diff --git a/lib/channels/accbands/accbands.md b/lib/channels/accbands/accbands.md index 3c1cdd91..55e794c6 100644 --- a/lib/channels/accbands/accbands.md +++ b/lib/channels/accbands/accbands.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [accbands.pine](accbands.pine) | -- Acceleration Bands construct a volatility envelope using the intra-bar high-low range rather than close-to-close standard deviation, creating chann... +- Acceleration Bands construct a volatility envelope using the intra-bar high-low range rather than close-to-close standard deviation, creating channels that accommodate the full price excursion of the underlying asset. - **Similar:** [BBands](../bbands/bbands.md), [KC](../kc/kc.md) | **Complementary:** ADX for trend strength | **Trading note:** Wider than Bollinger Bands; effective for breakout trading using high-low range volatility. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/apchannel/apchannel.md b/lib/channels/apchannel/apchannel.md index 3b274afe..1cb5b13b 100644 --- a/lib/channels/apchannel/apchannel.md +++ b/lib/channels/apchannel/apchannel.md @@ -12,7 +12,7 @@ | **Warmup** | `⌈3/alpha⌉` bars (default 15) | | **PineScript** | [apchannel.pine](apchannel.pine) | -- APCHANNEL applies exponential smoothing independently to price highs and lows, creating a dynamic envelope that "remembers" significant extremes wh... +- APCHANNEL applies exponential smoothing independently to price highs and lows, creating a dynamic envelope that "remembers" significant extremes while gradually fading their influence over time. - **Similar:** [RegChannel](../regchannel/regchannel.md) | **Complementary:** Volume for breakout confirmation | **Trading note:** Based on pivot points; useful for identifying median price paths and potential support/resistance. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/apz/apz.md b/lib/channels/apz/apz.md index c56d3fd6..dbe61202 100644 --- a/lib/channels/apz/apz.md +++ b/lib/channels/apz/apz.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [apz.pine](apz.pine) | -- APZ constructs a volatility-adaptive envelope using double-smoothed exponential moving averages with an aggressive smoothing factor derived from $\... +- APZ constructs a volatility-adaptive envelope using double-smoothed exponential moving averages with an aggressive smoothing factor derived from $\sqrt{\text{period}}$, making it significantly faster than standard EMA-based channels. - **Similar:** [BBands](../bbands/bbands.md), [KC](../kc/kc.md) | **Complementary:** RSI for overbought/oversold confirmation | **Trading note:** EMA-based deviation adapts faster than standard deviation bands; responsive to recent volatility changes. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/decaychannel/decaychannel.md b/lib/channels/decaychannel/decaychannel.md index b72da65c..3b3a1caa 100644 --- a/lib/channels/decaychannel/decaychannel.md +++ b/lib/channels/decaychannel/decaychannel.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [decaychannel.pine](decaychannel.pine) | -- Decay Channel combines the absolute price boundaries of Donchian Channels with exponential decay toward the midpoint, creating an envelope that exp... +- Decay Channel combines the absolute price boundaries of Donchian Channels with exponential decay toward the midpoint, creating an envelope that expands instantly on new volatility but contracts smoothly during consolidation. - **Similar:** [DC](../dc/dc.md), [PC](../pc/pc.md) | **Complementary:** Trend indicators like ADX | **Trading note:** Bands decay toward price when no new extremes form, reducing lag compared to traditional channels. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/fcb/fcb.md b/lib/channels/fcb/fcb.md index 980238fb..1f9673e9 100644 --- a/lib/channels/fcb/fcb.md +++ b/lib/channels/fcb/fcb.md @@ -12,7 +12,7 @@ | **Warmup** | `period + 2` bars | | **PineScript** | [fcb.pine](fcb.pine) | -- Fractal Chaos Bands filter raw price action through Bill Williams' fractal detection logic, tracking the highest confirmed fractal high and lowest ... +- Fractal Chaos Bands filter raw price action through Bill Williams' fractal detection logic, tracking the highest confirmed fractal high and lowest confirmed fractal low over a lookback period. - **Similar:** [DC](../dc/dc.md), [PC](../pc/pc.md) | **Complementary:** Williams Fractals for additional confirmation | **Trading note:** Based on Bill Williams' fractal theory; bands update only on fractal pivots, creating a staircase pattern. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/jbands/jbands.md b/lib/channels/jbands/jbands.md index 820a1251..887c0be6 100644 --- a/lib/channels/jbands/jbands.md +++ b/lib/channels/jbands/jbands.md @@ -12,7 +12,7 @@ | **Warmup** | `⌈20 + 80 × period^0.36⌉` bars | | **PineScript** | [Jbands.pine](Jbands.pine) | -- JBANDS expose the internal adaptive envelope mechanism of the Jurik Moving Average (JMA), producing asymmetric bands that snap instantly to new pri... +- JBANDS expose the internal adaptive envelope mechanism of the Jurik Moving Average (JMA), producing asymmetric bands that snap instantly to new price extremes and decay exponentially during consolidation. - **Similar:** [BBands](../bbands/bbands.md), [KC](../kc/kc.md) | **Complementary:** Momentum oscillators for reversal timing | **Trading note:** Uses JMA (Jurik Moving Average) as center line for smoother, lower-lag bands compared to standard Bollinger. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/regchannel/regchannel.md b/lib/channels/regchannel/regchannel.md index 80fb3759..e76fc49e 100644 --- a/lib/channels/regchannel/regchannel.md +++ b/lib/channels/regchannel/regchannel.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [regchannel.pine](regchannel.pine) | -- Linear Regression Channel plots a best-fit line through price data over a specified period with parallel bands at a configurable standard deviation... +- Linear Regression Channel plots a best-fit line through price data over a specified period with parallel bands at a configurable standard deviation of residuals. - **Similar:** [SDChannel](../sdchannel/sdchannel.md), [BBands](../bbands/bbands.md) | **Complementary:** R-squared for trend strength | **Trading note:** Linear regression channel; mean-reversion trades at band extremes. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/sdchannel/sdchannel.md b/lib/channels/sdchannel/sdchannel.md index 579bc27a..a71214d0 100644 --- a/lib/channels/sdchannel/sdchannel.md +++ b/lib/channels/sdchannel/sdchannel.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [sdchannel.pine](sdchannel.pine) | -- Standard Deviation Channel plots a linear regression line through price data with parallel bands at a specified number of standard deviations of re... +- Standard Deviation Channel plots a linear regression line through price data with parallel bands at a specified number of standard deviations of residuals above and below. - **Similar:** [BBands](../bbands/bbands.md), [RegChannel](../regchannel/regchannel.md) | **Complementary:** LinReg slope for trend direction | **Trading note:** Standard deviation channel around linear regression; tighter than Bollinger for trending markets. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/starchannel/starchannel.md b/lib/channels/starchannel/starchannel.md index 06bf82f5..77c266c6 100644 --- a/lib/channels/starchannel/starchannel.md +++ b/lib/channels/starchannel/starchannel.md @@ -12,7 +12,7 @@ | **Warmup** | `Math.Max(period, effectiveAtrPeriod)` bars | | **PineScript** | [starchannel.pine](starchannel.pine) | -- Stoller Average Range Channel creates a volatility-adaptive price envelope using Average True Range (ATR) to determine band width around a simple m... +- Stoller Average Range Channel creates a volatility-adaptive price envelope using Average True Range (ATR) to determine band width around a simple moving average centerline. - **Similar:** [KC](../kc/kc.md), [ATRBands](../atrbands/atrbands.md) | **Complementary:** ADX for trend confirmation | **Trading note:** Stoller Average Range Channel; ATR-based bands around a moving average. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/stbands/stbands.md b/lib/channels/stbands/stbands.md index 1162f994..b975526d 100644 --- a/lib/channels/stbands/stbands.md +++ b/lib/channels/stbands/stbands.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [stbands.pine](stbands.pine) | -- Super Trend Bands provide ATR-based dynamic support and resistance levels with asymmetric ratchet logic: the upper band only tightens downward duri... +- Super Trend Bands provide ATR-based dynamic support and resistance levels with asymmetric ratchet logic: the upper band only tightens downward during downtrends, and the lower band only tightens upward during uptrends. - **Similar:** [BBands](../bbands/bbands.md), [KC](../kc/kc.md) | **Complementary:** Volume for breakout validation | **Trading note:** Stoller bands use ATR multiplier instead of standard deviation. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/ttm_lrc/TtmLrc.md b/lib/channels/ttm_lrc/TtmLrc.md index 80e43a7e..b9a17025 100644 --- a/lib/channels/ttm_lrc/TtmLrc.md +++ b/lib/channels/ttm_lrc/TtmLrc.md @@ -11,7 +11,7 @@ | **Output range** | Tracks input | | **Warmup** | `period` bars | -- TTM Linear Regression Channel plots a least-squares regression line through price data with dual standard deviation bands at $\pm 1\sigma$ and $\pm... +- TTM Linear Regression Channel plots a least-squares regression line through price data with dual standard deviation bands at $\pm 1\sigma$ and $\pm 2\sigma$. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. TTM Linear Regression Channel plots a least-squares regression line through price data with dual standard deviation bands at $\pm 1\sigma$ and $\pm 2\sigma$. Developed by John Carter as part of his TTM (Trade The Markets) indicator suite, it extends the standard regression channel by providing two band levels that create statistically meaningful trading zones. The algorithm is identical to REGCHANNEL/SDCHANNEL in its regression and residual computation, but uses a longer default period (100) and emits four bands instead of two. diff --git a/lib/channels/ubands/ubands.md b/lib/channels/ubands/ubands.md index 7215d1d0..06072d67 100644 --- a/lib/channels/ubands/ubands.md +++ b/lib/channels/ubands/ubands.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [ubands.pine](ubands.pine) | -- Ehlers Ultimate Bands replace the conventional SMA foundation of Bollinger Bands with the Ultrasmooth Filter (USF), a 2-pole IIR filter with zero o... +- Ehlers Ultimate Bands replace the conventional SMA foundation of Bollinger Bands with the Ultrasmooth Filter (USF), a 2-pole IIR filter with zero overshoot and minimal lag. - **Similar:** [BBands](../bbands/bbands.md), [SDChannel](../sdchannel/sdchannel.md) | **Complementary:** RSI for overbought/oversold | **Trading note:** Uncertainty bands; statistical confidence intervals around a moving average. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/uchannel/uchannel.md b/lib/channels/uchannel/uchannel.md index cfd60519..45fbd9c7 100644 --- a/lib/channels/uchannel/uchannel.md +++ b/lib/channels/uchannel/uchannel.md @@ -12,7 +12,7 @@ | **Warmup** | `Math.Max(strPeriod, centerPeriod)` bars | | **PineScript** | [uchannel.pine](uchannel.pine) | -- Ehlers Ultimate Channel applies the Ultrasmooth Filter (USF) twice: once to the close price for the centerline and once to True Range for band widt... +- Ehlers Ultimate Channel applies the Ultrasmooth Filter (USF) twice: once to the close price for the centerline and once to True Range for band width, creating a channel where both the trend estimate and the volatility measure share the same low-lag, zero-overshoot filter characteristics. - **Similar:** [DC](../dc/dc.md), [PC](../pc/pc.md) | **Complementary:** Volume for breakout confirmation | **Trading note:** Upper/lower channel based on recent price extremes. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/vwapbands/vwapbands.md b/lib/channels/vwapbands/vwapbands.md index bc9880cb..1f7a216a 100644 --- a/lib/channels/vwapbands/vwapbands.md +++ b/lib/channels/vwapbands/vwapbands.md @@ -12,7 +12,7 @@ | **Warmup** | `2` bars | | **PineScript** | [vwapbands.pine](vwapbands.pine) | -- VWAP Bands extend the Volume Weighted Average Price with dual standard deviation bands at $\pm 1\sigma$ and $\pm 2\sigma$ levels, creating a five-l... +- VWAP Bands extend the Volume Weighted Average Price with dual standard deviation bands at $\pm 1\sigma$ and $\pm 2\sigma$ levels, creating a five-line channel system anchored to volume-weighted fair value. - **Similar:** [VwapSD](../vwapsd/vwapsd.md), [BBands](../bbands/bbands.md) | **Complementary:** Volume profile | **Trading note:** VWAP with deviation bands; institutional benchmark for intraday fair value. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/channels/vwapsd/vwapsd.md b/lib/channels/vwapsd/vwapsd.md index b796e78e..146c5a4f 100644 --- a/lib/channels/vwapsd/vwapsd.md +++ b/lib/channels/vwapsd/vwapsd.md @@ -12,7 +12,7 @@ | **Warmup** | `2` bars | | **PineScript** | [vwapsd.pine](vwapsd.pine) | -- VWAP with Standard Deviation Bands combines the Volume Weighted Average Price with a single configurable standard deviation band pair, providing a ... +- VWAP with Standard Deviation Bands combines the Volume Weighted Average Price with a single configurable standard deviation band pair, providing a simpler alternative to VWAPBANDS (which uses dual $\pm 1\sigma$ and $\pm 2\sigma$ levels). - **Similar:** [VwapBands](../vwapbands/vwapbands.md), [BBands](../bbands/bbands.md) | **Complementary:** Cumulative volume delta | **Trading note:** VWAP standard deviation bands; 1σ/2σ/3σ levels used for institutional mean-reversion. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/core/midprice/Midprice.md b/lib/core/midprice/Midprice.md index dadf7576..600a8367 100644 --- a/lib/core/midprice/Midprice.md +++ b/lib/core/midprice/Midprice.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [midprice.pine](midprice.pine) | -- MIDPRICE computes the center of a rolling price channel by averaging the highest High and lowest Low over the past $N$ bars: $(\text{Highest}(H, N)... +- MIDPRICE computes the center of a rolling price channel by averaging the highest High and lowest Low over the past $N$ bars: $(\text{Highest}(H, N) + \text{Lowest}(L, N)) \times 0.5$. - **Similar:** [MidPoint](../midpoint/Midpoint.md), [TypPrice](../typprice/typprice.md) | **Trading note:** (High+Low)/2; common price proxy for indicators avoiding close bias. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/cycles/ccor/Ccor.md b/lib/cycles/ccor/Ccor.md index cbac74aa..3619bcee 100644 --- a/lib/cycles/ccor/Ccor.md +++ b/lib/cycles/ccor/Ccor.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [ccor.pine](ccor.pine) | -- CCOR extracts cycle phase by computing Pearson correlation of a price window against cosine (Real) and negative-sine (Imaginary) reference waves of... +- CCOR extracts cycle phase by computing Pearson correlation of a price window against cosine (Real) and negative-sine (Imaginary) reference waves of a presumed fixed period, converting the resulting phasor to an angle with a monotonic constraint, and classifying the market state as trending or cycling based on the angle rate of change. - **Similar:** [Ccyc](../ccyc/Ccyc.md), [CG](../cg/cg.md) | **Complementary:** Hilbert Transform for phase analysis | **Trading note:** Cycle correlation; detects dominant cycle period in price data. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/cycles/ccyc/Ccyc.md b/lib/cycles/ccyc/Ccyc.md index 0ea11a68..a6a5131e 100644 --- a/lib/cycles/ccyc/Ccyc.md +++ b/lib/cycles/ccyc/Ccyc.md @@ -12,7 +12,7 @@ | **Warmup** | `7` bars | | **PineScript** | [ccyc.pine](ccyc.pine) | -- CCYC isolates the dominant cycle component from price data using a 2-pole high-pass IIR filter applied to a 4-tap FIR-smoothed input, producing an ... +- CCYC isolates the dominant cycle component from price data using a 2-pole high-pass IIR filter applied to a 4-tap FIR-smoothed input, producing an oscillator that strips trend while preserving cyclical content with minimal lag. - **Similar:** [Ccor](../ccor/Ccor.md), [CG](../cg/cg.md) | **Complementary:** EBSW for trend/cycle mode | **Trading note:** Cyber Cycle; Ehlers' bandpass approach to isolate dominant market cycles. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/cycles/dsp/dsp.md b/lib/cycles/dsp/dsp.md index 76c2a9b0..3a29eae7 100644 --- a/lib/cycles/dsp/dsp.md +++ b/lib/cycles/dsp/dsp.md @@ -12,7 +12,7 @@ | **Warmup** | `slowPeriod * 3` bars | | **PineScript** | [dsp.pine](dsp.pine) | -- DSP creates a zero-centered oscillator by subtracting a half-cycle EMA from a quarter-cycle EMA, isolating the dominant cyclical component of price... +- DSP creates a zero-centered oscillator by subtracting a half-cycle EMA from a quarter-cycle EMA, isolating the dominant cyclical component of price while cancelling longer-term trends. - **Similar:** [SSFDSP](../ssfdsp/Ssfdsp.md), [Ccyc](../ccyc/Ccyc.md) | **Complementary:** ATR for volatility filter | **Trading note:** Digital Signal Processing filter; separates signal from noise in price data. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/cycles/ebsw/ebsw.md b/lib/cycles/ebsw/ebsw.md index 507ec5c0..90a4e67f 100644 --- a/lib/cycles/ebsw/ebsw.md +++ b/lib/cycles/ebsw/ebsw.md @@ -12,7 +12,7 @@ | **Warmup** | `Math.Max(hpLength, ssfLength) + 3` bars (default 43) | | **PineScript** | [ebsw.pine](ebsw.pine) | -- EBSW is a refined cycle oscillator that combines a high-pass filter (trend removal), a Super-Smoother filter (noise removal), and Automatic Gain Co... +- EBSW is a refined cycle oscillator that combines a high-pass filter (trend removal), a Super-Smoother filter (noise removal), and Automatic Gain Control to produce a normalized $[-1, +1]$ output representing the current position within the dominant market cycle. - **Similar:** [HT_TrendMode](../../dynamics/ht_trendmode/HtTrendmode.md), [VHF](../../dynamics/vhf/Vhf.md) | **Complementary:** ADX for trend strength | **Trading note:** Even Better Sine Wave; classifies market as trending or cycling. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/cycles/homod/homod.md b/lib/cycles/homod/homod.md index 57d3ee24..e1e1e027 100644 --- a/lib/cycles/homod/homod.md +++ b/lib/cycles/homod/homod.md @@ -12,7 +12,7 @@ | **Warmup** | `maxPeriod * 2` bars (default 100) | | **PineScript** | [homod.pine](homod.pine) | -- HOMOD estimates the dominant cycle period of a market using homodyne mixing, a technique from radio engineering where a signal is multiplied by a d... +- HOMOD estimates the dominant cycle period of a market using homodyne mixing, a technique from radio engineering where a signal is multiplied by a delayed copy of itself to expose the angular phase change between samples. - **Similar:** [HT_Phasor](../ht_phasor/HtPhasor.md), [HT_Sine](../ht_sine/HtSine.md) | **Complementary:** Cycle period for context | **Trading note:** Homodyne discriminator; Ehlers' phase detection for cycle turning points. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/cycles/ssfdsp/Ssfdsp.md b/lib/cycles/ssfdsp/Ssfdsp.md index 36ef593e..0102d46d 100644 --- a/lib/cycles/ssfdsp/Ssfdsp.md +++ b/lib/cycles/ssfdsp/Ssfdsp.md @@ -12,7 +12,7 @@ | **Warmup** | `slowPeriod * 2` bars | | **PineScript** | [ssfdsp.pine](ssfdsp.pine) | -- SSFDSP isolates the dominant cycle by subtracting a half-cycle Super-Smoother from a quarter-cycle Super-Smoother, producing a zero-centered oscill... +- SSFDSP isolates the dominant cycle by subtracting a half-cycle Super-Smoother from a quarter-cycle Super-Smoother, producing a zero-centered oscillator with superior noise rejection compared to the EMA-based DSP. - **Similar:** [DSP](../dsp/dsp.md), [SSF2](../../filters/ssf2/Ssf2.md) | **Complementary:** Roofing filter for preprocessing | **Trading note:** Super Smoother with DSP; combines Ehlers' smoothing with signal processing. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/adx/Adx.md b/lib/dynamics/adx/Adx.md index 6c35bc45..bf3b6fee 100644 --- a/lib/dynamics/adx/Adx.md +++ b/lib/dynamics/adx/Adx.md @@ -12,7 +12,7 @@ | **Warmup** | `period * 2` bars | | **PineScript** | [adx.pine](adx.pine) | -- The Average Directional Index is the industry-standard measure of trend strength, ignoring direction entirely to focus on the velocity of price exp... +- The Average Directional Index is the industry-standard measure of trend strength, ignoring direction entirely to focus on the velocity of price expansion. - **Similar:** [ADXR](../adxr/Adxr.md), [DX](../dx/Dx.md) | **Complementary:** Moving averages for direction | **Trading note:** Wilder's trend strength gauge; >25 trending, <20 ranging. Does not indicate direction. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/adxr/Adxr.md b/lib/dynamics/adxr/Adxr.md index 022517d3..9d177c0c 100644 --- a/lib/dynamics/adxr/Adxr.md +++ b/lib/dynamics/adxr/Adxr.md @@ -12,7 +12,7 @@ | **Warmup** | `adx.WarmupPeriod + period - 1` bars | | **PineScript** | [adxr.pine](adxr.pine) | -- The Average Directional Movement Rating is a smoothed version of ADX that dampens short-term fluctuations in trend strength by averaging the curren... +- The Average Directional Movement Rating is a smoothed version of ADX that dampens short-term fluctuations in trend strength by averaging the current ADX with a historical ADX value. - **Similar:** [ADX](../adx/Adx.md), [DX](../dx/Dx.md) | **Complementary:** Aroon for trend timing | **Trading note:** Smoothed ADX; slower but fewer false signals. Used in Wilder's Directional Movement System. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/alligator/Alligator.md b/lib/dynamics/alligator/Alligator.md index 35d21037..a7cec95f 100644 --- a/lib/dynamics/alligator/Alligator.md +++ b/lib/dynamics/alligator/Alligator.md @@ -12,7 +12,7 @@ | **Warmup** | `Math.Max(Math.Max(jawPeriod, teethPeriod), lipsPeriod)` bars | | **PineScript** | [alligator.pine](alligator.pine) | -- The Williams Alligator is a trend-following system that uses three Smoothed Moving Averages (SMMA/RMA) with different periods and forward display o... +- The Williams Alligator is a trend-following system that uses three Smoothed Moving Averages (SMMA/RMA) with different periods and forward display offsets to visualize market phases. - **Similar:** [AMAT](../amat/Amat.md), [Ichimoku](../ichimoku/Ichimoku.md) | **Complementary:** Fractal indicator for entry signals | **Trading note:** Bill Williams' Alligator; three displaced SMAs (Jaw/Teeth/Lips) indicate trend state. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/amat/Amat.md b/lib/dynamics/amat/Amat.md index f9eb6710..57ca316e 100644 --- a/lib/dynamics/amat/Amat.md +++ b/lib/dynamics/amat/Amat.md @@ -12,7 +12,7 @@ | **Warmup** | `slowPeriod` bars | | **PineScript** | [amat.pine](amat.pine) | -- The Archer Moving Averages Trends indicator is a triple-confirmation trend identification system that uses dual EMAs to produce discrete directiona... +- The Archer Moving Averages Trends indicator is a triple-confirmation trend identification system that uses dual EMAs to produce discrete directional signals (+1 bullish, -1 bearish, 0 neutral). - **Similar:** [Alligator](../alligator/Alligator.md), [Ichimoku](../ichimoku/Ichimoku.md) | **Complementary:** ADX for trend strength | **Trading note:** Archer Moving Average Trend; uses MA crossover zones to classify trend phases. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/aroon/Aroon.md b/lib/dynamics/aroon/Aroon.md index 41c7d973..6f7d918a 100644 --- a/lib/dynamics/aroon/Aroon.md +++ b/lib/dynamics/aroon/Aroon.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [aroon.pine](aroon.pine) | -- The Aroon indicator measures the temporal freshness of price extremes, answering not "how much did price move?" but "how long ago did it make a new... +- The Aroon indicator measures the temporal freshness of price extremes, answering not "how much did price move?" but "how long ago did it make a new high or low?" Aroon Up tracks the recency of the highest high within the lookback window; Aroon Down tracks the recency of the lowest low. - **Similar:** [AroonOsc](../aroonosc/AroonOsc.md), [ADX](../adx/Adx.md) | **Complementary:** Volume for confirmation | **Trading note:** Aroon Up/Down measures time since highest high or lowest low; 100 = new high/low this period. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/dmx/Dmx.md b/lib/dynamics/dmx/Dmx.md index fb36c7c7..0c633dd9 100644 --- a/lib/dynamics/dmx/Dmx.md +++ b/lib/dynamics/dmx/Dmx.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [dmx.pine](dmx.pine) | -- The DMX is Mark Jurik's modernized overhaul of Wilder's Directional Movement system, replacing the sluggish RMA smoothing with the Jurik Moving Ave... +- The DMX is Mark Jurik's modernized overhaul of Wilder's Directional Movement system, replacing the sluggish RMA smoothing with the Jurik Moving Average (JMA) to achieve faster trend detection with superior noise rejection. - **Similar:** [ADX](../adx/Adx.md), [DX](../dx/Dx.md) | **Complementary:** +DI/-DI for direction | **Trading note:** Directional Movement extended; enhanced version of Wilder's DM system. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/ghla/Ghla.md b/lib/dynamics/ghla/Ghla.md index 10e4c618..7c917913 100644 --- a/lib/dynamics/ghla/Ghla.md +++ b/lib/dynamics/ghla/Ghla.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [ghla.pine](ghla.pine) | -- The Gann High-Low Activator (GHLA) is a trend-following stop/reversal indicator that alternates between the Simple Moving Average of Highs and the ... +- The Gann High-Low Activator (GHLA) is a trend-following stop/reversal indicator that alternates between the Simple Moving Average of Highs and the Simple Moving Average of Lows based on a three-state crossover rule. - **Similar:** [Super](../super/Super.md), [SAR](../../reversals/sar/Sar.md) | **Complementary:** ATR for stop placement | **Trading note:** Gann High-Low Activator; trend-following stop based on prior period's median. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/ht_trendmode/HtTrendmode.md b/lib/dynamics/ht_trendmode/HtTrendmode.md index a7456883..5ab08b1e 100644 --- a/lib/dynamics/ht_trendmode/HtTrendmode.md +++ b/lib/dynamics/ht_trendmode/HtTrendmode.md @@ -12,7 +12,7 @@ | **Warmup** | `LOOKBACK` bars | | **PineScript** | [ht_trendmode.pine](ht_trendmode.pine) | -- The Hilbert Transform Trend Mode indicator is a binary regime classifier that determines whether price action is dominated by trending behavior (ou... +- The Hilbert Transform Trend Mode indicator is a binary regime classifier that determines whether price action is dominated by trending behavior (output = 1) or cyclical/mean-reverting behavior (output = 0). - No configurable parameters; computation is stateless per bar. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/ichimoku/Ichimoku.md b/lib/dynamics/ichimoku/Ichimoku.md index cf8a010d..92a6c1e5 100644 --- a/lib/dynamics/ichimoku/Ichimoku.md +++ b/lib/dynamics/ichimoku/Ichimoku.md @@ -12,7 +12,7 @@ | **Warmup** | `maxPeriod` bars | | **PineScript** | [ichimoku.pine](ichimoku.pine) | -- Ichimoku Kinko Hyo ("One Glance Equilibrium Chart") is a comprehensive trend-following system that provides five distinct components revealing tren... +- Ichimoku Kinko Hyo ("One Glance Equilibrium Chart") is a comprehensive trend-following system that provides five distinct components revealing trend direction, momentum, support/resistance levels, and potential future price zones simultaneously. - **Similar:** [Alligator](../alligator/Alligator.md), [AMAT](../amat/Amat.md) | **Complementary:** Volume for cloud breakout confirmation | **Trading note:** Five-line system: Tenkan, Kijun, Senkou A/B, Chikou. Cloud defines support/resistance zones. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/impulse/Impulse.md b/lib/dynamics/impulse/Impulse.md index 98180abc..e51364e3 100644 --- a/lib/dynamics/impulse/Impulse.md +++ b/lib/dynamics/impulse/Impulse.md @@ -11,7 +11,7 @@ | **Output range** | Varies (see docs) | | **Warmup** | `Math.Max(emaPeriod, macdSlow) + macdSignal - 1` bars (default 34) | -- The Elder Impulse System combines a 13-period EMA (trend inertia) with the MACD(12,26,9) histogram (momentum acceleration) to classify each bar as ... +- The Elder Impulse System combines a 13-period EMA (trend inertia) with the MACD(12,26,9) histogram (momentum acceleration) to classify each bar as bullish (+1), bearish (-1), or neutral (0). - Validated against TA-Lib, Skender, and Tulip reference implementations where available. The Elder Impulse System combines a 13-period EMA (trend inertia) with the MACD(12,26,9) histogram (momentum acceleration) to classify each bar as bullish (+1), bearish (-1), or neutral (0). Both EMA slope and histogram slope must agree for a directional signal; disagreement forces neutral. The system functions as a permission filter rather than a signal generator, requiring 34 bars warmup and running at O(1) per bar through composition of two child indicators. diff --git a/lib/dynamics/pfe/Pfe.md b/lib/dynamics/pfe/Pfe.md index 3959e3ac..0d8d5702 100644 --- a/lib/dynamics/pfe/Pfe.md +++ b/lib/dynamics/pfe/Pfe.md @@ -12,7 +12,7 @@ | **Warmup** | `period + 1` bars | | **PineScript** | [pfe.pine](pfe.pine) | -- Polarized Fractal Efficiency (PFE) quantifies trend strength by comparing the Euclidean distance a price series actually travels bar-to-bar against... +- Polarized Fractal Efficiency (PFE) quantifies trend strength by comparing the Euclidean distance a price series actually travels bar-to-bar against the straight-line distance between the endpoints over the same window. - **Similar:** [ADX](../adx/Adx.md), [VHF](../vhf/Vhf.md) | **Complementary:** Moving average for trend direction | **Trading note:** Polarized Fractal Efficiency; measures how efficiently price travels. ±100 scale. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/qstick/Qstick.md b/lib/dynamics/qstick/Qstick.md index 7e89b01d..1c17fe34 100644 --- a/lib/dynamics/qstick/Qstick.md +++ b/lib/dynamics/qstick/Qstick.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [qstick.pine](qstick.pine) | -- The Qstick indicator, developed by Tushar Chande, computes a moving average of the close-minus-open difference over a lookback period, quantifying ... +- The Qstick indicator, developed by Tushar Chande, computes a moving average of the close-minus-open difference over a lookback period, quantifying whether bars are predominantly bullish or bearish. - **Similar:** [CMO](../../momentum/cmo/Cmo.md), [Impulse](../impulse/Impulse.md) | **Complementary:** Volume for confirmation | **Trading note:** Qstick averages (Close−Open); positive = buying pressure, negative = selling pressure. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/ravi/Ravi.md b/lib/dynamics/ravi/Ravi.md index bf322317..e700b768 100644 --- a/lib/dynamics/ravi/Ravi.md +++ b/lib/dynamics/ravi/Ravi.md @@ -12,7 +12,7 @@ | **Warmup** | `longPeriod` bars (default 65) | | **PineScript** | [ravi.pine](ravi.pine) | -- RAVI (Range Action Verification Index) measures trend strength by computing the absolute percentage divergence between a short-period SMA and a lon... +- RAVI (Range Action Verification Index) measures trend strength by computing the absolute percentage divergence between a short-period SMA and a long-period SMA. - **Similar:** [ADX](../adx/Adx.md), [Chop](../chop/Chop.md) | **Complementary:** Moving average crossover for entries | **Trading note:** Range Action Verification Index; ratio of fast/slow MA difference to slow MA. Trend filter. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/super/Super.md b/lib/dynamics/super/Super.md index 0f3e40eb..3a187e35 100644 --- a/lib/dynamics/super/Super.md +++ b/lib/dynamics/super/Super.md @@ -12,7 +12,7 @@ | **Warmup** | `> period + 1` bars | | **PineScript** | [super.pine](super.pine) | -- SuperTrend is a trend-following overlay that uses ATR-scaled bands around the HL2 midpoint, switching between upper and lower bands based on close ... +- SuperTrend is a trend-following overlay that uses ATR-scaled bands around the HL2 midpoint, switching between upper and lower bands based on close price breakouts. - **Similar:** [SAR](../../reversals/sar/Sar.md), [Ghla](../ghla/Ghla.md) | **Complementary:** ADX for trend strength | **Trading note:** SuperTrend; ATR-based trailing stop that flips direction. Popular in crypto and forex. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/ttm_squeeze/TtmSqueeze.md b/lib/dynamics/ttm_squeeze/TtmSqueeze.md index 42eeb1e6..230a3c26 100644 --- a/lib/dynamics/ttm_squeeze/TtmSqueeze.md +++ b/lib/dynamics/ttm_squeeze/TtmSqueeze.md @@ -11,7 +11,7 @@ | **Output range** | Varies (see docs) | | **Warmup** | `Math.Max(Math.Max(bbPeriod, kcPeriod), momPeriod)` bars | -- John Carter's TTM Squeeze detects low-volatility compression by comparing Bollinger Band width against Keltner Channel width: when BB fits inside K... +- John Carter's TTM Squeeze detects low-volatility compression by comparing Bollinger Band width against Keltner Channel width: when BB fits inside KC, a "squeeze" is on, signaling imminent breakout. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. John Carter's TTM Squeeze detects low-volatility compression by comparing Bollinger Band width against Keltner Channel width: when BB fits inside KC, a "squeeze" is on, signaling imminent breakout. The momentum component uses linear regression of price deviation from the Donchian midline to indicate direction. The indicator outputs a boolean squeeze state plus a continuous momentum histogram, requiring BB(20,2.0) and KC(20,1.5) as default parameters with a combined warmup of 20 bars. diff --git a/lib/dynamics/vhf/Vhf.md b/lib/dynamics/vhf/Vhf.md index 1486412e..1961e5b9 100644 --- a/lib/dynamics/vhf/Vhf.md +++ b/lib/dynamics/vhf/Vhf.md @@ -12,7 +12,7 @@ | **Warmup** | `period + 1` bars | | **PineScript** | [vhf.pine](vhf.pine) | -- VHF (Vertical Horizontal Filter) measures trend strength by dividing the price range over $N$ periods by the total absolute bar-to-bar path distanc... +- VHF (Vertical Horizontal Filter) measures trend strength by dividing the price range over $N$ periods by the total absolute bar-to-bar path distance over the same window. - **Similar:** [ADX](../adx/Adx.md), [Chop](../chop/Chop.md) | **Complementary:** Moving averages for direction | **Trading note:** Vertical Horizontal Filter; ratio of price range to cumulative movement. High = trending. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/dynamics/vortex/Vortex.md b/lib/dynamics/vortex/Vortex.md index 9ad92921..9765098a 100644 --- a/lib/dynamics/vortex/Vortex.md +++ b/lib/dynamics/vortex/Vortex.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [vortex.pine](vortex.pine) | -- The Vortex Indicator measures upward and downward trend momentum by computing the ratio of positive and negative vortex movements to true range ove... +- The Vortex Indicator measures upward and downward trend momentum by computing the ratio of positive and negative vortex movements to true range over a rolling window. - **Similar:** [ADX](../adx/Adx.md), [Aroon](../aroon/Aroon.md) | **Complementary:** Volume for confirmation | **Trading note:** VI+ and VI− oscillate around 1.0; crossovers signal trend changes. Inspired by Viktor Schauberger's vortex theory. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/errors/maape/Maape.md b/lib/errors/maape/Maape.md index da53a843..f1f772de 100644 --- a/lib/errors/maape/Maape.md +++ b/lib/errors/maape/Maape.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [maape.pine](maape.pine) | -- Mean Arctangent Absolute Percentage Error (MAAPE) transforms percentage errors through the arctangent function, naturally bounding the metric betwe... +- Mean Arctangent Absolute Percentage Error (MAAPE) transforms percentage errors through the arctangent function, naturally bounding the metric between 0 and π/2. - **Similar:** [MAPE](../mape/Mape.md), [SMAPE](../smape/Smape.md) | **Trading note:** Mean Arctangent Absolute Percentage Error; bounded and symmetric, handles zero values unlike MAPE. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/errors/mapd/Mapd.md b/lib/errors/mapd/Mapd.md index 16ef2611..1d0142be 100644 --- a/lib/errors/mapd/Mapd.md +++ b/lib/errors/mapd/Mapd.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [mapd.pine](mapd.pine) | -- Mean Absolute Percentage Deviation (MAPD) measures the average absolute percentage difference between actual and predicted values, using the predic... +- Mean Absolute Percentage Deviation (MAPD) measures the average absolute percentage difference between actual and predicted values, using the predicted value as the denominator. - **Similar:** [MAPE](../mape/Mape.md), [WMAPE](../wmape/Wmape.md) | **Trading note:** Mean Absolute Percentage Deviation; total absolute error divided by total actual values. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/errors/mase/Mase.md b/lib/errors/mase/Mase.md index 90030a08..f9fcb0ca 100644 --- a/lib/errors/mase/Mase.md +++ b/lib/errors/mase/Mase.md @@ -12,7 +12,7 @@ | **Warmup** | `period + 1` bars | | **PineScript** | [mase.pine](mase.pine) | -- Mean Absolute Scaled Error (MASE) normalizes forecast errors by the average error of a naive "random walk" forecast (using the previous value as th... +- Mean Absolute Scaled Error (MASE) normalizes forecast errors by the average error of a naive "random walk" forecast (using the previous value as the prediction). - **Similar:** [MAE](../mae/Mae.md), [RAE](../rae/Rae.md) | **Trading note:** Mean Absolute Scaled Error; compares forecast to naïve random-walk baseline. <1 = better than naïve. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/errors/rae/Rae.md b/lib/errors/rae/Rae.md index 82f4903c..7273e59e 100644 --- a/lib/errors/rae/Rae.md +++ b/lib/errors/rae/Rae.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [rae.pine](rae.pine) | -- Relative Absolute Error (RAE) measures the total absolute error of predictions relative to the total absolute error of a simple baseline predictor ... +- Relative Absolute Error (RAE) measures the total absolute error of predictions relative to the total absolute error of a simple baseline predictor that always predicts the mean of actual values. - **Similar:** [MASE](../mase/Mase.md), [MRAE](../mrae/Mrae.md) | **Trading note:** Relative Absolute Error; total absolute error relative to naïve model. <1 = outperforms naïve. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/errors/rmse/Rmse.md b/lib/errors/rmse/Rmse.md index 87eeb5de..4328cfb1 100644 --- a/lib/errors/rmse/Rmse.md +++ b/lib/errors/rmse/Rmse.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [rmse.pine](rmse.pine) | -- Root Mean Squared Error (RMSE) is the square root of MSE, providing an error metric in the same units as the original data while retaining sensitiv... +- Root Mean Squared Error (RMSE) is the square root of MSE, providing an error metric in the same units as the original data while retaining sensitivity to large errors. - **Similar:** [MSE](../mse/Mse.md), [MAE](../mae/Mae.md) | **Trading note:** Root Mean Squared Error; same units as input, emphasizes large deviations. Most common accuracy metric. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/errors/rse/Rse.md b/lib/errors/rse/Rse.md index c273651f..8949f6ed 100644 --- a/lib/errors/rse/Rse.md +++ b/lib/errors/rse/Rse.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [rse.pine](rse.pine) | -- Relative Squared Error (RSE) measures the total squared error of predictions relative to the total squared error of a simple baseline predictor tha... +- Relative Squared Error (RSE) measures the total squared error of predictions relative to the total squared error of a simple baseline predictor that always predicts the mean. - **Similar:** [RMSE](../rmse/Rmse.md), [Rsquared](../rsquared/Rsquared.md) | **Trading note:** Relative Squared Error; normalized by variance of actuals. >1 = worse than mean prediction. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/errors/smape/Smape.md b/lib/errors/smape/Smape.md index d3bde796..056cc041 100644 --- a/lib/errors/smape/Smape.md +++ b/lib/errors/smape/Smape.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [smape.pine](smape.pine) | -- Symmetric Mean Absolute Percentage Error addresses a fundamental asymmetry in MAPE: the fact that over-predictions and under-predictions of the sam... +- Symmetric Mean Absolute Percentage Error addresses a fundamental asymmetry in MAPE: the fact that over-predictions and under-predictions of the same magnitude receive different penalties. - **Similar:** [MAPE](../mape/Mape.md), [MAAPE](../maape/Maape.md) | **Trading note:** Symmetric MAPE; bounded 0–200%, handles zeros better than MAPE. Common in forecasting competitions. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/errors/wrmse/Wrmse.md b/lib/errors/wrmse/Wrmse.md index 57a53e7c..90bf42b1 100644 --- a/lib/errors/wrmse/Wrmse.md +++ b/lib/errors/wrmse/Wrmse.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [wrmse.pine](wrmse.pine) | -- WRMSE extends the classic RMSE by incorporating weights for each observation, enabling analysts to emphasize critical data points such as recent ob... +- WRMSE extends the classic RMSE by incorporating weights for each observation, enabling analysts to emphasize critical data points such as recent observations, high-volume periods, or specific market regimes. - **Similar:** [RMSE](../rmse/Rmse.md), [WMAPE](../wmape/Wmape.md) | **Trading note:** Weighted RMSE; emphasizes accuracy at specific points. Useful for time-decay weighting. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/alaguerre/ALaguerre.md b/lib/filters/alaguerre/ALaguerre.md index d5f27590..d1f582c1 100644 --- a/lib/filters/alaguerre/ALaguerre.md +++ b/lib/filters/alaguerre/ALaguerre.md @@ -13,7 +13,7 @@ | **PineScript** | [alaguerre.pine](alaguerre.pine) | | **Signature** | [alaguerre_signature](alaguerre_signature.md) | -- The Adaptive Laguerre Filter extends Ehlers' four-element all-pass cascade by replacing the fixed damping factor with a per-bar adaptive alpha deri... +- The Adaptive Laguerre Filter extends Ehlers' four-element all-pass cascade by replacing the fixed damping factor with a per-bar adaptive alpha derived from tracking-error normalization. - **Similar:** [Laguerre](../laguerre/Laguerre.md), [SSF2](../ssf2/Ssf2.md) | **Complementary:** RSI for momentum | **Trading note:** Adaptive Laguerre filter by Ehlers; adjusts damping based on market conditions. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/baxterking/BaxterKing.md b/lib/filters/baxterking/BaxterKing.md index 1604e534..a89db773 100644 --- a/lib/filters/baxterking/BaxterKing.md +++ b/lib/filters/baxterking/BaxterKing.md @@ -12,7 +12,7 @@ | **Warmup** | `2K+1` bars (default 25) | | **PineScript** | [baxterking.pine](baxterking.pine) | -- The **Baxter-King Band-Pass Filter** is a symmetric finite impulse response (FIR) filter that approximates the ideal spectral band-pass by truncati... +- The **Baxter-King Band-Pass Filter** is a symmetric finite impulse response (FIR) filter that approximates the ideal spectral band-pass by truncating the infinite sinc-like impulse response at lag $K$ and normalizing the weights to sum to zero. - **Similar:** [Cfitz](../cfitz/Cfitz.md), [BPF](../bpf/Bpf.md) | **Complementary:** Hilbert Transform for phase | **Trading note:** Baxter-King bandpass filter; isolates business cycle frequencies. Symmetric FIR. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/butter3/Butter3.md b/lib/filters/butter3/Butter3.md index cfc4ddf0..c03bbef2 100644 --- a/lib/filters/butter3/Butter3.md +++ b/lib/filters/butter3/Butter3.md @@ -13,7 +13,7 @@ | **PineScript** | [butter3.pine](butter3.pine) | | **Signature** | [butter3_signature](butter3_signature.md) | -- The 3-Pole Butterworth Filter (BUTTER3) extends the classic Butterworth design to third order, providing -60 dB/decade rolloff compared to -40 dB/d... +- The 3-Pole Butterworth Filter (BUTTER3) extends the classic Butterworth design to third order, providing -60 dB/decade rolloff compared to -40 dB/decade for the 2-pole variant. - **Similar:** [Butter2](../butter2/Butter2.md), [Elliptic](../elliptic/Elliptic.md) | **Complementary:** Phase analysis tools | **Trading note:** 3rd-order Butterworth; steeper rolloff than 2nd-order but more phase distortion. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/cfitz/Cfitz.md b/lib/filters/cfitz/Cfitz.md index 5fc6666d..912d9ad0 100644 --- a/lib/filters/cfitz/Cfitz.md +++ b/lib/filters/cfitz/Cfitz.md @@ -12,7 +12,7 @@ | **Warmup** | `2` bars | | **PineScript** | [cfitz.pine](cfitz.pine) | -- The **Christiano-Fitzgerald Band-Pass Filter** is an asymmetric full-sample filter that approximates the ideal spectral band-pass by using time-var... +- The **Christiano-Fitzgerald Band-Pass Filter** is an asymmetric full-sample filter that approximates the ideal spectral band-pass by using time-varying weights that adapt to each bar's position in the sample. - **Similar:** [BaxterKing](../baxterking/BaxterKing.md), [HP](../hp/Hp.md) | **Complementary:** Trend indicators | **Trading note:** Christiano-Fitzgerald bandpass filter; asymmetric, optimal for finite samples. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/cheby1/Cheby1.md b/lib/filters/cheby1/Cheby1.md index bbca0639..5ddcc95b 100644 --- a/lib/filters/cheby1/Cheby1.md +++ b/lib/filters/cheby1/Cheby1.md @@ -13,7 +13,7 @@ | **PineScript** | [cheby1.pine](cheby1.pine) | | **Signature** | [cheby1_signature](cheby1_signature.md) | -- The Chebyshev Type I filter minimizes the error between the idealized and the actual filter characteristic over the range of the passband, but with... +- The Chebyshev Type I filter minimizes the error between the idealized and the actual filter characteristic over the range of the passband, but with ripples in the passband. - **Similar:** [Cheby2](../cheby2/Cheby2.md), [Elliptic](../elliptic/Elliptic.md) | **Complementary:** ATR for stop distance | **Trading note:** Chebyshev Type I; passband ripple for sharper transition. Steeper than Butterworth. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/lms/Lms.md b/lib/filters/lms/Lms.md index f7d9d3b3..60dfb9e6 100644 --- a/lib/filters/lms/Lms.md +++ b/lib/filters/lms/Lms.md @@ -12,7 +12,7 @@ | **Warmup** | `order + 1` bars | | **PineScript** | [lms.pine](lms.pine) | -- The **Least Mean Squares (LMS) Adaptive Filter** is the Widrow-Hoff adaptive FIR filter, the simplest and most widely deployed adaptive algorithm i... +- The **Least Mean Squares (LMS) Adaptive Filter** is the Widrow-Hoff adaptive FIR filter, the simplest and most widely deployed adaptive algorithm in signal processing. - **Similar:** [RLS](../rls/Rls.md), [Kalman](../kalman/Kalman.md) | **Complementary:** Error metrics for convergence monitoring | **Trading note:** Least Mean Squares adaptive filter; tracks changing signal statistics. Low computational cost. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/rmed/Rmed.md b/lib/filters/rmed/Rmed.md index 43e6db73..6c9c739f 100644 --- a/lib/filters/rmed/Rmed.md +++ b/lib/filters/rmed/Rmed.md @@ -13,7 +13,7 @@ | **PineScript** | [rmed.pine](rmed.pine) | | **Signature** | [rmed_signature](rmed_signature.md) | -- RMED applies exponential smoothing to a 5-bar running median, creating a nonlinear IIR filter that rejects impulsive spike noise while providing sm... +- RMED applies exponential smoothing to a 5-bar running median, creating a nonlinear IIR filter that rejects impulsive spike noise while providing smooth recursive tracking. - **Similar:** [Bilateral](../bilateral/Bilateral.md), [Loess](../loess/Loess.md) | **Complementary:** ATR for volatility | **Trading note:** Running median filter; non-linear, completely removes impulse noise. Preserves edges. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/sgf/Sgf.md b/lib/filters/sgf/Sgf.md index 8b579954..28536fd4 100644 --- a/lib/filters/sgf/Sgf.md +++ b/lib/filters/sgf/Sgf.md @@ -13,7 +13,7 @@ | **PineScript** | [sgf.pine](sgf.pine) | | **Signature** | [sgf_signature](sgf_signature.md) | -- SGF (Savitzky-Golay Filter) is a digital signal processing technique that smoothes data by fitting successive sub-sets of adjacent data points with... +- SGF (Savitzky-Golay Filter) is a digital signal processing technique that smoothes data by fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares. - **Similar:** [Loess](../loess/Loess.md), [NW](../nw/Nw.md) | **Complementary:** Polynomial order selection | **Trading note:** Savitzky-Golay filter; polynomial smoothing preserving higher moments. Good for derivative estimation. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/spbf/Spbf.md b/lib/filters/spbf/Spbf.md index 45d8683c..dcdc35f0 100644 --- a/lib/filters/spbf/Spbf.md +++ b/lib/filters/spbf/Spbf.md @@ -12,7 +12,7 @@ | **Warmup** | `max(longPeriod, rmsPeriod)` bars (default 60) | | **PineScript** | [spbf.pine](spbf.pine) | -- The **Super Passband Filter** is John Ehlers' wide-band bandpass constructed by differencing two z-transformed EMAs with Ehlers-style smoothing ($\... +- The **Super Passband Filter** is John Ehlers' wide-band bandpass constructed by differencing two z-transformed EMAs with Ehlers-style smoothing ($\alpha = 5/N$). - **Similar:** [Bilateral](../bilateral/Bilateral.md), [RMed](../rmed/Rmed.md) | **Complementary:** ATR for volatility context | **Trading note:** Spectral bilateral filter; edge-preserving smoother in frequency domain. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/ssf3/Ssf3.md b/lib/filters/ssf3/Ssf3.md index 0c9e8d7d..6be982fe 100644 --- a/lib/filters/ssf3/Ssf3.md +++ b/lib/filters/ssf3/Ssf3.md @@ -13,7 +13,7 @@ | **PineScript** | [ssf3.pine](ssf3.pine) | | **Signature** | [ssf3_signature](ssf3_signature.md) | -- The 3-Pole Super Smoother Filter (SSF3) extends Ehlers' Super Smoother concept to third order, providing -60 dB/decade rolloff compared to -40 dB/d... +- The 3-Pole Super Smoother Filter (SSF3) extends Ehlers' Super Smoother concept to third order, providing -60 dB/decade rolloff compared to -40 dB/decade for the 2-pole variant (SSF2). - **Similar:** [SSF2](../ssf2/Ssf2.md), [Butter3](../butter3/Butter3.md) | **Complementary:** Cycle analysis | **Trading note:** Ehlers' 3-pole Super Smoother; even smoother than 2-pole but more lag. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/usf/Usf.md b/lib/filters/usf/Usf.md index 9831d154..bd669a73 100644 --- a/lib/filters/usf/Usf.md +++ b/lib/filters/usf/Usf.md @@ -13,7 +13,7 @@ | **PineScript** | [usf.pine](usf.pine) | | **Signature** | [usf_signature](usf_signature.md) | -- The Ultimate Smoother Filter (USF) is a zero-lag smoothing filter introduced by John Ehlers in the April 2024 issue of *Technical Analysis of Stock... +- The Ultimate Smoother Filter (USF) is a zero-lag smoothing filter introduced by John Ehlers in the April 2024 issue of *Technical Analysis of Stocks & Commodities*. - **Similar:** [SSF2](../ssf2/Ssf2.md), [Kalman](../kalman/Kalman.md) | **Complementary:** ATR for volatility | **Trading note:** Universal Smoothing Filter; combines multiple filter approaches adaptively. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/voss/Voss.md b/lib/filters/voss/Voss.md index ebeab3f4..cf9a3d55 100644 --- a/lib/filters/voss/Voss.md +++ b/lib/filters/voss/Voss.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [voss.pine](voss.pine) | -- The Voss Predictive Filter is a two-stage signal processing pipeline that extracts a dominant cycle from noisy price data and then predicts its fut... +- The Voss Predictive Filter is a two-stage signal processing pipeline that extracts a dominant cycle from noisy price data and then predicts its future trajectory using negative group delay. - **Similar:** [BPF](../bpf/Bpf.md), [Roofing](../roofing/Roofing.md) | **Complementary:** Cycle period indicators | **Trading note:** Voss predictive filter; attempts to predict the next cycle value. Zero-lag by design. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/wavelet/Wavelet.md b/lib/filters/wavelet/Wavelet.md index 0c89ebcf..10f05e69 100644 --- a/lib/filters/wavelet/Wavelet.md +++ b/lib/filters/wavelet/Wavelet.md @@ -14,7 +14,7 @@ | **Signature** | [wavelet_signature](wavelet_signature.md) | -- The Wavelet Denoising Filter applies an *à trous* (with holes) Haar wavelet decomposition with soft thresholding to remove high-frequency noise fro... +- The Wavelet Denoising Filter applies an *à trous* (with holes) Haar wavelet decomposition with soft thresholding to remove high-frequency noise from price series while preserving trend structure and edges. - **Similar:** [SGF](../sgf/Sgf.md), [Modf](../modf/Modf.md) | **Complementary:** Multi-timeframe analysis | **Trading note:** Wavelet denoising; multi-resolution analysis separates signal at different time scales. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/filters/wiener/Wiener.md b/lib/filters/wiener/Wiener.md index 85bbbac0..4f3fad41 100644 --- a/lib/filters/wiener/Wiener.md +++ b/lib/filters/wiener/Wiener.md @@ -13,7 +13,7 @@ | **PineScript** | [wiener.pine](wiener.pine) | | **Signature** | [wiener_signature](wiener_signature.md) | -- The Wiener Filter is an optimal linear filter that attempts to minimize the mean square error between the estimated random process and the desired ... +- The Wiener Filter is an optimal linear filter that attempts to minimize the mean square error between the estimated random process and the desired process. - **Similar:** [Kalman](../kalman/Kalman.md), [RLS](../rls/Rls.md) | **Complementary:** Noise estimation | **Trading note:** Wiener filter; optimal linear filter minimizing MSE. Assumes stationary signals. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/forecasts/afirma/Afirma.md b/lib/forecasts/afirma/Afirma.md index 3c193189..2a9f09ee 100644 --- a/lib/forecasts/afirma/Afirma.md +++ b/lib/forecasts/afirma/Afirma.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [afirma.pine](afirma.pine) | -- AFIRMA is a Windowed Weighted Moving Average that replaces standard linear weighting with weights derived from signal processing window functions (... +- AFIRMA is a Windowed Weighted Moving Average that replaces standard linear weighting with weights derived from signal processing window functions (Hanning, Hamming, Blackman, Blackman-Harris). - **Similar:** [TSF](../../trends_FIR/tsf/Tsf.md), [LinReg](../../statistics/linreg/LinReg.md) | **Complementary:** Error metrics for accuracy | **Trading note:** Adaptive FIR Moving Average for forecasting; projects price using optimized FIR coefficients. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/momentum/cfb/Cfb.md b/lib/momentum/cfb/Cfb.md index 4cc39fa3..ae639992 100644 --- a/lib/momentum/cfb/Cfb.md +++ b/lib/momentum/cfb/Cfb.md @@ -12,7 +12,7 @@ | **Warmup** | `maxLen` bars (192 default) | | **PineScript** | [cfb.pine](cfb.pine) | -- The Composite Fractal Behavior index measures trend duration by analyzing fractal efficiency across 96 simultaneous lookback periods (2 to 192 bars... +- The Composite Fractal Behavior index measures trend duration by analyzing fractal efficiency across 96 simultaneous lookback periods (2 to 192 bars by default). - **Similar:** [RSI](../rsi/Rsi.md), [CMO](../cmo/Cmo.md) | **Complementary:** Volume for confirmation | **Trading note:** Composite Force Index; combines price change magnitude and direction. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/momentum/sam/Sam.md b/lib/momentum/sam/Sam.md index 269c65bc..a90be7a0 100644 --- a/lib/momentum/sam/Sam.md +++ b/lib/momentum/sam/Sam.md @@ -12,7 +12,7 @@ | **Warmup** | `MaxCyclePeriod * 2` bars | | **PineScript** | [sam.pine](sam.pine) | -- The Smoothed Adaptive Momentum oscillator measures price momentum over an adaptively determined lookback period equal to the dominant cycle length,... +- The Smoothed Adaptive Momentum oscillator measures price momentum over an adaptively determined lookback period equal to the dominant cycle length, then smooths the result with a 2-pole Super Smoother filter. - **Similar:** [MOM](../mom/Mom.md), [ROC](../roc/Roc.md) | **Complementary:** Moving average for trend | **Trading note:** Simple Accumulative Momentum; cumulative sum of momentum values. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/momentum/tsi/Tsi.md b/lib/momentum/tsi/Tsi.md index 481fca93..32cfda9d 100644 --- a/lib/momentum/tsi/Tsi.md +++ b/lib/momentum/tsi/Tsi.md @@ -12,7 +12,7 @@ | **Warmup** | `longPeriod + shortPeriod + signalPeriod` bars (51 default) | | **PineScript** | [tsi.pine](tsi.pine) | -- The True Strength Index (TSI) is a momentum oscillator developed by William Blau that uses double-smoothed exponential moving averages of price mom... +- The True Strength Index (TSI) is a momentum oscillator developed by William Blau that uses double-smoothed exponential moving averages of price momentum to reduce noise and identify trend strength and direction. - **Similar:** [MACD](../macd/Macd.md), [PMO](../pmo/Pmo.md) | **Complementary:** Signal line crossovers | **Trading note:** True Strength Index; double-smoothed momentum ratio. Range ±100. Good for divergence analysis. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/binomdist/Binomdist.md b/lib/numerics/binomdist/Binomdist.md index c5317678..7c6b1b05 100644 --- a/lib/numerics/binomdist/Binomdist.md +++ b/lib/numerics/binomdist/Binomdist.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [binomdist.pine](binomdist.pine) | -- BINOMDIST computes the cumulative distribution function of the Binomial distribution, mapping a min-max normalized price to a success probability $... +- BINOMDIST computes the cumulative distribution function of the Binomial distribution, mapping a min-max normalized price to a success probability $p$ and evaluating $P(X \leq k)$ for $X \sim \text{Binomial}(n, p)$. - **Trading note:** Binomial distribution; models success/failure sequences. Win streak probability in trading. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/cwt/Cwt.md b/lib/numerics/cwt/Cwt.md index 354f7233..9d843b4e 100644 --- a/lib/numerics/cwt/Cwt.md +++ b/lib/numerics/cwt/Cwt.md @@ -12,7 +12,7 @@ | **Warmup** | windowSize (2K+1) bars, where K = round(3 × scale) | | **PineScript** | [cwt.pine](cwt.pine) | -- CWT computes the magnitude of the Continuous Wavelet Transform at a specified scale using the Morlet wavelet, providing a time-frequency decomposit... +- CWT computes the magnitude of the Continuous Wavelet Transform at a specified scale using the Morlet wavelet, providing a time-frequency decomposition that measures the energy content of a specific frequency band at each point in time. - **Similar:** [DWT](../dwt/Dwt.md), [FFT](../fft/Fft.md) | **Trading note:** Continuous Wavelet Transform; multi-resolution time-frequency analysis for cycle detection. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/dwt/Dwt.md b/lib/numerics/dwt/Dwt.md index 9e7ac3db..51cb92eb 100644 --- a/lib/numerics/dwt/Dwt.md +++ b/lib/numerics/dwt/Dwt.md @@ -12,7 +12,7 @@ | **Warmup** | `bufferSize` bars | | **PineScript** | [dwt.pine](dwt.pine) | -- The Discrete Wavelet Transform decomposes a price series into multi-resolution frequency components using the a trous (with holes) stationary Haar ... +- The Discrete Wavelet Transform decomposes a price series into multi-resolution frequency components using the a trous (with holes) stationary Haar wavelet. - **Similar:** [CWT](../cwt/Cwt.md), [FFT](../fft/Fft.md) | **Trading note:** Discrete Wavelet Transform; decomposes signal into frequency bands at different scales. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/expdist/Expdist.md b/lib/numerics/expdist/Expdist.md index cebe7902..6fb26ff4 100644 --- a/lib/numerics/expdist/Expdist.md +++ b/lib/numerics/expdist/Expdist.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [expdist.pine](expdist.pine) | -- The Exponential Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the exponential distribution, p... +- The Exponential Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the exponential distribution, producing an output in $[0, 1]$. - **Trading note:** Exponential distribution; models time between events. Used for trade arrival rate analysis. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/fdist/Fdist.md b/lib/numerics/fdist/Fdist.md index e80a8a6b..df299de3 100644 --- a/lib/numerics/fdist/Fdist.md +++ b/lib/numerics/fdist/Fdist.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [fdist.pine](fdist.pine) | -- The F-Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the F-distribution (Fisher-Snedecor distr... +- The F-Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the F-distribution (Fisher-Snedecor distribution), producing an output in $[0, 1]$. - **Trading note:** F-distribution; used in ANOVA and regression significance tests. Compares model variances. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/gammadist/Gammadist.md b/lib/numerics/gammadist/Gammadist.md index d3c01f63..5b4df8aa 100644 --- a/lib/numerics/gammadist/Gammadist.md +++ b/lib/numerics/gammadist/Gammadist.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [gammadist.pine](gammadist.pine) | -- The Gamma Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the gamma distribution, producing an ... +- The Gamma Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the gamma distribution, producing an output in $[0, 1]$. - **Trading note:** Gamma distribution; models waiting times and aggregate claims. Used in risk modeling. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/lognormdist/Lognormdist.md b/lib/numerics/lognormdist/Lognormdist.md index 5c32f808..21bbdbe2 100644 --- a/lib/numerics/lognormdist/Lognormdist.md +++ b/lib/numerics/lognormdist/Lognormdist.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [lognormdist.pine](lognormdist.pine) | -- The Log-Normal Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the log-normal distribution, pro... +- The Log-Normal Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the log-normal distribution, producing an output in $[0, 1]$. - **Trading note:** Log-normal distribution; models multiplicative processes like returns. Foundation of Black-Scholes. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/normalize/Normalize.md b/lib/numerics/normalize/Normalize.md index 729b9562..76568fb1 100644 --- a/lib/numerics/normalize/Normalize.md +++ b/lib/numerics/normalize/Normalize.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [normalize.pine](normalize.pine) | -- The Normalize transformer applies min-max scaling to map any value series into the bounded range [0, 1] based on the observed minimum and maximum w... +- The Normalize transformer applies min-max scaling to map any value series into the bounded range [0, 1] based on the observed minimum and maximum within a rolling lookback window. - **Trading note:** Min-max normalization to [0,1]; makes indicators comparable across different scales. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/normdist/Normdist.md b/lib/numerics/normdist/Normdist.md index e364a6ca..74a6cf02 100644 --- a/lib/numerics/normdist/Normdist.md +++ b/lib/numerics/normdist/Normdist.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [normdist.pine](normdist.pine) | -- The Normal Distribution CDF transforms a z-score normalized price into the cumulative distribution function of the Gaussian distribution, producing... +- The Normal Distribution CDF transforms a z-score normalized price into the cumulative distribution function of the Gaussian distribution, producing an output in $[0, 1]$. - **Trading note:** Normal (Gaussian) distribution; foundational for z-scores, confidence intervals, and VaR calculations. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/poissondist/Poissondist.md b/lib/numerics/poissondist/Poissondist.md index 5ff2777a..f72b3bcc 100644 --- a/lib/numerics/poissondist/Poissondist.md +++ b/lib/numerics/poissondist/Poissondist.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [poissondist.pine](poissondist.pine) | -- The Poisson Distribution CDF computes the probability $P(X \le k)$ for a Poisson random variable whose rate parameter $\lambda$ is derived from the... +- The Poisson Distribution CDF computes the probability $P(X \le k)$ for a Poisson random variable whose rate parameter $\lambda$ is derived from the min-max normalized price. - **Trading note:** Poisson distribution; models count of rare events. Trade signal frequency analysis. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/tdist/Tdist.md b/lib/numerics/tdist/Tdist.md index 97387f70..746ede2f 100644 --- a/lib/numerics/tdist/Tdist.md +++ b/lib/numerics/tdist/Tdist.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [tdist.pine](tdist.pine) | -- The Student's t-Distribution CDF transforms a min-max normalized price into the cumulative distribution function of Student's t-distribution, produ... +- The Student's t-Distribution CDF transforms a min-max normalized price into the cumulative distribution function of Student's t-distribution, producing an output in $[0, 1]$. - **Trading note:** Student's t-distribution; used for hypothesis testing with small samples. Fatter tails than normal. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/numerics/weibulldist/Weibulldist.md b/lib/numerics/weibulldist/Weibulldist.md index 42ac848b..a4cb004b 100644 --- a/lib/numerics/weibulldist/Weibulldist.md +++ b/lib/numerics/weibulldist/Weibulldist.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [weibulldist.pine](weibulldist.pine) | -- The Weibull Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the Weibull distribution, producing... +- The Weibull Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the Weibull distribution, producing an output in $[0, 1]$. - **Trading note:** Weibull distribution; flexible lifetime/reliability model. Used for drawdown duration analysis. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/brar/Brar.md b/lib/oscillators/brar/Brar.md index 3dc37c10..2c89423a 100644 --- a/lib/oscillators/brar/Brar.md +++ b/lib/oscillators/brar/Brar.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [brar.pine](brar.pine) | -- BRAR is a dual-output sentiment oscillator from the Japanese technical analysis tradition that decomposes market pressure into two independent rati... +- BRAR is a dual-output sentiment oscillator from the Japanese technical analysis tradition that decomposes market pressure into two independent ratios: BR (Buying Ratio), which measures upside thrust relative to the previous close, and AR (Atmosphere Ratio), which measures intraday range asymmetry relative to the open. - **Similar:** [ERI](../eri/Eri.md), [FI](../fi/Fi.md) | **Complementary:** Volume | **Trading note:** BRAR (Buying/Selling Power); AR measures opening vs H/L, BR measures close vs H/L. Popular in Asian markets. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/coppock/Coppock.md b/lib/oscillators/coppock/Coppock.md index f7923656..628a3492 100644 --- a/lib/oscillators/coppock/Coppock.md +++ b/lib/oscillators/coppock/Coppock.md @@ -12,7 +12,7 @@ | **Warmup** | 1 bar | | **PineScript** | [coppock.pine](coppock.pine) | -- The Coppock Curve is a long-term momentum oscillator that applies a Weighted Moving Average to the sum of two Rate of Change calculations at differ... +- The Coppock Curve is a long-term momentum oscillator that applies a Weighted Moving Average to the sum of two Rate of Change calculations at different lookback periods. - **Similar:** [MACD](../../momentum/macd/Macd.md), [KST](../kst/Kst.md) | **Complementary:** Trend confirmation | **Trading note:** Coppock Curve; designed for monthly S&P 500 buy signals. WMA of summed ROCs. Zero-line crossover. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/crsi/Crsi.md b/lib/oscillators/crsi/Crsi.md index 2ff06031..c24947ce 100644 --- a/lib/oscillators/crsi/Crsi.md +++ b/lib/oscillators/crsi/Crsi.md @@ -12,7 +12,7 @@ | **Warmup** | 1 bar | | **PineScript** | [crsi.pine](crsi.pine) | -- Connors RSI is a composite momentum oscillator that combines three independent measurements of price behavior into a single bounded (0-100) output:... +- Connors RSI is a composite momentum oscillator that combines three independent measurements of price behavior into a single bounded (0-100) output: a short-term RSI of price, an RSI of the consecutive up/down streak length, and a percentile rank of the current rate of change within its recent history. - **Similar:** [RSI](../../momentum/rsi/Rsi.md), [StochRSI](../stochrsi/Stochrsi.md) | **Complementary:** Volume | **Trading note:** Connors RSI; combines RSI, streak RSI, and percentile rank. Short-term mean-reversion signal. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/cti/Cti.md b/lib/oscillators/cti/Cti.md index cef6b356..78de5732 100644 --- a/lib/oscillators/cti/Cti.md +++ b/lib/oscillators/cti/Cti.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [cti.pine](cti.pine) | -- The Correlation Trend Indicator computes the Pearson correlation coefficient between the price series and a linear time index over a rolling window... +- The Correlation Trend Indicator computes the Pearson correlation coefficient between the price series and a linear time index over a rolling window, producing a bounded oscillator in the range $[-1, +1]$. - **Similar:** [LinReg](../../statistics/linreg/LinReg.md), [CFO](../cfo/Cfo.md) | **Complementary:** ADX | **Trading note:** Correlation Trend Indicator; Pearson correlation of price vs time. +1 = perfect uptrend, −1 = downtrend. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/dem/Dem.md b/lib/oscillators/dem/Dem.md index 25b546e4..f443698e 100644 --- a/lib/oscillators/dem/Dem.md +++ b/lib/oscillators/dem/Dem.md @@ -12,7 +12,7 @@ | **Warmup** | `period + 1` bars | | **PineScript** | [dem.pine](dem.pine) | -- DEM (DeMarker Oscillator) is a bounded [0, 1] momentum oscillator that measures sequential demand pressure by comparing each bar's high and low aga... +- DEM (DeMarker Oscillator) is a bounded [0, 1] momentum oscillator that measures sequential demand pressure by comparing each bar's high and low against the previous bar's high and low. - **Similar:** [MACD](../../momentum/macd/Macd.md), [AO](../ao/Ao.md) | **Complementary:** Volume | **Trading note:** DeMarker; compares current high/low to previous. Overbought >0.7, oversold <0.3. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/dosc/Dosc.md b/lib/oscillators/dosc/Dosc.md index b0945034..c22452fe 100644 --- a/lib/oscillators/dosc/Dosc.md +++ b/lib/oscillators/dosc/Dosc.md @@ -12,7 +12,7 @@ | **Warmup** | `rsiPeriod + sigPeriod` bars | | **PineScript** | [dosc.pine](dosc.pine) | -- The Derivative Oscillator applies a four-stage signal processing pipeline to extract momentum inflection points: RSI via Wilder's smoothing, double... +- The Derivative Oscillator applies a four-stage signal processing pipeline to extract momentum inflection points: RSI via Wilder's smoothing, double EMA smoothing of the RSI, an SMA signal line of the double-smoothed result, and finally the difference between the smoothed RSI and its signal. - **Similar:** [MACD](../../momentum/macd/Macd.md), [PPO](../../momentum/ppo/Ppo.md) | **Complementary:** Volume | **Trading note:** Derivative Oscillator; RSI smoothed with EMA, then differenced. Catches RSI turning points early. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/dymi/dymi.md b/lib/oscillators/dymi/dymi.md index 1b4bcea1..bb3fc640 100644 --- a/lib/oscillators/dymi/dymi.md +++ b/lib/oscillators/dymi/dymi.md @@ -12,7 +12,7 @@ | **Warmup** | 1 bar | | **PineScript** | [dymi.pine](dymi.pine) | -- DYMI is a volatility-adaptive RSI: when recent price swings are large relative to longer-term swings, the RSI period shortens and the indicator be... +- DYMI is a volatility-adaptive RSI: when recent price swings are large relative to longer-term swings, the RSI period shortens and the indicator becomes more responsive; when price action tightens, the period extends and the output smooths. - **Similar:** [RSI](../../momentum/rsi/Rsi.md), [Stoch](../stoch/Stoch.md) | **Complementary:** ATR | **Trading note:** Dynamic Momentum Index; RSI with variable lookback based on volatility. Faster in calm, slower in volatile markets. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/imi/Imi.md b/lib/oscillators/imi/Imi.md index 0b3f3cfc..a724c871 100644 --- a/lib/oscillators/imi/Imi.md +++ b/lib/oscillators/imi/Imi.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [imi.pine](imi.pine) | -- The Intraday Momentum Index measures buying and selling pressure using the open-to-close relationship within each bar, rather than the close-to-clo... +- The Intraday Momentum Index measures buying and selling pressure using the open-to-close relationship within each bar, rather than the close-to-close changes used by RSI. - **Similar:** [RSI](../../momentum/rsi/Rsi.md), [MFI](../../volume/mfi/Mfi.md) | **Complementary:** Volume | **Trading note:** Intraday Momentum Index; RSI variant using open-close relationship. Measures intrabar conviction. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/kst/Kst.md b/lib/oscillators/kst/Kst.md index afa12bea..ac6606f7 100644 --- a/lib/oscillators/kst/Kst.md +++ b/lib/oscillators/kst/Kst.md @@ -14,9 +14,7 @@ + Math.Max(Math.Max(s1, s2), Math.Max(s3, s4)) + sigPeriod - 2` bars | -- The Know Sure Thing is a multi-timeframe momentum oscillator that computes four Rate of Change values at progressively longer lookback periods, smo... - + Math.Max(Math.Max(s1, s2), Math.Max(s3, s4)) - + sigPeriod - 2` bars of warmup before first valid output (IsHot = true). +- The Know Sure Thing is a multi-timeframe momentum oscillator that computes four Rate of Change values at progressively longer lookback periods, smooths each with an independent SMA, then combines them using linearly increasing weights (1, 2, 3, 4) to produce a single composite momentum line. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. The Know Sure Thing is a multi-timeframe momentum oscillator that computes four Rate of Change values at progressively longer lookback periods, smooths each with an independent SMA, then combines them using linearly increasing weights (1, 2, 3, 4) to produce a single composite momentum line. A signal line (SMA of the KST) provides crossover triggers. The weighted summation ensures longer-term momentum dominates the output while shorter-term components contribute responsiveness, creating a momentum indicator that reflects multiple cycle lengths simultaneously. diff --git a/lib/oscillators/lrsi/Lrsi.md b/lib/oscillators/lrsi/Lrsi.md index 36ba5d9a..f51d3da1 100644 --- a/lib/oscillators/lrsi/Lrsi.md +++ b/lib/oscillators/lrsi/Lrsi.md @@ -12,7 +12,7 @@ | **Warmup** | `4` bars | | **PineScript** | [lrsi.pine](lrsi.pine) | -- Laguerre RSI is an adaptive oscillator invented by John Ehlers that replaces standard RSI's Wilder-smoothed gain/loss averages with a 4-stage casca... +- Laguerre RSI is an adaptive oscillator invented by John Ehlers that replaces standard RSI's Wilder-smoothed gain/loss averages with a 4-stage cascaded Laguerre filter. - **Similar:** [RSI](../../momentum/rsi/Rsi.md), [Fisher](../fisher/Fisher.md) | **Complementary:** Volume | **Trading note:** Laguerre RSI by Ehlers; applies Laguerre filter to RSI calculation. Faster response, fewer whipsaws. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/mstoch/Mstoch.md b/lib/oscillators/mstoch/Mstoch.md index 934f8ac6..84603265 100644 --- a/lib/oscillators/mstoch/Mstoch.md +++ b/lib/oscillators/mstoch/Mstoch.md @@ -12,7 +12,7 @@ | **Warmup** | 1 bar | | **PineScript** | [mstoch.pine](mstoch.pine) | -- The MESA Stochastic applies John Ehlers' Roofing Filter as a preprocessing stage before computing a stochastic oscillator, then smooths the stochas... +- The MESA Stochastic applies John Ehlers' Roofing Filter as a preprocessing stage before computing a stochastic oscillator, then smooths the stochastic output with a Super Smoother. - **Similar:** [Stoch](../stoch/Stoch.md), [KDJ](../kdj/Kdj.md) | **Complementary:** MACD | **Trading note:** Modified Stochastic; enhanced stochastic oscillator with additional smoothing or lookback variation. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/qqe/Qqe.md b/lib/oscillators/qqe/Qqe.md index 02b106f3..a22e9b5e 100644 --- a/lib/oscillators/qqe/Qqe.md +++ b/lib/oscillators/qqe/Qqe.md @@ -12,7 +12,7 @@ | **Warmup** | `rsiPeriod + smoothFactor + darPeriod * 2` bars | | **PineScript** | [qqe.pine](qqe.pine) | -- Quantitative Qualitative Estimation applies a multi-stage smoothing pipeline to RSI and then constructs dynamic volatility-based trailing bands aro... +- Quantitative Qualitative Estimation applies a multi-stage smoothing pipeline to RSI and then constructs dynamic volatility-based trailing bands around the smoothed result. - **Similar:** [RSI](../../momentum/rsi/Rsi.md), [StochRSI](../stochrsi/Stochrsi.md) | **Complementary:** ATR | **Trading note:** Quantitative Qualitative Estimation; smoothed RSI with dynamic trailing levels. Reduces false signals. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/reflex/Reflex.md b/lib/oscillators/reflex/Reflex.md index 030970fd..d831d5a0 100644 --- a/lib/oscillators/reflex/Reflex.md +++ b/lib/oscillators/reflex/Reflex.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [reflex.pine](reflex.pine) | -- REFLEX is a zero-lag oscillator that measures the reversal tendency of price by comparing a Super-Smoother-filtered price against a linear extrapol... +- REFLEX is a zero-lag oscillator that measures the reversal tendency of price by comparing a Super-Smoother-filtered price against a linear extrapolation from $N$ bars ago. - **Similar:** [Trendflex](../trendflex/Trendflex.md), [Deco](../deco/Deco.md) | **Complementary:** Cycle indicators | **Trading note:** Ehlers' Reflex indicator; cycle-mode oscillator using Super Smoother. Leading turns at zero crossings. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/reverseema/ReverseEma.md b/lib/oscillators/reverseema/ReverseEma.md index 315f32d3..284f099f 100644 --- a/lib/oscillators/reverseema/ReverseEma.md +++ b/lib/oscillators/reverseema/ReverseEma.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [reverseema.pine](reverseema.pine) | -- The Reverse EMA applies an 8-stage cascaded Z-transform inversion to a compensated EMA, progressively extracting and subtracting the accumulated la... +- The Reverse EMA applies an 8-stage cascaded Z-transform inversion to a compensated EMA, progressively extracting and subtracting the accumulated lag component. - **Similar:** [EMA](../../trends_IIR/ema/ema.md), [Zlema](../../trends_IIR/zlema/zlema.md) | **Complementary:** StdDev | **Trading note:** Reverse-engineers price from EMA; finds the price that would produce a given EMA value. Useful for target levels. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/rvgi/Rvgi.md b/lib/oscillators/rvgi/Rvgi.md index e1d3b22c..a41e3eb0 100644 --- a/lib/oscillators/rvgi/Rvgi.md +++ b/lib/oscillators/rvgi/Rvgi.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [rvgi.pine](rvgi.pine) | -- The Relative Vigor Index measures the conviction of a price move by comparing closing strength (close minus open) to the total intrabar range (high... +- The Relative Vigor Index measures the conviction of a price move by comparing closing strength (close minus open) to the total intrabar range (high minus low), smoothed through a symmetrically weighted moving average and then averaged over a lookback period. - **Similar:** [AO](../ao/Ao.md), [Fisher](../fisher/Fisher.md) | **Complementary:** Volume | **Trading note:** Relative Vigor Index; compares close−open to high−low. Rising = bullish vigor. Signal-line crossovers. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/squeeze/Squeeze.md b/lib/oscillators/squeeze/Squeeze.md index 4336d11c..3820daf5 100644 --- a/lib/oscillators/squeeze/Squeeze.md +++ b/lib/oscillators/squeeze/Squeeze.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [squeeze.pine](squeeze.pine) | -- Squeeze Momentum combines Bollinger Band and Keltner Channel width analysis to detect low-volatility compression ("squeeze") states, while simultan... +- Squeeze Momentum combines Bollinger Band and Keltner Channel width analysis to detect low-volatility compression ("squeeze") states, while simultaneously measuring directional momentum via linear regression of a detrended price series. - **Similar:** [TTM_Squeeze](../../dynamics/ttm_squeeze/TtmSqueeze.md), [BBB](../bbb/Bbb.md) | **Complementary:** Momentum histogram | **Trading note:** Squeeze indicator; detects low-volatility compression. Bollinger inside Keltner = squeeze on. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/stc/stc.md b/lib/oscillators/stc/stc.md index d7ad8549..b8490813 100644 --- a/lib/oscillators/stc/stc.md +++ b/lib/oscillators/stc/stc.md @@ -12,7 +12,7 @@ | **Warmup** | 1 bar | | **PineScript** | [stc.pine](stc.pine) | -- The Schaff Trend Cycle is a cyclometric oscillator that applies double-Stochastic normalization to MACD, extracting the cyclical phase hidden withi... +- The Schaff Trend Cycle is a cyclometric oscillator that applies double-Stochastic normalization to MACD, extracting the cyclical phase hidden within the trend itself. - **Similar:** [MACD](../../momentum/macd/Macd.md), [Stoch](../stoch/Stoch.md) | **Complementary:** ADX | **Trading note:** Schaff Trend Cycle; double Stochastic of MACD. Faster trend detection. 25/75 signal levels. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/td_seq/Td_seq.md b/lib/oscillators/td_seq/Td_seq.md index e60e1f3b..ff0c5ea4 100644 --- a/lib/oscillators/td_seq/Td_seq.md +++ b/lib/oscillators/td_seq/Td_seq.md @@ -12,7 +12,7 @@ | **Warmup** | `comparePeriod + 1` bars | | **PineScript** | [td_seq.pine](td_seq.pine) | -- TD Sequential is Tom DeMark's exhaustion counting system that identifies potential trend reversals through two phases: a 9-count Setup phase that d... +- TD Sequential is Tom DeMark's exhaustion counting system that identifies potential trend reversals through two phases: a 9-count Setup phase that detects overextended trends, and a 13-count Countdown phase that pinpoints probable reversal timing. - No configurable parameters; computation is stateless per bar. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/oscillators/trendflex/Trendflex.md b/lib/oscillators/trendflex/Trendflex.md index 1bc2275c..71e37bc3 100644 --- a/lib/oscillators/trendflex/Trendflex.md +++ b/lib/oscillators/trendflex/Trendflex.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [trendflex.pine](trendflex.pine) | -- The Trendflex indicator combines a 2-pole Butterworth low-pass pre-filter (Super Smoother) with an O(1) cumulative slope measurement and exponentia... +- The Trendflex indicator combines a 2-pole Butterworth low-pass pre-filter (Super Smoother) with an O(1) cumulative slope measurement and exponential RMS normalization to produce a zero-centered oscillator that quantifies trend strength. - **Similar:** [Reflex](../reflex/Reflex.md), [Deco](../deco/Deco.md) | **Complementary:** ADX | **Trading note:** Ehlers' Trendflex; trend-mode companion to Reflex. Positive = uptrend, negative = downtrend. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/reversals/chandelier/Chandelier.md b/lib/reversals/chandelier/Chandelier.md index 99e4dc39..e23bbd91 100644 --- a/lib/reversals/chandelier/Chandelier.md +++ b/lib/reversals/chandelier/Chandelier.md @@ -12,7 +12,7 @@ | **Warmup** | `period + 1` bars | | **PineScript** | [chandelier.pine](chandelier.pine) | -- The Chandelier Exit computes ATR-based trailing stop levels that hang from the highest high (for longs) or rise from the lowest low (for shorts) ov... +- The Chandelier Exit computes ATR-based trailing stop levels that hang from the highest high (for longs) or rise from the lowest low (for shorts) over a lookback period. - **Similar:** [SAR](../sar/Sar.md), [Super](../../dynamics/super/Super.md) | **Complementary:** ADX for trend strength | **Trading note:** Chandelier Exit; ATR-based trailing stop from highest high. Risk management tool. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/reversals/fractals/Fractals.md b/lib/reversals/fractals/Fractals.md index 53b72cfe..e165c2cd 100644 --- a/lib/reversals/fractals/Fractals.md +++ b/lib/reversals/fractals/Fractals.md @@ -12,7 +12,7 @@ | **Warmup** | 1 bar | | **PineScript** | [fractals.pine](fractals.pine) | -- Williams Fractals detect local price extremes using a strict five-bar pattern: an Up Fractal marks a bar whose high exceeds the highs of the two ba... +- Williams Fractals detect local price extremes using a strict five-bar pattern: an Up Fractal marks a bar whose high exceeds the highs of the two bars before and after it; a Down Fractal marks a bar whose low undercuts the lows of the two bars before and after it. - No configurable parameters; computation is stateless per bar. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/reversals/pivotwood/Pivotwood.md b/lib/reversals/pivotwood/Pivotwood.md index 62261325..d8f57682 100644 --- a/lib/reversals/pivotwood/Pivotwood.md +++ b/lib/reversals/pivotwood/Pivotwood.md @@ -12,7 +12,7 @@ | **Warmup** | `2` bars | | **PineScript** | [pivotwood.pine](pivotwood.pine) | -- Woodie's Pivot Points weight the closing price twice in the pivot calculation, biasing the central pivot toward where the market actually settled r... +- Woodie's Pivot Points weight the closing price twice in the pivot calculation, biasing the central pivot toward where the market actually settled rather than treating high, low, and close equally. - No configurable parameters; computation is stateless per bar. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/statistics/cointegration/Cointegration.md b/lib/statistics/cointegration/Cointegration.md index 878a168b..17a7cae2 100644 --- a/lib/statistics/cointegration/Cointegration.md +++ b/lib/statistics/cointegration/Cointegration.md @@ -12,7 +12,7 @@ | **Warmup** | `period + 1` bars | | **PineScript** | [cointegration.pine](cointegration.pine) | -- The Cointegration indicator measures the long-run equilibrium relationship between two price series using the Engle-Granger two-step method with an... +- The Cointegration indicator measures the long-run equilibrium relationship between two price series using the Engle-Granger two-step method with an Augmented Dickey-Fuller (ADF) test. - **Similar:** [Correl](../correl/Correl.md), [Granger](../granger/Granger.md) | **Trading note:** Tests if two series share a long-run equilibrium. Foundation of statistical arbitrage (pairs trading). - Validated against TradingView PineScript reference and statistical property tests. diff --git a/lib/statistics/correl/Correl.md b/lib/statistics/correl/Correl.md index 13c96875..1b758690 100644 --- a/lib/statistics/correl/Correl.md +++ b/lib/statistics/correl/Correl.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [correl.pine](correl.pine) | -- The Pearson Correlation Coefficient measures the linear relationship between two variables, returning a value from -1 (perfect negative correlation... +- The Pearson Correlation Coefficient measures the linear relationship between two variables, returning a value from -1 (perfect negative correlation) to +1 (perfect positive correlation). - **Similar:** [Spearman](../spearman/Spearman.md), [Kendall](../kendall/Kendall.md) | **Trading note:** Pearson correlation; measures linear relationship strength. Used for portfolio diversification and pairs trading. - Validated against TradingView reference behavior and mathematical invariants. diff --git a/lib/statistics/granger/Granger.md b/lib/statistics/granger/Granger.md index 2de6f94e..70c6b383 100644 --- a/lib/statistics/granger/Granger.md +++ b/lib/statistics/granger/Granger.md @@ -12,7 +12,7 @@ | **Warmup** | `period + 1` bars | | **PineScript** | [granger.pine](granger.pine) | -- The Granger Causality test asks a precise, falsifiable question: does knowing the history of series X improve your ability to predict series Y, bey... +- The Granger Causality test asks a precise, falsifiable question: does knowing the history of series X improve your ability to predict series Y, beyond what Y's own history already provides? The answer arrives as an F-statistic from comparing two OLS regression models. - **Similar:** [Cointegration](../cointegration/Cointegration.md), [Correl](../correl/Correl.md) | **Trading note:** Granger causality test; determines if one time series can forecast another. Lead-lag detection. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/statistics/pacf/Pacf.md b/lib/statistics/pacf/Pacf.md index dfadb029..adbebe30 100644 --- a/lib/statistics/pacf/Pacf.md +++ b/lib/statistics/pacf/Pacf.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [pacf.pine](pacf.pine) | -- The Partial Autocorrelation Function (PACF) measures the correlation between a time series and its lagged values, after removing the effects of all... +- The Partial Autocorrelation Function (PACF) measures the correlation between a time series and its lagged values, after removing the effects of all intermediate lags. - **Similar:** [ACF](../acf/Acf.md), [LinReg](../linreg/LinReg.md) | **Trading note:** Partial autocorrelation; isolates direct lag relationships. Used for ARIMA model order selection. - Validated against mathematical properties and Durbin-Levinson recursion expectations. diff --git a/lib/statistics/polyfit/Polyfit.md b/lib/statistics/polyfit/Polyfit.md index 4a30c0b5..5e6b97b0 100644 --- a/lib/statistics/polyfit/Polyfit.md +++ b/lib/statistics/polyfit/Polyfit.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [polyfit.pine](polyfit.pine) | -- Polynomial Fitting computes a rolling polynomial regression of configurable degree over a lookback window, returning the fitted value at the curren... +- Polynomial Fitting computes a rolling polynomial regression of configurable degree over a lookback window, returning the fitted value at the current bar. - **Similar:** [LinReg](../linreg/LinReg.md), [TSF](../../trends_FIR/tsf/Tsf.md) | **Trading note:** Polynomial curve fitting; captures non-linear trends. Higher order = more responsive but risk of overfitting. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/statistics/sum/Sum.md b/lib/statistics/sum/Sum.md index 45f9c6a2..e2ec0e80 100644 --- a/lib/statistics/sum/Sum.md +++ b/lib/statistics/sum/Sum.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [sum.pine](sum.pine) | -- The Sum indicator calculates a rolling window summation using the Kahan-Babuška algorithm (also known as "improved Kahan" or "second-order compensa... +- The Sum indicator calculates a rolling window summation using the Kahan-Babuška algorithm (also known as "improved Kahan" or "second-order compensated summation") for maximum numerical precision. - **Trading note:** Rolling sum; cumulative total over lookback window. Building block for many indicators (e.g., OBV, A/D). - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/statistics/trim/Trim.md b/lib/statistics/trim/Trim.md index 6daf6553..42c73ae6 100644 --- a/lib/statistics/trim/Trim.md +++ b/lib/statistics/trim/Trim.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [trim.pine](trim.pine) | -- The Trimmed Mean Moving Average computes a rolling average after discarding a configurable percentage of the most extreme values from each tail of ... +- The Trimmed Mean Moving Average computes a rolling average after discarding a configurable percentage of the most extreme values from each tail of the sorted lookback window. - **Similar:** [Wins](../wins/Wins.md), [Median](../median/Median.md) | **Trading note:** Trimmed mean; excludes extreme percentiles. Robust average for volatile data. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/statistics/wavg/Wavg.md b/lib/statistics/wavg/Wavg.md index f85020db..446a05b7 100644 --- a/lib/statistics/wavg/Wavg.md +++ b/lib/statistics/wavg/Wavg.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [wavg.pine](wavg.pine) | -- The Weighted Average computes a rolling linearly-weighted mean where the most recent observation receives weight $N$ and the oldest receives weight... +- The Weighted Average computes a rolling linearly-weighted mean where the most recent observation receives weight $N$ and the oldest receives weight 1, making it mathematically identical to the Weighted Moving Average (WMA) but categorized as a statistical measure. - **Similar:** [WMA](../../trends_FIR/wma/wma.md), [EMA](../../trends_IIR/ema/ema.md) | **Trading note:** Weighted average with custom weights; flexible aggregation for composite indicators. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/statistics/wins/Wins.md b/lib/statistics/wins/Wins.md index 9fb6f954..d68d3d0a 100644 --- a/lib/statistics/wins/Wins.md +++ b/lib/statistics/wins/Wins.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [wins.pine](wins.pine) | -- The Winsorized Mean Moving Average computes a rolling average after replacing (not discarding) the most extreme values in each tail with the bounda... +- The Winsorized Mean Moving Average computes a rolling average after replacing (not discarding) the most extreme values in each tail with the boundary values at the trim point. - **Similar:** [Trim](../trim/Trim.md), [Percentile](../percentile/Percentile.md) | **Trading note:** Winsorized mean; replaces extreme values instead of removing them. Preserves sample size. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/statistics/ztest/Ztest.md b/lib/statistics/ztest/Ztest.md index 4f0034b9..6aca18cc 100644 --- a/lib/statistics/ztest/Ztest.md +++ b/lib/statistics/ztest/Ztest.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [ztest.pine](ztest.pine) | -- ZTEST computes the **one-sample t-statistic**, measuring how many standard errors the rolling sample mean deviates from a hypothesized population m... +- ZTEST computes the **one-sample t-statistic**, measuring how many standard errors the rolling sample mean deviates from a hypothesized population mean $\mu_0$. - **Similar:** [JB](../jb/Jb.md), [Zscore](../zscore/Zscore.md) | **Trading note:** Z-test; tests if sample mean differs from population mean. Used to validate trading edge significance. - Validated against manual computation, PineScript parity, and testable statistical properties. diff --git a/lib/trends_FIR/crma/Crma.md b/lib/trends_FIR/crma/Crma.md index cbe03a46..eea4a4fe 100644 --- a/lib/trends_FIR/crma/Crma.md +++ b/lib/trends_FIR/crma/Crma.md @@ -13,7 +13,7 @@ | **PineScript** | [crma.pine](crma.pine) | | **Signature** | [crma_signature](crma_signature.md) | -- CRMA fits a degree-3 polynomial $y = a_0 + a_1 x + a_2 x^2 + a_3 x^3$ to the most recent $N$ bars via ordinary least squares, then returns the fitt... +- CRMA fits a degree-3 polynomial $y = a_0 + a_1 x + a_2 x^2 + a_3 x^3$ to the most recent $N$ bars via ordinary least squares, then returns the fitted endpoint value $a_0$. - **Similar:** [SMA](../sma/Sma.md), [TrIMA](../trima/trima.md) | **Complementary:** Trend strength indicators | **Trading note:** Cubic-Root weighted MA; gentle weighting profile between uniform (SMA) and triangular (TrIMA). - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/hend/Hend.md b/lib/trends_FIR/hend/Hend.md index 7de25f5f..51dd90f9 100644 --- a/lib/trends_FIR/hend/Hend.md +++ b/lib/trends_FIR/hend/Hend.md @@ -13,7 +13,7 @@ | **PineScript** | [hend.pine](hend.pine) | | **Signature** | [hend_signature](hend_signature.md) | -- HEND is a symmetric FIR filter derived from the Henderson (1916) closed-form weight formula, designed to pass cubic polynomial trends without disto... +- HEND is a symmetric FIR filter derived from the Henderson (1916) closed-form weight formula, designed to pass cubic polynomial trends without distortion while maximally suppressing irregular noise. - **Similar:** [LSMA](../lsma/lsma.md), [TSF](../tsf/Tsf.md) | **Complementary:** StdDev | **Trading note:** Henderson MA; used by Australian Bureau of Statistics. Optimal for extracting smooth trend from noisy data. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/ilrs/Ilrs.md b/lib/trends_FIR/ilrs/Ilrs.md index 52c6c2b8..4b9ea899 100644 --- a/lib/trends_FIR/ilrs/Ilrs.md +++ b/lib/trends_FIR/ilrs/Ilrs.md @@ -13,7 +13,7 @@ | **PineScript** | [ilrs.pine](ilrs.pine) | | **Signature** | [ilrs_signature](ilrs_signature.md) | -- ILRS computes the linear regression slope over a rolling window, then accumulates it via discrete integration (running sum) to reconstruct a smooth... +- ILRS computes the linear regression slope over a rolling window, then accumulates it via discrete integration (running sum) to reconstruct a smoothed price-level signal. - **Similar:** [LSMA](../lsma/lsma.md), [LinReg](../../statistics/linreg/LinReg.md) | **Complementary:** R² for fit quality | **Trading note:** Integral of Linear Regression Slope; smoothed trend derived from cumulative regression. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/kaiser/Kaiser.md b/lib/trends_FIR/kaiser/Kaiser.md index de53e95c..2e684b25 100644 --- a/lib/trends_FIR/kaiser/Kaiser.md +++ b/lib/trends_FIR/kaiser/Kaiser.md @@ -13,7 +13,7 @@ | **PineScript** | [kaiser.pine](kaiser.pine) | | **Signature** | [kaiser_signature](kaiser_signature.md) | -- KAISER applies the Kaiser-Bessel window function as FIR filter weights, providing a single parameter ($\beta$) that continuously controls the trade... +- KAISER applies the Kaiser-Bessel window function as FIR filter weights, providing a single parameter ($\beta$) that continuously controls the trade-off between main lobe width (transition band sharpness) and sidelobe attenuation (stopband rejection). - **Similar:** [ALMA](../alma/alma.md), [BLMA](../blma/blma.md) | **Complementary:** Cycle analysis | **Trading note:** Kaiser-windowed MA; adjustable sidelobe suppression via beta parameter. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/lanczos/Lanczos.md b/lib/trends_FIR/lanczos/Lanczos.md index f11fb2a0..80313f85 100644 --- a/lib/trends_FIR/lanczos/Lanczos.md +++ b/lib/trends_FIR/lanczos/Lanczos.md @@ -13,7 +13,7 @@ | **PineScript** | [lanczos.pine](lanczos.pine) | | **Signature** | [lanczos_signature](lanczos_signature.md) | -- LANCZOS applies the normalized sinc function $\text{sinc}(x) = \sin(\pi x)/(\pi x)$ as a symmetric FIR window, producing a moving average with near... +- LANCZOS applies the normalized sinc function $\text{sinc}(x) = \sin(\pi x)/(\pi x)$ as a symmetric FIR window, producing a moving average with near-ideal low-pass frequency characteristics. - **Similar:** [SinEma](../sinema/sinema.md), [NyqMA](../nyqma/Nyqma.md) | **Complementary:** FFT for frequency analysis | **Trading note:** Lanczos filter; sinc function with Lanczos window. Near-ideal low-pass with sharp cutoff. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/lsma/Lsma.md b/lib/trends_FIR/lsma/Lsma.md index 11c3ecae..acf58752 100644 --- a/lib/trends_FIR/lsma/Lsma.md +++ b/lib/trends_FIR/lsma/Lsma.md @@ -13,7 +13,7 @@ | **PineScript** | [lsma.pine](lsma.pine) | | **Signature** | [lsma_signature](lsma_signature.md) | -- LSMA (Least Squares Moving Average), also known as the Moving Linear Regression or Endpoint Moving Average, calculates the least squares regression... +- LSMA (Least Squares Moving Average), also known as the Moving Linear Regression or Endpoint Moving Average, calculates the least squares regression line for the preceding time periods. - **Similar:** [Linear Regression](../../statistics/linreg/LinReg.md), [ALMA](../alma/Alma.md) | **Complementary:** R-squared for regression quality | **Trading note:** Least Squares MA; linear regression value at current bar, minimizing squared deviations. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/nyqma/Nyqma.md b/lib/trends_FIR/nyqma/Nyqma.md index 65644adc..d5991ec1 100644 --- a/lib/trends_FIR/nyqma/Nyqma.md +++ b/lib/trends_FIR/nyqma/Nyqma.md @@ -13,7 +13,7 @@ | **PineScript** | [nyqma.pine](nyqma.pine) | | **Signature** | [nyqma_signature](nyqma_signature.md) | -- NYQMA combines a primary LWMA (Linear Weighted Moving Average) with a secondary LWMA applied to the first, using lag-compensating extrapolation: $\... +- NYQMA combines a primary LWMA (Linear Weighted Moving Average) with a secondary LWMA applied to the first, using lag-compensating extrapolation: $\text{NYQMA} = (1+\alpha) \cdot \text{MA}_1 - \alpha \cdot \text{MA}_2$, where $\alpha = N_2 / (N_1 - N_2)$. - **Similar:** [Lanczos](../lanczos/Lanczos.md), [SinEma](../sinema/sinema.md) | **Complementary:** Cycle detection | **Trading note:** Nyquist MA; designed around Nyquist frequency. Optimal for eliminating aliased cycles. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/parzen/Parzen.md b/lib/trends_FIR/parzen/Parzen.md index 4e42f330..c99810e2 100644 --- a/lib/trends_FIR/parzen/Parzen.md +++ b/lib/trends_FIR/parzen/Parzen.md @@ -13,7 +13,7 @@ | **PineScript** | [parzen.pine](parzen.pine) | | **Signature** | [parzen_signature](parzen_signature.md) | -- PARZEN applies the Parzen (de la Vallée-Poussin) window function as FIR filter weights, producing a moving average with exceptional sidelobe suppre... +- PARZEN applies the Parzen (de la Vallée-Poussin) window function as FIR filter weights, producing a moving average with exceptional sidelobe suppression ($-24$ dB/octave rolloff) and a smooth bell-shaped kernel. - **Similar:** [GWMA](../gwma/gwma.md), [BWMA](../bwma/Bwma.md) | **Complementary:** ATR | **Trading note:** Parzen-window MA; piecewise-cubic taper. Very smooth with low spectral leakage. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/pma/Pma.md b/lib/trends_FIR/pma/Pma.md index a3abb7ff..e1ba9ec8 100644 --- a/lib/trends_FIR/pma/Pma.md +++ b/lib/trends_FIR/pma/Pma.md @@ -13,7 +13,7 @@ | **PineScript** | [pma.pine](pma.pine) | | **Signature** | [pma_signature](pma_signature.md) | -- PMA (Predictive Moving Average) is a lag-cancellation filter that uses linear extrapolation of dual WMA (Weighted Moving Average) cascades to predi... +- PMA (Predictive Moving Average) is a lag-cancellation filter that uses linear extrapolation of dual WMA (Weighted Moving Average) cascades to predict price direction. - **Similar:** [LSMA](../lsma/lsma.md), [Polyfit](../../statistics/polyfit/Polyfit.md) | **Complementary:** R² for trend quality | **Trading note:** Polynomial MA; fits nth-degree polynomial. Captures curves better than linear regression. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/qrma/Qrma.md b/lib/trends_FIR/qrma/Qrma.md index 49ece5d3..f1b81885 100644 --- a/lib/trends_FIR/qrma/Qrma.md +++ b/lib/trends_FIR/qrma/Qrma.md @@ -13,7 +13,7 @@ | **PineScript** | [qrma.pine](qrma.pine) | | **Signature** | [qrma_signature](qrma_signature.md) | -- QRMA fits a second-degree polynomial $y = a + bx + cx^2$ to the most recent $N$ bars via ordinary least squares, then returns the fitted value at t... +- QRMA fits a second-degree polynomial $y = a + bx + cx^2$ to the most recent $N$ bars via ordinary least squares, then returns the fitted value at the endpoint (newest bar). - **Similar:** [LSMA](../lsma/lsma.md), [PMA](../pma/Pma.md) | **Complementary:** Trend indicators | **Trading note:** Quadratic Regression MA; 2nd-order polynomial fit. Captures parabolic acceleration. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/rain/Rain.md b/lib/trends_FIR/rain/Rain.md index 35b7f8d6..bf4fcd3d 100644 --- a/lib/trends_FIR/rain/Rain.md +++ b/lib/trends_FIR/rain/Rain.md @@ -13,7 +13,7 @@ | **PineScript** | [rain.pine](rain.pine) | | **Signature** | [rain_signature](rain_signature.md) | -- RAIN recursively applies SMA 10 times, producing 10 layers of progressively smoother price representation, then computes a weighted average across ... +- RAIN recursively applies SMA 10 times, producing 10 layers of progressively smoother price representation, then computes a weighted average across all layers. - **Similar:** [ALMA](../alma/alma.md), [FWMA](../fwma/fwma.md) | **Complementary:** ATR | **Trading note:** Raised-cosine MA; smooth taper at edges. Good sidelobe suppression for noise reduction. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/rwma/Rwma.md b/lib/trends_FIR/rwma/Rwma.md index 3a8acf69..f6dd86cd 100644 --- a/lib/trends_FIR/rwma/Rwma.md +++ b/lib/trends_FIR/rwma/Rwma.md @@ -12,7 +12,7 @@ | **Warmup** | `> period` bars | | **PineScript** | [rwma.pine](rwma.pine) | -- RWMA weights each bar's contribution to the average by its price range (high minus low), giving greater influence to volatile bars and less to narr... +- RWMA weights each bar's contribution to the average by its price range (high minus low), giving greater influence to volatile bars and less to narrow-range, indecisive bars. - **Similar:** [WMA](../wma/wma.md), [EMA](../../trends_IIR/ema/ema.md) | **Trading note:** Right-weighted MA; concentrates weight on recent data while maintaining FIR structure. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/sgma/Sgma.md b/lib/trends_FIR/sgma/Sgma.md index 28707b5e..962155a1 100644 --- a/lib/trends_FIR/sgma/Sgma.md +++ b/lib/trends_FIR/sgma/Sgma.md @@ -13,7 +13,7 @@ | **PineScript** | [sgma.pine](sgma.pine) | | **Signature** | [sgma_signature](sgma_signature.md) | -- SGMA is a Finite Impulse Response (FIR) filter that uses polynomial fitting to smooth data while preserving higher moments (peaks, valleys, and inf... +- SGMA is a Finite Impulse Response (FIR) filter that uses polynomial fitting to smooth data while preserving higher moments (peaks, valleys, and inflection points). - **Similar:** [SGF](../../filters/sgf/Sgf.md), [LSMA](../lsma/lsma.md) | **Trading note:** Savitzky-Golay MA; polynomial smoothing that preserves higher moments. Good for derivative estimation. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_FIR/tukey_w/Tukey_w.md b/lib/trends_FIR/tukey_w/Tukey_w.md index a5f9414d..5963fdf4 100644 --- a/lib/trends_FIR/tukey_w/Tukey_w.md +++ b/lib/trends_FIR/tukey_w/Tukey_w.md @@ -13,7 +13,7 @@ | **PineScript** | [tukey_w.pine](tukey_w.pine) | | **Signature** | [tukey_w_signature](tukey_w_signature.md) | -- TUKEY_W applies the Tukey (tapered cosine) window as FIR filter weights, offering a single parameter $\alpha$ that controls the fraction of the win... +- TUKEY_W applies the Tukey (tapered cosine) window as FIR filter weights, offering a single parameter $\alpha$ that controls the fraction of the window that is cosine-tapered. - **Similar:** [HanMA](../hanma/hanma.md), [BWMA](../bwma/Bwma.md) | **Trading note:** Tukey-window MA; adjustable taper parameter between rectangular and Hann. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_IIR/coral/Coral.md b/lib/trends_IIR/coral/Coral.md index 4ab7af97..b9b1e318 100644 --- a/lib/trends_IIR/coral/Coral.md +++ b/lib/trends_IIR/coral/Coral.md @@ -13,7 +13,7 @@ | **PineScript** | [coral.pine](coral.pine) | | **Signature** | [coral_signature](coral_signature.md) | -- The **Coral** filter is a smooth, low-lag trend indicator that chains six cascaded EMA passes and combines stages 3–6 using polynomial coefficients... +- The **Coral** filter is a smooth, low-lag trend indicator that chains six cascaded EMA passes and combines stages 3–6 using polynomial coefficients derived from a "Constant D" parameter. - **Similar:** [DEMA](../dema/dema.md), [TEMA](../tema/tema.md) | **Complementary:** Trend direction filters | **Trading note:** Coral trend indicator; smooth, low-lag modified exponential filter. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_IIR/dsma/Dsma.md b/lib/trends_IIR/dsma/Dsma.md index c1aad625..4788c0d7 100644 --- a/lib/trends_IIR/dsma/Dsma.md +++ b/lib/trends_IIR/dsma/Dsma.md @@ -13,7 +13,7 @@ | **PineScript** | [dsma.pine](dsma.pine) | | **Signature** | [dsma_signature](dsma_signature.md) | -- DSMA (Deviation-Scaled Moving Average) is a volatility-adaptive trend filter that combines a Super Smoother (2-pole Butterworth IIR filter) with RM... +- DSMA (Deviation-Scaled Moving Average) is a volatility-adaptive trend filter that combines a Super Smoother (2-pole Butterworth IIR filter) with RMS-based deviation scaling. - **Similar:** [DEMA](../dema/dema.md), [KAMA](../kama/kama.md) | **Complementary:** ADX for trend confirmation | **Trading note:** Deviation-Scaled MA; adapts smoothing based on price deviation. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_IIR/gdema/Gdema.md b/lib/trends_IIR/gdema/Gdema.md index a94e4f15..a2833225 100644 --- a/lib/trends_IIR/gdema/Gdema.md +++ b/lib/trends_IIR/gdema/Gdema.md @@ -13,7 +13,7 @@ | **PineScript** | [gdema.pine](gdema.pine) | | **Signature** | [gdema_signature](gdema_signature.md) | -- GDEMA extends the standard DEMA (Double Exponential Moving Average) with a tunable gain factor $v$ that controls the aggressiveness of lag compensa... +- GDEMA extends the standard DEMA (Double Exponential Moving Average) with a tunable gain factor $v$ that controls the aggressiveness of lag compensation. - **Similar:** [DEMA](../dema/dema.md), [T3](../t3/t3.md) | **Complementary:** Signal crossovers | **Trading note:** Generalized DEMA; tunable volume factor between EMA and DEMA behavior. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_IIR/hwma/Hwma.md b/lib/trends_IIR/hwma/Hwma.md index 06b028ad..148551e3 100644 --- a/lib/trends_IIR/hwma/Hwma.md +++ b/lib/trends_IIR/hwma/Hwma.md @@ -13,7 +13,7 @@ | **PineScript** | [hwma.pine](hwma.pine) | | **Signature** | [hwma_signature](hwma_signature.md) | -- HWMA is an Infinite Impulse Response (IIR) filter that applies triple exponential smoothing with level (F), velocity (V), and acceleration (A) comp... +- HWMA is an Infinite Impulse Response (IIR) filter that applies triple exponential smoothing with level (F), velocity (V), and acceleration (A) components. - **Similar:** [HOLT](../holt/holt.md) | **Complementary:** Seasonal analysis | **Trading note:** Holt-Winters MA; triple exponential smoothing with seasonal component. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_IIR/mama/Mama.md b/lib/trends_IIR/mama/Mama.md index 4b323432..63302dee 100644 --- a/lib/trends_IIR/mama/Mama.md +++ b/lib/trends_IIR/mama/Mama.md @@ -14,7 +14,7 @@ | **Signature** | [mama_signature](mama_signature.md) | -- MAMA (MESA Adaptive Moving Average) is a unique adaptive moving average that uses the Hilbert Transform to determine the phase rate of change of th... +- MAMA (MESA Adaptive Moving Average) is a unique adaptive moving average that uses the Hilbert Transform to determine the phase rate of change of the market cycle. - **Similar:** [FRAMA](../frama/frama.md), [KAMA](../kama/kama.md) | **Complementary:** FAMA crossover | **Trading note:** MESA Adaptive MA by Ehlers; Hilbert Transform cycle-adaptive smoothing. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_IIR/mma/Mma.md b/lib/trends_IIR/mma/Mma.md index 0e4a96b5..90cb87f3 100644 --- a/lib/trends_IIR/mma/Mma.md +++ b/lib/trends_IIR/mma/Mma.md @@ -13,7 +13,7 @@ | **PineScript** | [mma.pine](mma.pine) | | **Signature** | [mma_signature](mma_signature.md) | -- MMA (Modified Moving Average) uses a **simple mean** as a baseline, then adds a **weighted correction** based on the position of values within the ... +- MMA (Modified Moving Average) uses a **simple mean** as a baseline, then adds a **weighted correction** based on the position of values within the buffer. - **Similar:** [SMMA](../rma/Rma.md), [EMA](../ema/Ema.md) | **Complementary:** RSI/ATR (use MMA internally) | **Trading note:** Modified MA (identical to SMMA/RMA); Wilders smoothing. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_IIR/nma/Nma.md b/lib/trends_IIR/nma/Nma.md index 6eea3540..282df6c5 100644 --- a/lib/trends_IIR/nma/Nma.md +++ b/lib/trends_IIR/nma/Nma.md @@ -13,7 +13,7 @@ | **PineScript** | [nma.pine](nma.pine) | | **Signature** | [nma_signature](nma_signature.md) | -- NMA is an adaptive IIR filter whose smoothing ratio is derived from a volatility-weighted square-root kernel analysis of log-price movements over a... +- NMA is an adaptive IIR filter whose smoothing ratio is derived from a volatility-weighted square-root kernel analysis of log-price movements over a lookback window. - **Similar:** [KAMA](../kama/kama.md), [VIDYA](../vidya/vidya.md) | **Complementary:** Noise filters | **Trading note:** Noise-elimination MA; adapts to signal-to-noise ratio. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_IIR/qema/Qema.md b/lib/trends_IIR/qema/Qema.md index e02e8e53..b7545ebf 100644 --- a/lib/trends_IIR/qema/Qema.md +++ b/lib/trends_IIR/qema/Qema.md @@ -13,7 +13,7 @@ | **PineScript** | [qema.pine](qema.pine) | | **Signature** | [qema_signature](qema_signature.md) | -- QEMA (Quad Exponential Moving Average) is a zero-lag smoothing filter that cascades four EMAs with geometrically ramped alphas and combines them us... +- QEMA (Quad Exponential Moving Average) is a zero-lag smoothing filter that cascades four EMAs with geometrically ramped alphas and combines them using minimum-energy weights. - **Similar:** [DEMA](../dema/dema.md), [TEMA](../tema/tema.md) | **Complementary:** Signal line crossovers | **Trading note:** Quadruple EMA; 4th-order lag reduction with overshoot risk. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_IIR/rema/Rema.md b/lib/trends_IIR/rema/Rema.md index b8099911..757ce4d6 100644 --- a/lib/trends_IIR/rema/Rema.md +++ b/lib/trends_IIR/rema/Rema.md @@ -13,7 +13,7 @@ | **PineScript** | [rema.pine](rema.pine) | | **Signature** | [rema_signature](rema_signature.md) | -- REMA (Regularized Exponential Moving Average) combines exponential smoothing with a regularization term that penalizes deviations from the previous... +- REMA (Regularized Exponential Moving Average) combines exponential smoothing with a regularization term that penalizes deviations from the previous trend direction. - **Similar:** [EMA](../ema/ema.md), [DEMA](../dema/dema.md) | **Complementary:** Volatility filters | **Trading note:** Regularized EMA; lambda term reduces whipsaws. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/trends_IIR/trama/Trama.md b/lib/trends_IIR/trama/Trama.md index e00cad65..ae2a913d 100644 --- a/lib/trends_IIR/trama/Trama.md +++ b/lib/trends_IIR/trama/Trama.md @@ -13,7 +13,7 @@ | **PineScript** | [trama.pine](trama.pine) | | **Signature** | [trama_signature](trama_signature.md) | -- TRAMA is an adaptive EMA where the smoothing factor derives from the "trend regularity" of the lookback window, measured as the fraction of bars th... +- TRAMA is an adaptive EMA where the smoothing factor derives from the "trend regularity" of the lookback window, measured as the fraction of bars that produce either a new highest-high (HH) or a new lowest-low (LL). - **Similar:** [KAMA](../kama/kama.md), [VIDYA](../vidya/vidya.md) | **Complementary:** Volatility filters | **Trading note:** Triangular Adaptive MA; uses triangular window in adaptive mode. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volatility/bbwn/Bbwn.md b/lib/volatility/bbwn/Bbwn.md index 15d7af32..4c6bd875 100644 --- a/lib/volatility/bbwn/Bbwn.md +++ b/lib/volatility/bbwn/Bbwn.md @@ -12,7 +12,7 @@ | **Warmup** | `period + lookback` bars | | **PineScript** | [bbwn.pine](bbwn.pine) | -- Bollinger Band Width Normalized (BBWN) extends the standard BBW by normalizing it to a [0,1] range based on historical minimum and maximum values o... +- Bollinger Band Width Normalized (BBWN) extends the standard BBW by normalizing it to a [0,1] range based on historical minimum and maximum values over a lookback period. - **Similar:** [BBW](../bbw/bbw.md) | **Complementary:** Cross-asset comparison | **Trading note:** Normalized BandWidth for cross-asset comparison. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volatility/bbwp/Bbwp.md b/lib/volatility/bbwp/Bbwp.md index 29b6dd08..6c340647 100644 --- a/lib/volatility/bbwp/Bbwp.md +++ b/lib/volatility/bbwp/Bbwp.md @@ -12,7 +12,7 @@ | **Warmup** | `period + lookback` bars | | **PineScript** | [bbwp.pine](bbwp.pine) | -- BBWP (Bollinger Band Width Percentile) measures where the current Bollinger Band Width falls within its historical distribution, expressing the res... +- BBWP (Bollinger Band Width Percentile) measures where the current Bollinger Band Width falls within its historical distribution, expressing the result as a percentile rank between 0 and 1. - **Similar:** [BBW](../bbw/bbw.md) | **Complementary:** Percentile rank | **Trading note:** BandWidth Percentile; ranks current width in historical context. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volatility/cv/Cv.md b/lib/volatility/cv/Cv.md index e3a2b8a8..a501b0c2 100644 --- a/lib/volatility/cv/Cv.md +++ b/lib/volatility/cv/Cv.md @@ -12,7 +12,7 @@ | **Warmup** | `period + 1` bars | | **PineScript** | [cv.pine](cv.pine) | -- Conditional Volatility (CV) implements the GARCH(1,1) model for volatility forecasting, the most widely used time-varying volatility model in finan... +- Conditional Volatility (CV) implements the GARCH(1,1) model for volatility forecasting, the most widely used time-varying volatility model in financial econometrics. - **Similar:** [HV](../hv/hv.md) | **Complementary:** Volatility analysis | **Trading note:** Coefficient of Variation; ratio of std dev to mean. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volatility/gkv/Gkv.md b/lib/volatility/gkv/Gkv.md index cb473276..90364812 100644 --- a/lib/volatility/gkv/Gkv.md +++ b/lib/volatility/gkv/Gkv.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [gkv.pine](gkv.pine) | -- Garman-Klass Volatility (GKV) is a range-based volatility estimator that uses all four OHLC prices to provide more efficient volatility estimates t... +- Garman-Klass Volatility (GKV) is a range-based volatility estimator that uses all four OHLC prices to provide more efficient volatility estimates than traditional close-to-close methods. - **Similar:** [YZV](../yzv/yzv.md), [HV](../hv/hv.md) | **Complementary:** Options pricing | **Trading note:** Garman-Klass; full OHLC, more efficient than close-to-close. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volatility/hv/Hv.md b/lib/volatility/hv/Hv.md index 51504381..2596802f 100644 --- a/lib/volatility/hv/Hv.md +++ b/lib/volatility/hv/Hv.md @@ -12,7 +12,7 @@ | **Warmup** | `period + 1` bars | | **PineScript** | [hv.pine](hv.pine) | -- Historical Volatility (HV), also known as close-to-close volatility or realized volatility, is the classical measure of price volatility using the ... +- Historical Volatility (HV), also known as close-to-close volatility or realized volatility, is the classical measure of price volatility using the standard deviation of logarithmic returns. - **Similar:** [RVI](../rvi/rvi.md), [ATR](../atr/atr.md) | **Complementary:** Implied volatility for HV/IV ratio | **Trading note:** Historical Volatility; annualized std dev of log returns. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volatility/massi/Massi.md b/lib/volatility/massi/Massi.md index 279b3988..1e94e80f 100644 --- a/lib/volatility/massi/Massi.md +++ b/lib/volatility/massi/Massi.md @@ -12,7 +12,7 @@ | **Warmup** | 1 bar | | **PineScript** | [massi.pine](massi.pine) | -- The Mass Index, developed by Donald Dorsey and introduced in the June 1992 issue of *Technical Analysis of Stocks & Commodities*, identifies potent... +- The Mass Index, developed by Donald Dorsey and introduced in the June 1992 issue of *Technical Analysis of Stocks & Commodities*, identifies potential trend reversals by measuring the narrowing and widening of the range between high and low prices. - **Similar:** [BBW](../bbw/bbw.md) | **Complementary:** Reversal signals | **Trading note:** Mass Index; detects range bulges signaling reversals (>27 = reversal setup). - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volatility/rsv/Rsv.md b/lib/volatility/rsv/Rsv.md index f836bb95..64d249ce 100644 --- a/lib/volatility/rsv/Rsv.md +++ b/lib/volatility/rsv/Rsv.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [rsv.pine](rsv.pine) | -- Rogers-Satchell Volatility (RSV) is a drift-adjusted OHLC-based volatility estimator that uses all four price points (Open, High, Low, Close) to pr... +- Rogers-Satchell Volatility (RSV) is a drift-adjusted OHLC-based volatility estimator that uses all four price points (Open, High, Low, Close) to provide more accurate volatility estimates than simpler range-based methods. - **Similar:** [HV](../hv/hv.md) | **Complementary:** Options pricing | **Trading note:** Rogers-Satchell volatility; handles drift without bias. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volatility/rv/Rv.md b/lib/volatility/rv/Rv.md index 5ef8a6ab..1b503d1e 100644 --- a/lib/volatility/rv/Rv.md +++ b/lib/volatility/rv/Rv.md @@ -12,7 +12,7 @@ | **Warmup** | 1 bar | | **PineScript** | [rv.pine](rv.pine) | -- Realized Volatility (RV) measures price volatility using the sum of squared logarithmic returns over a rolling window, then applying SMA smoothing ... +- Realized Volatility (RV) measures price volatility using the sum of squared logarithmic returns over a rolling window, then applying SMA smoothing for stability. - **Similar:** [HV](../hv/hv.md), [EWMA](../ewma/ewma.md) | **Complementary:** High-frequency analysis | **Trading note:** Realized Volatility; sum of squared returns. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volatility/vr/Vr.md b/lib/volatility/vr/Vr.md index 12c4575c..f6da49d1 100644 --- a/lib/volatility/vr/Vr.md +++ b/lib/volatility/vr/Vr.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [vr.pine](vr.pine) | -- Volatility Ratio (VR) measures the current bar's True Range relative to its Average True Range (ATR), providing a normalized indicator of short-ter... +- Volatility Ratio (VR) measures the current bar's True Range relative to its Average True Range (ATR), providing a normalized indicator of short-term volatility expansion or contraction. - **Similar:** [HV](../hv/hv.md), [ATR](../atr/atr.md) | **Complementary:** Volatility regimes | **Trading note:** Volatility Ratio; current vs historical for regime detection. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volatility/yzv/Yzv.md b/lib/volatility/yzv/Yzv.md index 1887bf74..864738a1 100644 --- a/lib/volatility/yzv/Yzv.md +++ b/lib/volatility/yzv/Yzv.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [yzv.pine](yzv.pine) | -- Yang-Zhang Volatility is a sophisticated volatility estimator that combines overnight (close-to-open) returns with Rogers-Satchell intraday volatil... +- Yang-Zhang Volatility is a sophisticated volatility estimator that combines overnight (close-to-open) returns with Rogers-Satchell intraday volatility to capture the full spectrum of price dynamics. - **Similar:** [GKV](../gkv/gkv.md), [HV](../hv/hv.md) | **Complementary:** HV/IV comparison | **Trading note:** Yang-Zhang; most efficient OHLC estimator, handles gaps and drift. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volume/aobv/Aobv.md b/lib/volume/aobv/Aobv.md index ff025f67..237ace76 100644 --- a/lib/volume/aobv/Aobv.md +++ b/lib/volume/aobv/Aobv.md @@ -12,7 +12,7 @@ | **Warmup** | `> SlowPeriod` bars | | **PineScript** | [aobv.pine](aobv.pine) | -- Archer On-Balance Volume (AOBV) applies dual exponential smoothing to the classic On-Balance Volume indicator, creating a responsive yet noise-filt... +- Archer On-Balance Volume (AOBV) applies dual exponential smoothing to the classic On-Balance Volume indicator, creating a responsive yet noise-filtered momentum signal. - No configurable parameters; computation is stateless per bar. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volume/evwma/Evwma.md b/lib/volume/evwma/Evwma.md index 5e5204c9..644ec705 100644 --- a/lib/volume/evwma/Evwma.md +++ b/lib/volume/evwma/Evwma.md @@ -12,7 +12,7 @@ | **Warmup** | `> period` bars | | **PineScript** | [evwma.pine](evwma.pine) | -- EVWMA (Elastic Volume Weighted Moving Average) is a volume-adaptive moving average that weights each bar's contribution to the average by its volum... +- EVWMA (Elastic Volume Weighted Moving Average) is a volume-adaptive moving average that weights each bar's contribution to the average by its volume relative to a rolling volume sum. - **Similar:** [VWMA](../vwma/Vwma.md), [VWAP](../vwap/Vwap.md) | **Complementary:** OBV | **Trading note:** Elastic Volume-Weighted MA; adapts weighting dynamically based on volume flow. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volume/iii/Iii.md b/lib/volume/iii/Iii.md index 9ed15f41..873a32f2 100644 --- a/lib/volume/iii/Iii.md +++ b/lib/volume/iii/Iii.md @@ -12,7 +12,7 @@ | **Warmup** | `period` bars | | **PineScript** | [iii.pine](iii.pine) | -- The Intraday Intensity Index (III) measures buying and selling pressure by analyzing where the close price falls within the high-low range, weighte... +- The Intraday Intensity Index (III) measures buying and selling pressure by analyzing where the close price falls within the high-low range, weighted by volume. - **Similar:** [CMF](../cmf/Cmf.md), [MFI](../mfi/Mfi.md) | **Complementary:** Volume | **Trading note:** Intraday Intensity Index; measures close position within H-L range relative to volume. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volume/kvo/Kvo.md b/lib/volume/kvo/Kvo.md index 31b083a1..2b5b16b1 100644 --- a/lib/volume/kvo/Kvo.md +++ b/lib/volume/kvo/Kvo.md @@ -12,7 +12,7 @@ | **Warmup** | `slowPeriod` bars | | **PineScript** | [kvo.pine](kvo.pine) | -- The Klinger Volume Oscillator (KVO), developed by Stephen Klinger in the 1970s, measures the long-term trend of money flow while remaining sensitiv... +- The Klinger Volume Oscillator (KVO), developed by Stephen Klinger in the 1970s, measures the long-term trend of money flow while remaining sensitive to short-term fluctuations. - **Similar:** [CMF](../cmf/Cmf.md), [Adosc](../adosc/Adosc.md) | **Complementary:** MACD | **Trading note:** Klinger Volume Oscillator; volume-based trend indicator. Signal line crossovers for entries. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volume/pvo/Pvo.md b/lib/volume/pvo/Pvo.md index 7e2eeec4..93659f20 100644 --- a/lib/volume/pvo/Pvo.md +++ b/lib/volume/pvo/Pvo.md @@ -12,7 +12,7 @@ | **Warmup** | `slowPeriod` bars | | **PineScript** | [pvo.pine](pvo.pine) | -- The Percentage Volume Oscillator (PVO) measures the difference between two exponential moving averages of volume, expressed as a percentage of the ... +- The Percentage Volume Oscillator (PVO) measures the difference between two exponential moving averages of volume, expressed as a percentage of the slower EMA. - **Similar:** [PPO](../../momentum/ppo/Ppo.md), [VO](../vo/Vo.md) | **Complementary:** Price oscillators | **Trading note:** Percentage Volume Oscillator; MACD concept applied to volume. Detects volume surges. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volume/vf/Vf.md b/lib/volume/vf/Vf.md index 16369492..4add8c14 100644 --- a/lib/volume/vf/Vf.md +++ b/lib/volume/vf/Vf.md @@ -12,7 +12,7 @@ | **Warmup** | `> period` bars | | **PineScript** | [vf.pine](vf.pine) | -- Volume Force (VF) quantifies the strength of volume behind price movements by multiplying price change by volume and applying EMA smoothing with wa... +- Volume Force (VF) quantifies the strength of volume behind price movements by multiplying price change by volume and applying EMA smoothing with warmup compensation. - **Similar:** [MFI](../mfi/Mfi.md), [CMF](../cmf/Cmf.md) | **Complementary:** RSI | **Trading note:** Volume Force; measures directional volume pressure. Positive = buyers dominant. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volume/vwad/Vwad.md b/lib/volume/vwad/Vwad.md index fd64c08d..c2e24040 100644 --- a/lib/volume/vwad/Vwad.md +++ b/lib/volume/vwad/Vwad.md @@ -12,7 +12,7 @@ | **Warmup** | `> period` bars | | **PineScript** | [vwad.pine](vwad.pine) | -- Volume Weighted Accumulation/Distribution (VWAD) takes the classic ADL concept and asks a sharper question: not just "where did the close fall in t... +- Volume Weighted Accumulation/Distribution (VWAD) takes the classic ADL concept and asks a sharper question: not just "where did the close fall in the range?" but "how significant was this bar's volume compared to recent activity?" - **Similar:** [CMF](../cmf/Cmf.md), [OBV](../vwad/Vwad.md) | **Complementary:** MACD | **Trading note:** Volume-Weighted A/D; running sum of volume-weighted price position. Classic accumulation/distribution. - Validated against TA-Lib, Skender, and Tulip reference implementations where available. diff --git a/lib/volume/vwma/Vwma.md b/lib/volume/vwma/Vwma.md index 94683430..4533b2f5 100644 --- a/lib/volume/vwma/Vwma.md +++ b/lib/volume/vwma/Vwma.md @@ -12,7 +12,7 @@ | **Warmup** | `> period` bars | | **PineScript** | [vwma.pine](vwma.pine) | -- VWMA (Volume Weighted Moving Average) calculates a moving average where each price is weighted by its corresponding volume over a specified lookbac... +- VWMA (Volume Weighted Moving Average) calculates a moving average where each price is weighted by its corresponding volume over a specified lookback period. - **Similar:** [EVWMA](../evwma/Evwma.md), [SMA](../../trends_FIR/sma/Sma.md) | **Complementary:** OBV | **Trading note:** Volume-Weighted MA; weights price by volume. More responsive during high-volume bars. - Validated against TA-Lib, Skender, and Tulip reference implementations where available.