strategy construction.",
    "struct_name": "StandardDeviation",
    "source_file": "statistics",
    "boundary_kind": "scalar"
  },
  {
    "slug": "stoch",
    "name": "Stochastic Oscillator",
    "description": "A momentum indicator comparing a particular closing price of a security to a range of its prices over a certain period of time.",
    "usage": "Use to identify trend reversals by looking for crossovers and overbought/oversold levels. The %K and %D lines indicate when the momentum is shifting relative to the recent price range.",
    "category": "Classic",
    "keywords": [
      "momentum",
      "oscillator",
      "overbought",
      "oversold",
      "classic"
    ],
    "params": [
      {
        "name": "fastk_period",
        "default": "5",
        "description": "Fast %K period"
      },
      {
        "name": "slowk_period",
        "default": "3",
        "description": "Slow %K period"
      },
      {
        "name": "slowd_period",
        "default": "3",
        "description": "Slow %D period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/s/stochasticoscillator.asp",
    "formula_latex": "\n\\[\n\\%K = 100 \\times \\frac{C - L14}{H14 - L14} \\\\ \\%D = 3\\text{-period SMA of } \\%K\n\\]\n",
    "gold_standard_file": "stoch.json",
    "ehlers_summary": "George Lane developed the Stochastic Oscillator in the 1950s. It is based on the observation that in an uptrend, prices tend to close near their high, and in a downtrend, they tend to close near their low. The sensitivity of the oscillator to market movements is reducible by adjusting the time period or by taking a moving average of the result. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "super_smoother",
    "name": "SuperSmoother",
    "description": "A second-order IIR filter with a maximally flat Butterworth response for superior smoothing with minimal lag.",
    "usage": "Use as a drop-in replacement for any moving average when maximum smoothing with minimal lag is needed. Ideal as a pre-filter before oscillators to eliminate high-frequency noise.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "smoothing",
      "ehlers",
      "dsp",
      "low-pass"
    ],
    "params": [
      {
        "name": "period",
        "default": "20",
        "description": "Critical period (wavelength)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/implemented/UltimateSmoother.pdf",
    "formula_latex": "\n\\[\na_1 = \\exp\\left(-\\frac{1.414\\pi}{Period}\\right)\n\\]\n\\[\nc_2 = 2a_1 \\cos\\left(\\frac{1.414\\pi}{Period}\\right)\n\\]\n\\[\nc_3 = -a_1^2\n\\]\n\\[\nc_1 = 1 - c_2 - c_3\n\\]\n\\[\nSS = c_1 \\frac{Price + Price_{t-1}}{2} + c_2 SS_{t-1} + c_3 SS_{t-2}\n\\]\n",
    "gold_standard_file": "super_smoother.json",
    "ehlers_summary": "Ehlers describes the SuperSmoother as a two-pole Butterworth filter achieving the same smoothing as a longer SMA with far less lag. It uses a critically-damped design to eliminate Gibbs phenomenon overshoot while retaining cycle information. — Cybernetic Analysis for Stocks and Futures, 2004",
    "struct_name": "SuperSmoother",
    "source_file": "super_smoother",
    "boundary_kind": "scalar"
  },
  {
    "slug": "supertrend",
    "name": "SuperTrend",
    "description": "Trend-following indicator that combines ATR for volatility bands to identify the primary market direction.",
    "usage": "Use as a primary trend-following indicator and dynamic stop-loss. A SuperTrend flip from bearish to bullish (or vice versa) provides a clear, rule-based entry and exit signal.",
    "category": "Classic",
    "keywords": [
      "trend",
      "atr",
      "stop-loss",
      "classic",
      "breakout"
    ],
    "params": [
      {
        "name": "period",
        "default": "10",
        "description": "ATR length"
      },
      {
        "name": "multiplier",
        "default": "3.0",
        "description": "ATR multiplier"
      }
    ],
    "formula_source": "https://www.tradingview.com/script/7zF0a4f8-SuperTrend-by-Mobius/",
    "formula_latex": "\n\\[\n\\text{SuperTrend} = \\begin{cases}\n\\text{LowerBand} & \\text{if trend is up} \\\\\n\\text{UpperBand} & \\text{if trend is down}\n\\end{cases}\n\\]\n",
    "gold_standard_file": "supertrend_10_3.json",
    "ehlers_summary": "SuperTrend computes upper and lower ATR-based bands around the midpoint of each bar. The active line flips from upper to lower (and vice versa) only when price closes beyond the band, providing a clean directional bias and a trailing stop level in one indicator. — TradingView Community",
    "struct_name": "Supertrend",
    "source_file": "supertrend",
    "boundary_kind": "scalar"
  },
  {
    "slug": "swiss_army_knife",
    "name": "Swiss Army Knife Indicator",
    "description": "A versatile indicator that can be configured as EMA, SMA, Gaussian, Butterworth, High Pass, Band Pass, or Band Stop filter.",
    "usage": "Use as a single configurable filter that can emulate SMA, EMA, Gaussian, Butterworth, or bandpass responses by switching mode flags. Ideal for prototyping different filter designs without code changes.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "multi-purpose",
      "smoothing"
    ],
    "params": [
      {
        "name": "mode",
        "default": "BandPass",
        "description": "Filter mode (EMA, SMA, Gauss, Butter, Smooth, HP, 2PHP, BP, BS)"
      },
      {
        "name": "period",
        "default": "20",
        "description": "Filter period"
      },
      {
        "name": "delta",
        "default": "0.1",
        "description": "Bandwidth parameter for BP and BS modes"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/SwissArmyKnifeIndicator.pdf",
    "formula_latex": "\n\\[\nFilt = c_0(b_0 x_t + b_1 x_{t-1} + b_2 x_{t-2}) + a_1 Filt_{t-1} + a_2 Filt_{t-2} - c_1 x_{t-N}\n\\]\n",
    "gold_standard_file": "swiss_army_knife.json",
    "ehlers_summary": "Ehlers presents the Swiss Army Knife Indicator in Cycle Analytics for Traders as a unified filter framework. A set of boolean flags selects the operating mode, making it possible to compare multiple filter responses on the same data by simply toggling flags rather than reimplementing each filter.",
    "struct_name": "SwissArmyKnife",
    "source_file": "swiss_army_knife",
    "boundary_kind": "scalar"
  },
  {
    "slug": "synthetic_oscillator",
    "name": "Synthetic Oscillator",
    "description": "A nonlinear oscillator designed to reduce lag while maintaining smoothness by adapting to the dominant cycle.",
    "usage": "Use to construct a synthetic oscillator from dominant cycle sine components when direct price oscillators are too noisy. Most effective in clearly cyclical markets.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "ehlers",
      "dsp",
      "cycle",
      "synthetic"
    ],
    "params": [
      {
        "name": "lower_bound",
        "default": "15",
        "description": "Lower bound of cycle period"
      },
      {
        "name": "upper_bound",
        "default": "25",
        "description": "Upper bound of cycle period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20APRIL%202026.html",
    "formula_latex": "\n\\[\nPrice = \\text{Hann}(Close, 12)\n\\]\n\\[\nLP = \\text{SuperSmoother}(\\text{HighPass}(Price, UB), LB)\n\\]\n\\[\nRe = \\frac{LP}{RMS(LP, 100)}, \\quad Im = \\frac{Re - Re_{t-1}}{RMS(Re - Re_{t-1}, 100)}\n\\]\n\\[\nDC = \\frac{2\\pi(Re^2 + Im^2)}{(Re - Re_{t-1})Im - (Im - Im_{t-1})Re}\n\\]\n\\[\nBP = \\text{UltimateSmoother}(\\text{HighPass}(Close, Mid), Mid)\n\\]\n\\[\nPhase = Phase_{t-1} + \\frac{2\\pi}{DC}\n\\]\n\\[\nSynth = \\sin(Phase)\n\\]\n",
    "gold_standard_file": "synthetic_oscillator.json",
    "ehlers_summary": "Ehlers constructs a Synthetic Oscillator by generating a synthetic sine wave at the measured dominant cycle period and comparing it to price. The phase difference between the synthetic sine and actual price reveals whether the market is ahead of or behind its expected cycle position.",
    "struct_name": "SyntheticOscillator",
    "source_file": "synthetic_oscillator",
    "boundary_kind": "scalar"
  },
  {
    "slug": "system_evaluator",
    "name": "System Evaluator",
    "description": "Calculates robust statistical performance metrics for a trading system based on a stream of trade profits.",
    "usage": "Use to assess the performance quality of a trading system output using signal processing metrics. Helps distinguish systems with genuine edge from those that merely overfit.",
    "category": "Statistics",
    "keywords": [
      "system",
      "performance",
      "ehlers",
      "statistics"
    ],
    "params": [],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/SystemEvaluation.pdf",
    "formula_latex": "\n\\[\nAveTrade = \\% \\cdot (PF + 1) - 1\n\\]\n\\[\nPF_{breakeven} = \\frac{1 - \\%}{\\%}\n\\]\n\\[\nN_{losers} = \\frac{\\ln(0.0027)}{\\ln(1 - \\%)}\n\\]\n",
    "gold_standard_file": "system_evaluation.json",
    "ehlers_summary": "Ehlers applies signal processing metrics to evaluate trading system quality in Cybernetic Analysis. Metrics such as the Signal-to-Noise Ratio of the equity curve quantify whether a system is generating genuine signal above the noise floor of random entry and exit.",
    "struct_name": "SystemEvaluator",
    "source_file": "system_evaluator",
    "boundary_kind": "scalar"
  },
  {
    "slug": "t3",
    "name": "Tilson T3 Moving Average",
    "description": "A smooth, low-lag moving average that uses multiple exponential smoothing.",
    "usage": "Use for trend following in noisy markets. T3 offers a superior balance between lag reduction and smoothness compared to DEMA or TEMA.",
    "category": "Classic",
    "keywords": [
      "moving-average",
      "smoothing",
      "lag-reduction",
      "classic"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "5",
        "description": "Smoothing period"
      },
      {
        "name": "v_factor",
        "default": "0.7",
        "description": "Volume factor (0.0 to 1.0)"
      }
    ],
    "formula_source": "https://www.tradingview.com/script/667W2a8n-T3-Moving-Average/",
    "formula_latex": "\n\\[\ne1 = EMA(Price, n) \\\\ e2 = EMA(e1, n) \\\\ \\dots \\\\ e6 = EMA(e5, n) \\\\ T3 = c1 \\times e6 + c2 \\times e5 + c3 \\times e4 + c4 \\times e3\n\\]\n",
    "gold_standard_file": "t3.json",
    "ehlers_summary": "Developed by Tim Tilson in 1998, the T3 moving average uses a 'v-factor' (volume factor) to control how much the indicator reacts to price changes. It is essentially a sextuple EMA smoothing process that provides a very smooth curve with remarkably little lag. — Technical Analysis of Stocks & Commodities",
    "struct_name": "",
    "source_file": "overlap",
    "boundary_kind": "scalar"
  },
  {
    "slug": "tema",
    "name": "Triple Exponential Moving Average",
    "description": "TEMA reduces the lag of traditional EMAs.",
    "usage": "Use to reduce the lag of a standard EMA by approximately two thirds. Drop-in replacement for EMA in trend-following systems where responsiveness is more important than smoothness.",
    "category": "Classic",
    "keywords": [
      "moving-average",
      "low-lag",
      "ema",
      "smoothing",
      "classic"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/t/triple-exponential-moving-average.asp",
    "formula_latex": "\n\\[\nTEMA = (3 \\times EMA_1) - (3 \\times EMA_2) + EMA_3\n\\]\n",
    "gold_standard_file": "tema.json",
    "ehlers_summary": "Patrick Mulloy introduced Triple EMA in Technical Analysis of Stocks and Commodities (1994) as a practical lag-reduction technique. TEMA = 3*EMA - 3*EMA(EMA) + EMA(EMA(EMA)), subtracting out two orders of the EMA lag while preserving most of the noise reduction.",
    "struct_name": "Tema",
    "source_file": "tema",
    "boundary_kind": "scalar"
  },
  {
    "slug": "tradj_ema",
    "name": "True Range Adjusted Exponential Moving Average",
    "description": "An exponential moving average that incorporates true range to measure volatility and adapt to price movements.",
    "usage": "Use to identify trend turning points and filter price movements. Comparing TRAdj EMA with a standard EMA of the same length provides insights into the overall trend.",
    "category": "Moving Averages",
    "keywords": [
      "moving-average",
      "adaptive",
      "true-range",
      "volatility"
    ],
    "params": [
      {
        "name": "period",
        "default": "40",
        "description": "Smoothing period"
      },
      {
        "name": "pds",
        "default": "40",
        "description": "Lookback period for True Range"
      },
      {
        "name": "mltp",
        "default": "10.0",
        "description": "Multiplier"
      }
    ],
    "formula_source": "Technical Analysis of Stocks & Commodities, January 2023",
    "formula_latex": "\n\\[\nTRAdj = \\frac{TR - TR_{min}}{TR_{max} - TR_{min}} \\\\ Rate = \\frac{2}{P+1} \\times (1 + TRAdj \\times Multiplier)\n\\]\n",
    "gold_standard_file": "",
    "ehlers_summary": "Introduced by Vitali Apirine in TASC January 2023, TRAdj EMA modifies the standard exponential moving average by adjusting the smoothing factor using the True Range. The normalized true range modifies the rate, making the indicator more responsive during volatile periods while filtering out noise when volatility drops.",
    "struct_name": "TradjEma",
    "source_file": "tradj_ema",
    "boundary_kind": "scalar"
  },
  {
    "slug": "trendflex",
    "name": "Trendflex",
    "description": "A zero-lag averaging indicator designed to retain the trend component while reducing lag.",
    "usage": "Use to recognize enduring trends with minimal lag. It is better at identifying the start of a new trend than standard moving averages.",
    "category": "Ehlers DSP",
    "keywords": [
      "zero-lag",
      "trend",
      "ehlers",
      "dsp",
      "oscillator"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Assumed cycle period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/implemented/TRADERS’ TIPS - FEBRUARY 2020.html",
    "formula_latex": "\n\\[\nFilt = \\text{SuperSmoother}(Price, Length/2)\n\\]\n\\[\nSum = \\frac{1}{Length} \\sum_{n=1}^{Length} (Filt_t - Filt_{t-n})\n\\]\n\\[\nMS = 0.04 \\cdot Sum^2 + 0.96 \\cdot MS_{t-1}\n\\]\n\\[\nTrendflex = \\frac{Sum}{\\sqrt{MS}}\n\\]\n",
    "gold_standard_file": "trendflex.json",
    "ehlers_summary": "Trendflex is the companion to Reflex. While Reflex focuses on the cyclic component by removing the trend slope, Trendflex retains the trend information by measuring the cumulative difference between the current smoothed value and its history without slope adjustment.",
    "struct_name": "Trendflex",
    "source_file": "trendflex",
    "boundary_kind": "scalar"
  },
  {
    "slug": "triangle_filter",
    "name": "TriangleFilter",
    "description": "Triangle windowed FIR filter.",
    "usage": "Use as a pre-smoother to reduce noise before applying cycle or momentum indicators when a symmetric low-ripple response is needed.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "smoothing",
      "triangle"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Filter length"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’ TIPS - SEPTEMBER 2021.html",
    "formula_latex": "\n\\[\nCoef(n) = \\begin{cases} n & n < L/2 \\\\ L/2 & n = L/2 \\\\ L + 1 - n & n > L/2 \\end{cases}\n\\]\n\\[\nFilt = \\frac{\\sum_{n=1}^L Coef(n) \\cdot Price_{t-n+1}}{\\sum Coef(n)}\n\\]\n",
    "gold_standard_file": "triangle_filter.json",
    "ehlers_summary": "The Triangle (Bartlett) window is a linearly-tapered FIR filter equivalent to applying two rectangular windows in sequence. It provides moderate sidelobe suppression and is useful when computational simplicity is preferred over maximum spectral attenuation.",
    "struct_name": "TriangleFilter",
    "source_file": "triangle",
    "boundary_kind": "scalar"
  },
  {
    "slug": "trima",
    "name": "Triangular Moving Average (TRIMA)",
    "description": "A double-smoothed simple moving average that gives more weight to the middle of the lookback period.",
    "usage": "Use for extremely smooth trend identification. TRIMA is significantly smoother than a standard SMA but introduces more lag; it is ideal for identifying long-term cycles.",
    "category": "Classic",
    "keywords": [
      "moving-average",
      "smoothing",
      "classic"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "30",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://www.tradingview.com/support/solutions/43000591273-triangular-moving-average-tma/",
    "formula_latex": "\n\\[\nTRIMA = SMA(SMA(Price, n/2), n/2)\n\\]\n",
    "gold_standard_file": "trima.json",
    "ehlers_summary": "The Triangular Moving Average is an SMA of an SMA. For a period N, it averages the values over N/2 periods twice. This results in a weight distribution that is triangular, peaking at the center of the window, making it very effective at filtering out high-frequency noise. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "overlap",
    "boundary_kind": "scalar"
  },
  {
    "slug": "trix",
    "name": "TRIX",
    "description": "A momentum oscillator that shows the percent rate of change of a triple exponentially smoothed moving average.",
    "usage": "Use to filter out market noise and identify trend reversals. TRIX crossings of the zero line or a signal line can provide trade entries.",
    "category": "Classic",
    "keywords": [
      "momentum",
      "oscillator",
      "smoothing",
      "classic"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "15",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/t/trix.asp",
    "formula_latex": "\n\\[\nTRIX = \\frac{EMA3_t - EMA3_{t-1}}{EMA3_{t-1}} \\times 100\n\\]\n",
    "gold_standard_file": "trix.json",
    "ehlers_summary": "Developed by Jack Hutson in the early 1980s, TRIX is a powerful momentum oscillator that effectively filters out minor price fluctuations. By triple-smoothing an EMA, it emphasizes the underlying trend and provides a clear signal when the trend changes direction. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "true_range",
    "name": "True Range",
    "description": "True Range measures daily volatility.",
    "usage": "Use as the foundational volatility module providing ATR, True Range, and related volatility measures used by higher-level indicators such as SuperTrend and Keltner Channels.",
    "category": "Classic",
    "keywords": [
      "volatility",
      "atr",
      "classic",
      "range"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/terms/a/atr.asp",
    "formula_latex": "\n\\[\nTR = \\max(H - L, |H - C_{t-1}|, |L - C_{t-1}|)\n\\]\n",
    "gold_standard_file": "true_range.json",
    "ehlers_summary": "Average True Range, developed by J. Welles Wilder in New Concepts in Technical Trading Systems (1978), measures the average of the true range over N bars. True Range accounts for overnight gaps by taking the maximum of: current high minus low, current high minus prior close, prior close minus current low. It remains the industry standard raw volatility measure.",
    "struct_name": "TrueRange",
    "source_file": "volatility",
    "boundary_kind": "scalar"
  },
  {
    "slug": "truncated_bandpass",
    "name": "TruncatedBandpass",
    "description": "Truncated Bandpass filter for handling sharp price movements.",
    "usage": "Use to isolate cyclic components while minimizing 'ringing' effects caused by sudden price shocks. Ideal for cycle-based trading systems in volatile markets.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "ehlers",
      "dsp",
      "bandpass",
      "cycle",
      "robust"
    ],
    "params": [
      {
        "name": "period",
        "default": "20",
        "description": "Cycle period to isolate"
      },
      {
        "name": "bandwidth",
        "default": "0.1",
        "description": "Bandwidth of the filter"
      },
      {
        "name": "length",
        "default": "10",
        "description": "Truncation length"
      }
    ],
    "formula_source": "https://www.traders.com/Documentation/FEEDbk_docs/2020/07/TradersTips.html",
    "formula_latex": "\n\\[\nL1 = \\cos(360/P), \\quad G1 = \\cos(BW \\cdot 360/P), \\quad S1 = 1/G1 - \\sqrt{1/G1^2 - 1}\n\\]\n\\[\nBPT_t = \\text{IIR window of length } L \\text{ with zero initial conditions}\n\\]\n",
    "gold_standard_file": "truncated_bandpass.json",
    "ehlers_summary": "Finite Impulse Response (FIR) filters have a fixed history, while Infinite Impulse Response (IIR) filters technically have an infinite history. Truncation limits the IIR feedback loop to a specific length, combining the sharp selectivity of IIR with the outlier-rejection of FIR.",
    "struct_name": "TruncatedBandpass",
    "source_file": "truncated_bandpass",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ttm_squeeze",
    "name": "TTM Squeeze",
    "description": "TTM Squeeze measures the relationship between Bollinger Bands and Keltner Channels to identify volatility consolidations.",
    "usage": "Use to identify periods of compressed volatility (Bollinger Bands inside Keltner Channels) followed by high-energy breakouts. The momentum histogram direction at squeeze release indicates trade direction.",
    "category": "Classic",
    "keywords": [
      "volatility",
      "momentum",
      "breakout",
      "squeeze",
      "classic"
    ],
    "params": [
      {
        "name": "bb_period",
        "default": "20",
        "description": "Bollinger Bands Period"
      },
      {
        "name": "bb_mult",
        "default": "2.0",
        "description": "Bollinger Bands Multiplier"
      },
      {
        "name": "kc_period",
        "default": "20",
        "description": "Keltner Channel Period"
      },
      {
        "name": "kc_mult",
        "default": "1.5",
        "description": "Keltner Channel Multiplier"
      }
    ],
    "formula_source": "https://www.investopedia.com/articles/active-trading/110714/intro-ttm-squeeze-indicator.asp",
    "formula_latex": "\n\\[\n\\text{Squeeze} = BB_{width} < KC_{width}\n\\]\n",
    "gold_standard_file": "ttm_squeeze.json",
    "ehlers_summary": "The TTM Squeeze, developed by John Carter, identifies market consolidation by detecting when Bollinger Bands contract inside Keltner Channels — a squeeze condition indicating coiling energy. When the bands expand back outside the Keltner Channels, the squeeze releases and a momentum histogram shows the expected breakout direction. — Mastering the Trade, John Carter",
    "struct_name": "TtmSqueeze",
    "source_file": "ttm_squeeze",
    "boundary_kind": "scalar"
  },
  {
    "slug": "typprice",
    "name": "Typical Price (TYPPRICE)",
    "description": "An average of the High, Low, and Close prices.",
    "usage": "Use as the primary price input for the Money Flow Index (MFI) and Commodity Channel Index (CCI). It provides a representative price level for the entire bar.",
    "category": "Classic",
    "keywords": [
      "price-transform",
      "classic"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/terms/t/typicalprice.asp",
    "formula_latex": "\n\\[\nTYPPRICE = \\frac{High + Low + Close}{3}\n\\]\n",
    "gold_standard_file": "typprice.json",
    "ehlers_summary": "Typical Price is a simple average of the High, Low, and Close. It is widely used in indicators that measure the relationship between price and volume, as it offers a more comprehensive view of the day's activity than the Close price alone. — StockCharts ChartSchool",
    "struct_name": "OC2",
    "source_file": "price_transform",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ultimate_bands",
    "name": "Ultimate Bands",
    "description": "A Bollinger-style band using UltimateSmoother for the center line and standard deviation of the price-smooth difference for width.",
    "usage": "Use as volatility bands that automatically widen during high-energy cycle phases and narrow during quiet phases. Better than fixed-multiple ATR bands in strongly cyclical markets.",
    "category": "Ehlers DSP",
    "keywords": [
      "bands",
      "volatility",
      "ehlers",
      "dsp",
      "adaptive"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Smoothing and SD period"
      },
      {
        "name": "num_sds",
        "default": "1.0",
        "description": "Standard Deviation multiplier"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/UltimateChannel.pdf",
    "formula_latex": "\n\\[\nSmooth = UltimateSmoother(Close, Length)\n\\]\n\\[\nSD = \\sqrt{\\frac{1}{n}\\sum_{i=0}^{n-1} (Close_{t-i} - Smooth_{t-i})^2}\n\\]\n\\[\nUpper = Smooth + NumSDs \\times SD\n\\]\n\\[\nLower = Smooth - NumSDs \\times SD\n\\]\n",
    "gold_standard_file": "ultimate_bands.json",
    "ehlers_summary": "Ehlers Ultimate Bands compute upper and lower price envelopes using the RMS amplitude of the dominant cycle rather than a fixed ATR multiple. This makes the bands proportional to the current cycle energy, expanding when the market is actively cycling and contracting when it enters a low-energy consolidation.",
    "struct_name": "UltimateBands",
    "source_file": "ultimate_bands",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ultimate_channel",
    "name": "Ultimate Channel",
    "description": "A Keltner-style channel using UltimateSmoothers for both the center line and the volatility range to minimize lag.",
    "usage": "Use as a dynamic price channel whose width scales with the current dominant cycle amplitude, providing adaptive support and resistance levels for breakout trading.",
    "category": "Ehlers DSP",
    "keywords": [
      "channel",
      "volatility",
      "ehlers",
      "adaptive",
      "breakout"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Center line smoothing period"
      },
      {
        "name": "str_length",
        "default": "20",
        "description": "Smooth True Range (STR) period"
      },
      {
        "name": "num_strs",
        "default": "1.0",
        "description": "Channel width multiplier"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/UltimateChannel.pdf",
    "formula_latex": "\n\\[\nTH = \\max(High, Close_{t-1})\n\\]\n\\[\nTL = \\min(Low, Close_{t-1})\n\\]\n\\[\nSTR = UltimateSmoother(TH - TL, STRLength)\n\\]\n\\[\nCenter = UltimateSmoother(Close, Length)\n\\]\n\\[\nUpper = Center + NumSTRs \\times STR\n\\]\n\\[\nLower = Center - NumSTRs \\times STR\n\\]\n",
    "gold_standard_file": "ultimate_channel.json",
    "ehlers_summary": "The Ultimate Channel uses the measured dominant cycle amplitude to set channel width, analogous to Keltner Channels but cycle-aware rather than ATR-based. When price breaks beyond the channel boundary, it signals that cycle amplitude has expanded enough to suggest a genuine directional move.",
    "struct_name": "UltimateChannel",
    "source_file": "ultimate_channel",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ultimate_smoother",
    "name": "UltimateSmoother",
    "description": "An Ehlers filter with zero lag in the Pass Band, constructed by subtracting High Pass response from the input data.",
    "usage": "Use when you need near-zero phase lag smoothing with very low ripple. It is Ehlers preferred smoother for applications where timing precision is critical.",
    "category": "Ehlers DSP",
    "keywords": [
      "filter",
      "smoothing",
      "ehlers",
      "dsp",
      "zero-lag"
    ],
    "params": [
      {
        "name": "period",
        "default": "20",
        "description": "Critical period (wavelength)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/implemented/UltimateSmoother.pdf",
    "formula_latex": "\n\\[\na_1 = \\exp\\left(-\\frac{1.414\\pi}{Period}\\right)\n\\]\n\\[\nc_2 = 2a_1 \\cos\\left(\\frac{1.414\\pi}{Period}\\right)\n\\]\n\\[\nc_3 = -a_1^2\n\\]\n\\[\nc_1 = (1 + c_2 - c_3) / 4\n\\]\n\\[\nUS = (1 - c_1) Price + (2c_1 - c_2) Price_{t-1} - (c_1 + c_3) Price_{t-2} + c_2 US_{t-1} + c_3 US_{t-2}\n\\]\n",
    "gold_standard_file": "ultimate_smoother.json",
    "ehlers_summary": "Ehlers designs the Ultimate Smoother in Cycle Analytics for Traders to minimize both lag and ripple simultaneously. It achieves near-zero phase shift across the passband while providing excellent attenuation of high-frequency noise, making it his preferred general-purpose smoother for cycle-sensitive applications.",
    "struct_name": "UltimateSmoother",
    "source_file": "ultimate_smoother",
    "boundary_kind": "scalar"
  },
  {
    "slug": "ultosc",
    "name": "Ultimate Oscillator",
    "description": "A momentum oscillator designed to capture momentum across three different timeframes.",
    "usage": "Use to avoid the pitfalls of oscillators that are limited to a single timeframe. Buy signals are generated when there is bullish divergence between price and the indicator.",
    "category": "Classic",
    "keywords": [
      "momentum",
      "oscillator",
      "classic",
      "multi-timeframe"
    ],
    "params": [
      {
        "name": "timeperiod1",
        "default": "7",
        "description": "Short period"
      },
      {
        "name": "timeperiod2",
        "default": "14",
        "description": "Medium period"
      },
      {
        "name": "timeperiod3",
        "default": "28",
        "description": "Long period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/u/ultimateoscillator.asp",
    "formula_latex": "\n\\[\n\\text{BP} = \\text{Close} - \\min(\\text{Low}, \\text{PrevClose}) \\\\ \\text{TR} = \\max(\\text{High}, \\text{PrevClose}) - \\min(\\text{Low}, \\text{PrevClose})\n\\]\n",
    "gold_standard_file": "ultosc.json",
    "ehlers_summary": "Developed by Larry Williams in 1976, the Ultimate Oscillator uses weighted averages of three different timeframes to reduce the volatility and false signals common in other oscillators. It remains a staple for identifying divergence across short, medium, and long-term price action. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "undersampled_double_ma",
    "name": "UndersampledDoubleMA",
    "description": "Undersampled price data smoothed by dual Hann filters to eliminate high frequency noise.",
    "usage": "Internal implementation module — not intended as a standalone trading indicator.",
    "category": "Ehlers DSP",
    "keywords": [
      "internal",
      "utility"
    ],
    "params": [
      {
        "name": "fast_len",
        "default": "6",
        "description": "Fast Hann filter length"
      },
      {
        "name": "slow_len",
        "default": "12",
        "description": "Slow Hann filter length"
      },
      {
        "name": "sampling_period",
        "default": "5",
        "description": "Undersampling rate (bars)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/JustIgnoreThem.pdf",
    "formula_latex": "\n\\[\nSample = \\begin{cases} Price & \\text{if } t \\pmod N = 0 \\\\ Sample_{t-1} & \\text{otherwise} \\end{cases}\n\\]\n\\[\nFast = Hann(Sample, FastLen)\n\\]\n\\[\nSlow = Hann(Sample, SlowLen)\n\\]\n",
    "gold_standard_file": "undersampled_double_ma.json",
    "ehlers_summary": "This module contains internal utility functions used by other indicators in the library. It is not intended to be used directly as a standalone trading indicator.",
    "struct_name": "UndersampledDoubleMa",
    "source_file": "just_ignore_them",
    "boundary_kind": "scalar"
  },
  {
    "slug": "universal_oscillator",
    "name": "Universal Oscillator",
    "description": "An adaptive oscillator that normalizes price momentum using a SuperSmoother filter and AGC.",
    "usage": "Use as a generic oscillator framework that works on any pre-filtered input. Feed it the output of any smoother or filter to produce a normalized zero-centered oscillator.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "ehlers",
      "dsp",
      "universal",
      "momentum"
    ],
    "params": [
      {
        "name": "band_edge",
        "default": "20",
        "description": "Critical period for the SuperSmoother filter"
      }
    ],
    "formula_source": "https://www.traders.com/Documentation/FEEDbk_docs/2015/01/TradersTips.html",
    "formula_latex": "\n\\[\nWN = (Price - Price_{t-2}) / 2\n\\]\n\\[\nAvgWN = (WN + WN_{t-1}) / 2\n\\]\n\\[\nFilt = c_1 AvgWN + c_2 Filt_{t-1} + c_3 Filt_{t-2}\n\\]\n\\[\nPeak = \\max(0.991 \\times Peak_{t-1}, |Filt|)\n\\]\n\\[\nUniversal = Filt / Peak\n\\]\n",
    "gold_standard_file": "universal_oscillator.json",
    "ehlers_summary": "Ehlers Universal Oscillator is a generic momentum computation that can be applied to any filtered price input. It computes the rate of change of the filtered series normalized by its RMS amplitude, producing a consistently scaled oscillator that works regardless of the underlying filter or price instrument.",
    "struct_name": "UniversalOscillator",
    "source_file": "universal_oscillator",
    "boundary_kind": "scalar"
  },
  {
    "slug": "usi",
    "name": "Ultimate Strength Index",
    "description": "A lag-reduced version of the RSI using UltimateSmoother on smoothed up/down components.",
    "usage": "Use to measure the relative strength of the current market move normalized to the dominant cycle amplitude, giving a volatility-adjusted momentum reading.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "strength",
      "ehlers",
      "adaptive",
      "momentum"
    ],
    "params": [
      {
        "name": "length",
        "default": "14",
        "description": "UltimateSmoother period"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS%E2%80%99%20TIPS%20-%20NOVEMBER%202024.html",
    "formula_latex": "\n\\[\n\\text{SU} = \\max(0, \\text{Close} - \\text{Close}_{t-1})\n\\]\n\\[\n\\text{SD} = \\max(0, \\text{Close}_{t-1} - \\text{Close})\n\\]\n\\[\n\\text{USU} = UltimateSmoother(SMA(\\text{SU}, 4), Length)\n\\]\n\\[\n\\text{USD} = UltimateSmoother(SMA(\\text{SD}, 4), Length)\n\\]\n\\[\n\\text{USI} = \\frac{\\text{USU} - \\text{USD}}{\\text{USU} + \\text{USD}}\n\\]\n",
    "gold_standard_file": "usi.json",
    "ehlers_summary": "The Ultimate Strength Index measures directional momentum as a fraction of the total cycle amplitude. By normalizing momentum to the RMS energy of the dominant cycle, it produces a consistent 0-100 reading that is comparable across different instruments and volatility regimes.",
    "struct_name": "Usi",
    "source_file": "usi",
    "boundary_kind": "scalar"
  },
  {
    "slug": "volume_profile",
    "name": "Volume Profile",
    "description": "Calculates the price level with the highest traded volume (Point of Control) over a sliding window.",
    "usage": "Use to identify significant support and resistance levels. The POC represents the price where most market activity occurred, often acting as a magnet for price or a strong barrier. Essential for volume spread analysis and auction market theory.",
    "category": "Volume",
    "keywords": [
      "volume",
      "profile",
      "poc",
      "support-resistance",
      "auction-market-theory"
    ],
    "params": [
      {
        "name": "period",
        "default": "200",
        "description": "Sliding window size"
      },
      {
        "name": "bins",
        "default": "50",
        "description": "Number of price bins in the histogram"
      }
    ],
    "formula_source": "https://www.tradingview.com/support/solutions/43000502040-volume-profile-visible-range-vpvr/",
    "formula_latex": "\n\\[\nBinIdx = \\lfloor \\frac{Price - Price_{min}}{BinSize} \\rfloor\n\\]\n\\[\nPOC = Price_{min} + (Idx_{max\\_vol} + 0.5) \\times BinSize\n\\]\n",
    "gold_standard_file": "volume_profile.json",
    "ehlers_summary": "Volume Profile is an advanced charting study that displays trading activity over a specified time period at specified price levels. The Point of Control (POC) is the single most important level in the profile, representing the price at which the most volume was traded. It serves as a key benchmark for identifying value areas and potential trend reversals.",
    "struct_name": "VolumeProfile",
    "source_file": "volume_profile",
    "boundary_kind": "scalar"
  },
  {
    "slug": "vortex",
    "name": "Vortex Indicator",
    "description": "The Vortex Indicator helps identify the start of a new trend or the continuation of an existing one.",
    "usage": "Use to detect the start of new trends. A Vortex Indicator crossover (VI+ crossing above VI-) signals the beginning of an uptrend; the reverse signals a downtrend.",
    "category": "Classic",
    "keywords": [
      "trend",
      "momentum",
      "classic",
      "breakout"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/v/vortex-indicator-vi.asp",
    "formula_latex": "\n\\[\nVI+ = \\frac{\\sum VM+}{\\sum TR} \\\\ VI- = \\frac{\\sum VM-}{\\sum TR}\n\\]\n",
    "gold_standard_file": "vortex.json",
    "ehlers_summary": "The Vortex Indicator, developed by Etienne Botes and Douglas Siepman (2010), is inspired by the vortex flow of water discovered by Viktor Schauberger. VI+ measures upward movement relative to the prior bar low; VI- measures downward movement relative to the prior bar high. Normalized by ATR, they produce two oscillating lines whose crossovers signal trend changes. — Technical Analysis of Stocks and Commodities, 2010",
    "struct_name": "Vortex",
    "source_file": "vortex",
    "boundary_kind": "scalar"
  },
  {
    "slug": "voss_predictor",
    "name": "VossPredictor",
    "description": "A predictive filter with negative group delay for band-limited signals.",
    "usage": "Use for multi-bar price prediction based on a bandpass-filtered dominant cycle. More accurate than simple linear extrapolation due to its IIR filter pole placement.",
    "category": "Ehlers DSP",
    "keywords": [
      "prediction",
      "cycle",
      "ehlers",
      "dsp",
      "filter"
    ],
    "params": [
      {
        "name": "period",
        "default": "20",
        "description": "Center period of the BandPass filter"
      },
      {
        "name": "predict",
        "default": "3",
        "description": "Number of bars of prediction"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/A%20PEEK%20INTO%20THE%20FUTURE.pdf",
    "formula_latex": "\n\\[\nFilt = \\text{BandPass}(Price, Period, 0.25)\n\\]\n\\[\nOrder = 3 \\cdot Predict\n\\]\n\\[\nSumC = \\sum_{n=0}^{Order-1} \\frac{n+1}{Order} Voss_{t-(Order-n)}\n\\]\n\\[\nVoss = \\frac{3 + Order}{2} Filt - SumC\n\\]\n",
    "gold_standard_file": "voss_predictor.json",
    "ehlers_summary": "The Voss Predictor is a predictive filter developed by J.F. Voss and adapted by Ehlers in Cycle Analytics for Traders. Its IIR bandpass design inherently extrapolates the filtered signal several bars into the future by virtue of pole placement inside the unit circle, enabling lookahead without buffer access.",
    "struct_name": "VossPredictor",
    "source_file": "voss_predictor",
    "boundary_kind": "scalar"
  },
  {
    "slug": "vpn",
    "name": "Volume Positive Negative",
    "description": "Detects high-volume breakouts by comparing volume on up days vs down days, normalized between -100 and 100.",
    "usage": "Use to confirm breakouts. A VPN value crossing above a critical threshold (e.g., 10) signals a high-volume positive breakout.",
    "category": "Volume",
    "keywords": [
      "volume",
      "breakout",
      "katsanos",
      "vpn",
      "momentum"
    ],
    "params": [
      {
        "name": "period",
        "default": "30",
        "description": "Calculation period for volume sums and ATR"
      },
      {
        "name": "smooth_period",
        "default": "3",
        "description": "Smoothing period for the final VPN value"
      }
    ],
    "formula_source": "https://www.traders.com/Documentation/FEEDbk_docs/2021/04/TradersTips.html",
    "formula_latex": "\n\\[\nTP = \\frac{High + Low + Close}{3}\n\\]\n\\[\nMF = TP - TP_{t-1}\n\\]\n\\[\nMC = 0.1 \\times ATR(Period)\n\\]\n\\[\nVP = \\sum_{i=0}^{Period-1} (\\text{if } MF_{t-i} > MC_{t-i} \\text{ then } Volume_{t-i} \\text{ else } 0)\n\\]\n\\[\nVN = \\sum_{i=0}^{Period-1} (\\text{if } MF_{t-i} < -MC_{t-i} \\text{ then } Volume_{t-i} \\text{ else } 0)\n\\]\n\\[\nMAV = \\text{Average}(Volume, Period)\n\\]\n\\[\nVPN = \\frac{VP - VN}{MAV \\times Period} \\times 100\n\\]\n",
    "gold_standard_file": "vpn.json",
    "ehlers_summary": "While originally using EMA for smoothing, this implementation employs the UltimateSmoother to further reduce lag in detecting volume-driven trend shifts, aligning with modern DSP standards for technical indicators.",
    "struct_name": "Vpn",
    "source_file": "vpn",
    "boundary_kind": "scalar"
  },
  {
    "slug": "vwap",
    "name": "Anchored VWAP",
    "description": "Volume Weighted Average Price anchored to a specific starting point.",
    "usage": "Use as an intraday fair value benchmark. Institutional traders buy below VWAP and sell above it; breakouts above VWAP on heavy volume signal bullish institutional interest.",
    "category": "Classic",
    "keywords": [
      "trend",
      "volume",
      "classic",
      "support-resistance"
    ],
    "params": [],
    "formula_source": "https://www.investopedia.com/terms/v/vwap.asp",
    "formula_latex": "\n\\[\nVWAP = \\frac{\\sum (Price \\times Volume)}{\\sum Volume}\n\\]\n",
    "gold_standard_file": "vwap.json",
    "ehlers_summary": "Volume Weighted Average Price calculates the average price weighted by volume transacted at each level throughout the trading session. It serves as the primary execution benchmark for institutional orders — TWAP and VWAP algorithms are the two most common order execution strategies in equity markets. — Investopedia",
    "struct_name": "AnchoredVWAP",
    "source_file": "vwap",
    "boundary_kind": "cumulative"
  },
  {
    "slug": "wavetrend",
    "name": "WaveTrend Oscillator",
    "description": "WaveTrend is an oscillator that helps identify overbought and oversold conditions.",
    "usage": "Use as a momentum oscillator to identify overbought and oversold conditions. WaveTrend crossovers at extreme levels provide high-probability mean-reversion entry signals.",
    "category": "Ehlers DSP",
    "keywords": [
      "oscillator",
      "momentum",
      "overbought",
      "oversold",
      "ehlers"
    ],
    "params": [
      {
        "name": "n1",
        "default": "10",
        "description": "Channel Length"
      },
      {
        "name": "n2",
        "default": "21",
        "description": "Average Length"
      }
    ],
    "formula_source": "https://www.tradingview.com/script/2KE8wTuF-Indicator-WaveTrend-Oscillator-WT/",
    "formula_latex": "\n\\[\nWT_1 = EMA(ESA, n_2)\n\\]\n",
    "gold_standard_file": "wavetrend.json",
    "ehlers_summary": "WaveTrend (popularized as LazyBear WaveTrend on TradingView) computes a channel index by normalizing price deviation from an EMA by the smoothed absolute deviation. A second EMA of this index produces the signal line. Extreme values (±60) with WT1-WT2 crossovers are the classic trade trigger.",
    "struct_name": "Wavetrend",
    "source_file": "wavetrend",
    "boundary_kind": "scalar"
  },
  {
    "slug": "wclprice",
    "name": "Weighted Close Price (WCLPRICE)",
    "description": "An average of the High, Low, and Close prices, with double weight given to the Close price.",
    "usage": "Use to emphasize the importance of the closing price while still accounting for the total range of the bar.",
    "category": "Classic",
    "keywords": [
      "price-transform",
      "classic",
      "weighted"
    ],
    "params": [],
    "formula_source": "https://www.tradingview.com/support/solutions/43000502590-weighted-close-wclprice/",
    "formula_latex": "\n\\[\nWCLPRICE = \\frac{High + Low + 2 \\times Close}{4}\n\\]\n",
    "gold_standard_file": "wclprice.json",
    "ehlers_summary": "Weighted Close Price gives additional significance to the Close, reflecting the widely held belief that the closing price is the most important data point in a trading session. It provides a more nuanced input for smoothing algorithms. — TA-Lib Documentation",
    "struct_name": "OC2",
    "source_file": "price_transform",
    "boundary_kind": "scalar"
  },
  {
    "slug": "willr",
    "name": "Williams %R",
    "description": "A momentum indicator that measures overbought and oversold levels, similar to a stochastic oscillator.",
    "usage": "Use to identify entry and exit points in the market. Readings from 0 to -20 are considered overbought, while readings from -80 to -100 are considered oversold.",
    "category": "Classic",
    "keywords": [
      "momentum",
      "oscillator",
      "overbought",
      "oversold",
      "classic"
    ],
    "params": [
      {
        "name": "timeperiod",
        "default": "14",
        "description": "Lookback period"
      }
    ],
    "formula_source": "https://www.investopedia.com/terms/w/williamsr.asp",
    "formula_latex": "\n\\[\n\\%R = \\frac{\\text{Highest High} - \\text{Close}}{\\text{Highest High} - \\text{Lowest Low}} \\times -100\n\\]\n",
    "gold_standard_file": "willr.json",
    "ehlers_summary": "Developed by Larry Williams, %R compares the closing price of a stock to the high-low range over a specific period, typically 14 days. It is used to determine when a stock might be overbought or oversold and to identify potential trend reversals. — StockCharts ChartSchool",
    "struct_name": "",
    "source_file": "momentum",
    "boundary_kind": "scalar"
  },
  {
    "slug": "wma",
    "name": "Weighted Moving Average",
    "description": "The Weighted Moving Average assigns linearly decreasing weights.",
    "usage": "Use as the foundational smoothing module providing SMA, EMA, WMA, and SMMA implementations that power higher-level indicators across the library.",
    "category": "Classic",
    "keywords": [
      "moving-average",
      "smoothing",
      "classic",
      "ema"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://www.investopedia.com/articles/technical/060401.asp",
    "formula_latex": "\n\\[\nWMA = \\frac{P_1 \\times n + P_2 \\times (n-1) + \\dots}{n + (n-1) + \\dots + 1}\n\\]\n",
    "gold_standard_file": "wma.json",
    "ehlers_summary": "The core smoothing algorithms — SMA, EMA, WMA — are the building blocks of nearly all technical indicators. EMA applies exponential decay weighting (alpha = 2/(n+1)), SMA applies uniform weighting over N bars, and WMA applies linearly increasing weights emphasizing more recent bars.",
    "struct_name": "Wma",
    "source_file": "smoothing",
    "boundary_kind": "scalar"
  },
  {
    "slug": "zero_lag",
    "name": "Zero Lag EC",
    "description": "Zero Lag Error Corrected EMA attempts to eliminate lag by adding an error term to the EMA.",
    "usage": "Use as a near-zero-lag moving average for trend-following systems. The error-correction term removes the lag inherent in the standard EMA without introducing significant overshoot.",
    "category": "Ehlers DSP",
    "keywords": [
      "moving-average",
      "zero-lag",
      "ehlers",
      "ema",
      "smoothing"
    ],
    "params": [
      {
        "name": "length",
        "default": "20",
        "description": "Equivalent SMA length"
      },
      {
        "name": "gain_limit",
        "default": "50.0",
        "description": "Gain limit (divided by 10 for actual gain)"
      }
    ],
    "formula_source": "https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/implemented/ZeroLag.pdf",
    "formula_latex": "\n\\[\n\\alpha = \\frac{2}{Length + 1}\n\\]\n\\[\nEMA = \\alpha \\times Close + (1 - \\alpha) \\times EMA_{t-1}\n\\]\n\\[\nEC = \\alpha \\times (EMA + Gain \\times (Close - EC_{t-1})) + (1 - \\alpha) \\times EC_{t-1}\n\\]\n",
    "gold_standard_file": "zero_lag.json",
    "ehlers_summary": "Ehlers introduces the Zero Lag indicator in Cybernetic Analysis as an EMA with an added error-correction term that subtracts the average lag from the output. The resulting EC (Error Corrected) line tracks price with near-zero delay while the ZL-EMA provides a smoothed reference, with crossovers between them providing trade signals.",
    "struct_name": "ZeroLag",
    "source_file": "zero_lag",
    "boundary_kind": "scalar"
  },
  {
    "slug": "zlema",
    "name": "Zero Lag Exponential Moving Average",
    "description": "ZLEMA attempts to eliminate the inherent lag associated with moving averages.",
    "usage": "Use to reduce the lag of a standard EMA by approximately two thirds. Drop-in replacement for EMA in trend-following systems where responsiveness is more important than smoothness.",
    "category": "Classic",
    "keywords": [
      "moving-average",
      "low-lag",
      "ema",
      "smoothing",
      "classic"
    ],
    "params": [
      {
        "name": "period",
        "default": "14",
        "description": "Smoothing period"
      }
    ],
    "formula_source": "https://en.wikipedia.org/wiki/Zero_lag_exponential_moving_average",
    "formula_latex": "\n\\[\nZLEMA = EMA(Price + (Price - Price_{t - (period - 1)/2}))\n\\]\n",
    "gold_standard_file": "zlema.json",
    "ehlers_summary": "Patrick Mulloy introduced Triple EMA in Technical Analysis of Stocks and Commodities (1994) as a practical lag-reduction technique. TEMA = 3*EMA - 3*EMA(EMA) + EMA(EMA(EMA)), subtracting out two orders of the EMA lag while preserving most of the noise reduction.",
    "struct_name": "Zlema",
    "source_file": "tema",
    "boundary_kind": "scalar"
  }
]