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docs: audit and fix all category _index.md files

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lib/_index.md
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| Category | Count | Description |
| :----------------------------------- | :-----: | :----------------------------------------------- |
| [Core](core/_index.md) | 7 | Price transforms and fundamental building blocks |
| [Core](core/_index.md) | 8 | Price transforms and fundamental building blocks |
| [Trends (FIR)](trends_FIR/_index.md) | 33 | Finite Impulse Response moving averages |
| [Trends (IIR)](trends_IIR/_index.md) | 36 | Infinite Impulse Response moving averages |
| [Filters](filters/_index.md) | 37 | Signal processing filters |
| [Oscillators](oscillators/_index.md) | 47 | Indicators that fluctuate around a center line |
| [Oscillators](oscillators/_index.md) | 48 | Indicators that fluctuate around a center line |
| [Dynamics](dynamics/_index.md) | 21 | Trend strength and direction indicators |
| [Momentum](momentum/_index.md) | 19 | Momentum-based indicators |
| [Volatility](volatility/_index.md) | 26 | Volatility estimators and indicators |
@@ -20,7 +20,7 @@
| [Forecasts](forecasts/_index.md) | 1 | Predictive indicators |
| [Errors](errors/_index.md) | 26 | Error metrics and loss functions |
| [Numerics](numerics/_index.md) | 27 | Mathematical transformations |
| **Total** | **395** | |
| **Total** | **393** | |
## All Indicators
lib/errors/_index.md
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| :--- | :--- | :--- |
| [HUBER](huber/Huber.md) | Huber Loss | Combines MSE and MAE. Configurable outlier threshold δ. |
| [LOGCOSH](logcosh/Logcosh.md) | Log-Cosh Loss | Smooth approximation to MAE. Twice-differentiable. |
| [MAE](mae/Mae.md) | Mean Absolute Error | Average of absolute differences. Robust baseline. |
| [MAAPE](maape/Maape.md) | Mean Arctangent APE | Bounded percentage error using arctangent. Range: 0 to π/2. |
| [MAE](mae/Mae.md) | Mean Absolute Error | Average of absolute differences. Robust baseline. |
| [MAPD](mapd/Mapd.md) | Mean Absolute % Deviation | Percentage error relative to mean of actual and predicted. |
| [MAPE](mape/Mape.md) | Mean Absolute % Error | Percentage error relative to actual. Unbounded when actual≈0. |
| [MASE](mase/Mase.md) | Mean Absolute Scaled Error | Scale-free. Uses naive forecast as baseline. |
@@ -23,7 +23,7 @@ Error metrics and loss functions for model/strategy evaluation. All error indica
| [MSE](mse/Mse.md) | Mean Squared Error | Squared differences. Penalizes large errors heavily. |
| [MSLE](msle/Msle.md) | Mean Squared Log Error | MSE on log-transformed values. For multiplicative errors. |
| [PSEUDOHUBER](pseudohuber/Pseudohuber.md) | Pseudo-Huber Loss | Smooth Huber approximation. Fully differentiable. |
| [QUANTILE](quantile/Quantile.md) | Quantile Loss | Asymmetric loss for quantile regression. Pinball loss. |
| [QUANTILELOSS](quantileloss/Quantileloss.md) | Quantile Loss | Asymmetric loss for quantile regression. Pinball loss. |
| [RAE](rae/Rae.md) | Relative Absolute Error | Absolute error relative to mean predictor. |
| [RMSE](rmse/Rmse.md) | Root Mean Squared Error | √MSE. Same units as input. Penalizes outliers. |
| [RMSLE](rmsle/Rmsle.md) | Root Mean Squared Log Error | √MSLE. For multiplicative error structures. |
@@ -31,7 +31,6 @@ Error metrics and loss functions for model/strategy evaluation. All error indica
| [RSQUARED](rsquared/Rsquared.md) | R² (Coefficient of Determination) | Variance explained. 1 = perfect. Can be negative. |
| [SMAPE](smape/Smape.md) | Symmetric MAPE | Bounded 0-200%. Symmetric around zero. |
| [THEILU](theilu/Theilu.md) | Theil's U Statistic | Forecast vs naive. <1 beats naive. >1 worse than naive. |
| [TUKEY](tukey/Tukey.md) | Tukey Biweight Loss | Hard-rejects outliers beyond threshold. Redescending. |
| [TUKEYBIWEIGHT](tukeybiweight/Tukeybiweight.md) | Tukey Biweight Loss | Hard-rejects outliers beyond threshold. Redescending. |
| [WMAPE](wmape/Wmape.md) | Weighted MAPE | Volume-weighted percentage error. For heterogeneous data. |
| [WRMSE](wrmse/Wrmse.md) | Weighted RMSE | Weighted root mean squared error. Custom observation weighting. |
| STDERR | Standard Error | StdDev / √n. Measures sampling variability. |
lib/filters/_index.md
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| [RLS](rls/Rls.md) | Recursive Least Squares | Inverse correlation matrix. Faster convergence than LMS. O(order²) per bar. |
| [RMED](rmed/Rmed.md) | Ehlers Recursive Median Filter | Recursive median approximation via IIR structure. Outlier-resistant. |
| [ROOFING](roofing/Roofing.md) | Ehlers Roofing Filter | Ehlers. HP + SS cascade. Bandpass for cycle extraction. |
| SAK | Ehlers Swiss Army Knife | Configurable multi-mode filter (LP, HP, BP, BS). Single framework. |
| [SAK](sak/Sak.md) | Ehlers Swiss Army Knife | Configurable multi-mode filter (LP, HP, BP, BS). Single framework. |
| [SGF](sgf/Sgf.md) | Savitzky-Golay | Polynomial smoothing. Preserves higher moments (derivatives). |
| [SPBF](spbf/Spbf.md) | Ehlers Super Passband Filter | Ehlers. Wide-band bandpass via differenced EMAs with RMS envelope. |
| [SSF2](ssf2/Ssf2.md) | Ehlers 2-Pole Super Smoother Filter | Ehlers. 2-pole Butterworth variant. Standard cycle pre-filter. |
lib/numerics/_index.md
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| [EXPDIST](expdist/Expdist.md) | Exponential Distribution | Exponential probability distribution transform. |
| [EXPTRANS](exptrans/Exptrans.md) | Exponential Transform | e^x transform for log-space conversion reversal. |
| [FDIST](fdist/Fdist.md) | F-Distribution | Fisher-Snedecor probability distribution transform. |
| FFT | Fast Fourier Transform | Frequency-domain decomposition via FFT algorithm. |
| [FFT](fft/Fft.md) | Fast Fourier Transform | Frequency-domain decomposition via FFT algorithm. |
| [GAMMADIST](gammadist/Gammadist.md) | Gamma Distribution | Gamma probability distribution transform. |
| [HIGHEST](highest/Highest.md) | Rolling Maximum | Maximum value over lookback window. |
| IFFT | Inverse Fast Fourier Transform | Frequency-to-time domain reconstruction. |
| [IFFT](ifft/Ifft.md) | Inverse Fast Fourier Transform | Frequency-to-time domain reconstruction. |
| [JERK](jerk/Jerk.md) | Jerk | Rate of acceleration; third derivative of price. |
| [LINEARTRANS](lineartrans/Lineartrans.md) | Linear Transform | y = ax + b scaling transformation. |
| [LOGNORMDIST](lognormdist/Lognormdist.md) | Log-normal Distribution | Log-normal probability distribution transform. |
lib/oscillators/_index.md
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| [AO](ao/Ao.md) | Awesome Oscillator | 5-period SMA minus 34-period SMA of bar midpoint. Bill Williams creation. |
| [APO](apo/Apo.md) | Absolute Price Oscillator | Raw currency difference between fast and slow EMAs. Unbounded. |
| [BBB](bbb/Bbb.md) | Bollinger %B | Position within Bollinger Bands. 0=lower band, 1=upper band. |
| [BBI](bbi/Bbi.md) | Bulls Bears Index | Multi-period SMA composite. Measures aggregate trend strength. |
| [BBS](bbs/Bbs.md) | Bollinger Band Squeeze | BB width < KC width indicates consolidation. Breakout imminent. |
| BRAR | BRAR | Bull-Bear power ratio from open-relative ranges. Japanese origin. |
| [BRAR](brar/Brar.md) | BRAR | Bull-Bear power ratio from open-relative ranges. Japanese origin. |
| [CFO](cfo/Cfo.md) | Chande Forecast Oscillator | Percentage difference between price and linear regression forecast. Also known as FOSC. |
| COPPOCK | Coppock Curve | Long-term momentum via weighted sum of ROC periods. Buy signals only. |
| CRSI | Connors RSI | Composite of RSI, streak RSI, and percentile rank. Mean-reversion. |
| CTI | Correlation Trend Indicator | Linear regression correlation coefficient as trend strength. |
| [COPPOCK](coppock/Coppock.md) | Coppock Curve | Long-term momentum via weighted sum of ROC periods. Buy signals only. |
| [CRSI](crsi/Crsi.md) | Connors RSI | Composite of RSI, streak RSI, and percentile rank. Mean-reversion. |
| [CTI](cti/Cti.md) | Correlation Trend Indicator | Linear regression correlation coefficient as trend strength. |
| [DECO](deco/Deco.md) | Ehlers Decycler Oscillator | Dual HP bandpass isolating intermediate-frequency market cycles. |
| [DEM](dem/Dem.md) | DeMarker Oscillator | Bounded 0-1 oscillator comparing sequential highs and lows. |
| DOSC | Derivative Oscillator | Double-smoothed RSI minus signal line. Momentum acceleration. |
| [DOSC](dosc/Dosc.md) | Derivative Oscillator | Double-smoothed RSI minus signal line. Momentum acceleration. |
| [DPO](dpo/Dpo.md) | Detrended Price Oscillator | Removes trend via displaced SMA. Reveals cycles. |
| [DYMOI](dymoi/Dymoi.md) | Dynamic Momentum Index | RSI with volatility-adaptive period. Shorter in volatile markets. |
| [ER](er/Er.md) | Efficiency Ratio | Measures directional efficiency. Net movement / total path length. |
| [ERI](eri/Eri.md) | Elder Ray Index | Separates bull and bear power relative to EMA. |
| [FI](fi/Fi.md) | Force Index | Combines price change, direction, and volume to measure buying/selling power. |
| [FISHER](fisher/Fisher.md) | Ehlers Fisher Transform | Converts prices to Gaussian distribution. Sharp reversals. |
| [FISHER04](fisher04/Fisher04.md) | Ehlers Fisher Transform (2004) | Cybernetic Analysis variant with gentler arctanh scaling. |
| [GATOR](gator/Gator.md) | Williams Gator Oscillator | Dual histogram from Alligator SMMA lines. Visualizes trend convergence/divergence. |
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| [INERTIA](inertia/Inertia.md) | Inertia | Linear regression residual. Raw deviation from trend forecast. |
| [KDJ](kdj/Kdj.md) | KDJ Indicator | Enhanced Stochastic. J = 3K - 2D provides leading signal. |
| [KRI](kri/Kri.md) | Kairi Relative Index | Percentage deviation of price from SMA. Overbought/oversold. |
| KST | KST Oscillator | Summed weighted ROCs across 4 timeframes. Martin Pring. |
| [KST](kst/Kst.md) | KST Oscillator | Summed weighted ROCs across 4 timeframes. Martin Pring. |
| [LRSI](lrsi/Lrsi.md) | Ehlers Laguerre RSI | RSI computed over Laguerre filter stages. Single γ trades lag vs smoothness. Output [0,1]. |
| [MARKETFI](marketfi/Marketfi.md) | Market Facilitation Index | Bill Williams' price-range-per-unit-of-volume efficiency measure. O(1), no period. |
| MSTOCH | Ehlers MESA Stochastic | Hilbert Transform cycle-tuned Stochastic. Adaptive period. |
| [MSTOCH](mstoch/Mstoch.md) | Ehlers MESA Stochastic | Hilbert Transform cycle-tuned Stochastic. Adaptive period. |
| [PGO](pgo/Pgo.md) | Pretty Good Oscillator | Distance from SMA normalized by ATR. Units: ATR multiples. |
| [PSL](psl/Psl.md) | Psychological Line | Ratio of up periods to total periods. Crowd sentiment gauge. |
| QQE | Quantitative Qualitative Estimation | Smoothed RSI with dynamic volatility bands. |
| REFLEX | Ehlers Reflex | Ehlers zero-centered reversal oscillator using super smoother with normalized sum-of-differences. |
| [QQE](qqe/Qqe.md) | Quantitative Qualitative Estimation | Smoothed RSI with dynamic volatility bands. |
| [REFLEX](reflex/Reflex.md) | Ehlers Reflex | Ehlers zero-centered reversal oscillator using super smoother with normalized sum-of-differences. |
| [REVERSEEMA](reverseema/ReverseEma.md) | Ehlers Reverse EMA | 8-stage cascaded Z-transform inversion subtracts EMA lag, producing zero-centered oscillator signal. |
| RVGI | Relative Vigor Index | Open-close vs high-low ratio with SMA smoothing. Measures conviction. |
| [RVGI](rvgi/Rvgi.md) | Relative Vigor Index | Open-close vs high-low ratio with SMA smoothing. Measures conviction. |
| [SMI](smi/Smi.md) | Stochastic Momentum Index | Distance from range midpoint. More sensitive than classic Stochastic. |
| SQUEEZE | Squeeze | BB width < KC width indicates consolidation. Breakout imminent. |
| [SQUEEZE](squeeze/Squeeze.md) | Squeeze | BB width < KC width indicates consolidation. Breakout imminent. |
| [STC](stc/Stc.md) | Schaff Trend Cycle | MACD + double Stochastic smoothing. Fast momentum oscillator (0-100). |
| [STOCH](stoch/Stoch.md) | Stochastic Oscillator | Close position within N-period high-low range. Classic overbought/oversold. |
| [STOCHF](stochf/Stochf.md) | Stochastic Fast | Unsmoothed Stochastic. Faster but noisier. |
| [STOCHRSI](stochrsi/Stochrsi.md) | Stochastic RSI | Stochastic applied to RSI. More sensitive than either alone. |
| TD_SEQ | TD Sequential | DeMark sequential countdown. Exhaustion pattern recognition. |
| [TD_SEQ](td_seq/Td_seq.md) | TD Sequential | DeMark sequential countdown. Exhaustion pattern recognition. |
| [TRENDFLEX](trendflex/Trendflex.md) | Ehlers Trendflex | Ehlers zero-lag trend oscillator using super smoother with sum-of-differences normalization. |
| [TRIX](trix/Trix.md) | Triple Exponential Average | ROC of triple EMA. Filters noise through three smoothings. |
| [TTM_WAVE](ttm_wave/TtmWave.md) | TTM Wave | Fibonacci-period MACD composite (Waves A/B/C). John Carter. |
lib/statistics/_index.md
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| [ZTEST](ztest/Ztest.md) | Z-Test | One-sample t-test statistic against hypothesized mean. |
| [MEANDEV](meandev/MeanDev.md) | Mean Absolute Deviation | Outlier-robust dispersion. Core of CCI. MD ≈ 0.7979σ for normal data. |
| [STDERR](stderr/Stderr.md) | Standard Error of Regression | OLS residual scatter over rolling window. Quantifies trend fit quality. |
| POLYFIT | Polynomial Fitting | Least-squares polynomial regression. |
| TRIM | Trimmed Mean MA | Mean after discarding extreme percentiles. |
| WAVG | Weighted Average | Generic weighted mean. |
| WINS | Winsorized Mean MA | Mean with extreme values clamped to percentile bounds. |
| [POLYFIT](polyfit/Polyfit.md) | Polynomial Fitting | Least-squares polynomial regression. |
| [TRIM](trim/Trim.md) | Trimmed Mean MA | Mean after discarding extreme percentiles. |
| [WAVG](wavg/Wavg.md) | Weighted Average | Generic weighted mean. |
| [WINS](wins/Wins.md) | Winsorized Mean MA | Mean with extreme values clamped to percentile bounds. |
lib/trends_FIR/_index.md
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| [BLMA](blma/Blma.md) | Blackman MA | Blackman window. Excellent side-lobe suppression (-58 dB). |
| [BWMA](bwma/Bwma.md) | Bessel-Weighted MA | Bessel window function. Good frequency resolution. |
| [CONV](conv/Conv.md) | Convolution MA | Generic convolution with custom kernel. Building block for others. |
| [CRMA](crma/Crma.md) | Cubic Regression MA | Cubic polynomial regression endpoint. Higher-order trend fit. |
| [DWMA](dwma/Dwma.md) | Double Weighted MA | WMA of WMA. Smoother than single WMA. Triangular-like response. |
| [FWMA](fwma/Fwma.md) | Fibonacci Weighted MA | Fibonacci-number kernel convolution. Golden ratio weighting. |
| [GWMA](gwma/Gwma.md) | Gaussian Weighted MA | Centered Gaussian bell curve. No overshoot. σ controls width. |
| [HAMMA](hamma/Hamma.md) | Hamming MA | Hamming window. -43 dB side lobes. Good general purpose. |
| [HANMA](hanma/Hanma.md) | Hanning MA | Hanning (raised cosine). Zero at edges. Smooth roll-off. |
| [HEND](hend/Hend.md) | Henderson MA | Henderson window. Optimized for trend extraction. Minimal distortion. |
| [HMA](hma/Hma.md) | Hull MA | Reduced lag via weighted average differencing. Can overshoot. |
| [ILRS](ilrs/Ilrs.md) | Integral of Linear Regression Slope | Cumulative linear regression slope. Smooth trend tracking. |
| [KAISER](kaiser/Kaiser.md) | Kaiser Window MA | Kaiser-Bessel window. Adjustable β parameter for sidelobe control. |
| [LANCZOS](lanczos/Lanczos.md) | Lanczos (Sinc) Window MA | Windowed sinc function. Optimal frequency-domain characteristics. |
| [LSMA](lsma/Lsma.md) | Least Squares MA | Linear regression endpoint. Extrapolates trend. |
| [FWMA](fwma/Fwma.md) | Fibonacci Weighted MA | Fibonacci-number kernel convolution. Golden ratio weighting. |
| [NLMA](nlma/Nlma.md) | Non-Lag MA | Damped cosine kernel convolution. Near-zero lag FIR. |
| NYQMA | Nyquist MA | Dual LWMA cascade. Nyquist-compliant FIR smoothing. |
| [NYQMA](nyqma/Nyqma.md) | Nyquist MA | Dual LWMA cascade. Nyquist-compliant FIR smoothing. |
| [PARZEN](parzen/Parzen.md) | Parzen (de la Vallée-Poussin) Window MA | Parzen window. Piecewise cubic. Good spectral leakage control. |
| [PMA](pma/Pma.md) | Predictive Moving Average | Ehlers predictive filter combining WMA cascade with linear extrapolation. |
| [PWMA](pwma/Pwma.md) | Pascal Weighted MA | Pascal's triangle coefficients. Binomial distribution weights. |
| RAIN | Rainbow MA | 10× cascaded SMA. Extreme smoothing via FIR convolution. |
| [QRMA](qrma/Qrma.md) | Quadratic Regression MA | Quadratic polynomial regression endpoint. Captures curvature. |
| [RAIN](rain/Rain.md) | Rainbow MA | 10× cascaded SMA. Extreme smoothing via FIR convolution. |
| [RWMA](rwma/Rwma.md) | Range Weighted MA | Weights derived from bar range. Volatility-adaptive FIR. |
| [SGMA](sgma/Sgma.md) | Savitzky-Golay MA | Polynomial fit. Preserves higher moments. Shape-preserving. |
| [SINEMA](sinema/Sinema.md) | Sine-Weighted MA | Sine wave weighting. Smooth bell-shaped emphasis. |
| [SMA](sma/Sma.md) | Simple MA | Equal weights. Baseline reference. Lag = (N-1)/2. |
| [SP15](sp15/Sp15.md) | Spencer 15-Point MA | Spencer's 15-point symmetric filter. Classic statistical smoothing. |
| [SWMA](swma/Swma.md) | Symmetric Weighted MA | Symmetric linear weights. Equal emphasis on both tails. |
| [TRIMA](trima/Trima.md) | Triangular MA | Triangular weights. SMA of SMA. Emphasizes middle. |
| [TSF](tsf/Tsf.md) | Time Series Forecast | Linear regression projected one step ahead. Extrapolates trend. |
| [TUKEY_W](tukey_w/Tukey_w.md) | Tukey (Tapered Cosine) Window MA | Tukey window with adjustable taper ratio α. Flat-top cosine edges. |
| [WMA](wma/Wma.md) | Weighted MA | Linear weights. Recent prices weighted more. Lag < SMA. |
lib/trends_IIR/_index.md
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| Indicator | Full Name | Description |
| :--- | :--- | :--- |
| [ADXVMA](adxvma/Adxvma.md) | ADX Variable MA | ADX-based adaptive smoothing. Adjusts speed with trend strength. |
| [AHRENS](ahrens/Ahrens.md) | Ahrens MA | Ahrens recursive moving average. Simple IIR with minimal lag. |
| [CORAL](coral/Coral.md) | Coral Trend Filter | Six-stage cascaded EMA with polynomial combination using Constant D parameter for adaptive smoothing. |
| [DECYCLER](decycler/Decycler.md) | Ehlers Decycler | Ehlers Decycler — complementary HP filter that subtracts high-frequency components from price. |
| [DEMA](dema/Dema.md) | Double Exponential MA | Reduces lag by applying double exponential smoothing, enhancing responsiveness while maintaining signal quality. |
| [DSMA](dsma/Dsma.md) | Deviation-Scaled MA | Adaptive IIR filter that adjusts smoothing factor based on market volatility, increasing responsiveness during high-deviation periods. |
| [EMA](ema/Ema.md) | Exponential MA | Applies exponentially decreasing weights to price data, balancing responsiveness and stability. |
| [FRAMA](frama/Frama.md) | Ehlers Fractal Adaptive Moving Average | Adapts smoothing based on fractal dimension analysis, minimizing lag in trends and maximizing smoothing in consolidation. |
| [GDEMA](gdema/Gdema.md) | Generalized Double Exponential MA | Generalized DEMA with configurable volume factor for tunable lag/smoothness trade-off. |
| [HEMA](hema/Hema.md) | Hull Exponential MA | EMA-domain Hull analog using half-life timing and de-lagged EMA cascade. |
| [HOLT](holt/Holt.md) | Holt Exponential Smoothing | Double exponential smoothing with separate level and trend components for adaptive trend-following. |
| [HTIT](htit/Htit.md) | Ehlers Hilbert Transform Instantaneous Trend (also known as HT_TRENDLINE) | Utilizes Hilbert Transform to isolate instantaneous trend component, providing zero-lag trendline with hybrid FIR-in-IIR design. |
@@ -19,7 +22,7 @@ Trend indicators based on Infinite Impulse Response (IIR) filters. Recursive arc
| [JMA](jma/Jma.md) | Jurik MA | Adaptive filter achieving high noise reduction and low phase delay through multi-stage volatility normalization and dynamic parameter optimization. |
| [KAMA](kama/Kama.md) | Kaufman Adaptive MA | Automatically adjusts sensitivity based on market volatility using Efficiency Ratio, balancing responsiveness and stability. |
| [LEMA](lema/Lema.md) | Leader EMA | Dual EMA architecture: primary EMA(source) plus error-correction EMA(source − EMA), reducing lag while maintaining smoothness. |
| LTMA | Linear Trend MA | Linear trend extraction via recursive IIR smoothing. |
| [LTMA](ltma/Ltma.md) | Linear Trend MA | Linear trend extraction via recursive IIR smoothing. |
| [MAMA](mama/Mama.md) | Ehlers MESA Adaptive Moving Average | Applies Hilbert Transform for phase-based adaptation, using dual-line system (MAMA/FAMA) for cycle-sensitive smoothing. |
| [MAVP](mavp/Mavp.md) | Moving Average Variable Period | EMA with dynamically varying period per bar, clamped to configurable min/max range. |
| [MCNMA](mcnma/Mcnma.md) | McNicholl EMA | Six cascaded EMA stages forming inner TEMA + outer TEMA, combined as 2×TEMA(src) − TEMA(TEMA(src)) for superior lag reduction. |
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| [VWAP](vwap/Vwap.md) | Volume Weighted Average Price | Average price weighted by volume. Common execution benchmark and intraday reference. |
| [VWMA](vwma/Vwma.md) | Volume Weighted Moving Average | Moving average where each price point is weighted by its volume over a sliding window. |
| [WAD](wad/Wad.md) | Williams Accumulation/Distribution | Measures cumulative buying/selling pressure using True Range and volume. |
| MARKETFI | Market Facilitation Index | (High − Low) / Volume. Measures price efficiency per unit volume. |