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Regression

LibWghtLibrary "LibWght" This is a library of mathematical and statistical functions designed for quantitative analysis in Pine Script. Its core principle is the integration of a custom weighting series (e.g., volume) into a wide array of standard technical analysis calculations. Key Capabilities: 1. **Universal Weighting:** All exported functions accept a `weight` parameter. This allows standard calculations (like moving averages, RSI, and standard deviation) to be influenced by an external data series, such as volume or tick count. 2. **Weighted Averages and Indicators:** Includes a comprehensive collection of weighted functions: - **Moving Averages:** `wSma`, `wEma`, `wWma`, `wRma` (Wilder's), `wHma` (Hull), and `wLSma` (Least Squares / Linear Regression). - **Oscillators & Ranges:** `wRsi`, `wAtr` (Average True Range), `wTr` (True Range), and `wR` (High-Low Range). 3. **Volatility Decomposition:** Provides functions to decompose total variance into distinct components for market analysis. - **Two-Way Decomposition (`wTotVar`):** Separates variance into **between-bar** (directional) and **within-bar** (noise) components. - **Three-Way Decomposition (`wLRTotVar`):** Decomposes variance relative to a linear regression into **Trend** (explained by the LR slope), **Residual** (mean-reversion around the LR line), and **Within-Bar** (noise) components. - **Local Volatility (`wLRLocTotStdDev`):** Measures the total "noise" (within-bar + residual) around the trend line. 4. **Weighted Statistics and Regression:** Provides a robust function for Weighted Linear Regression (`wLinReg`) and a full suite of related statistical measures: - **Between-Bar Stats:** `wBtwVar`, `wBtwStdDev`, `wBtwStdErr`. - **Residual Stats:** `wResVar`, `wResStdDev`, `wResStdErr`. 5. **Fallback Mechanism:** All functions are designed for reliability. If the total weight over the lookback period is zero (e.g., in a no-volume period), the algorithms automatically fall back to their unweighted, uniform-weight equivalents (e.g., `wSma` becomes a standard `ta.sma`), preventing errors and ensuring continuous calculation. --- **DISCLAIMER** This library is provided "AS IS" and for informational and educational purposes only. It does not constitute financial, investment, or trading advice. The author assumes no liability for any errors, inaccuracies, or omissions in the code. Using this library to build trading indicators or strategies is entirely at your own risk. As a developer using this library, you are solely responsible for the rigorous testing, validation, and performance of any scripts you create based on these functions. The author shall not be held liable for any financial losses incurred directly or indirectly from the use of this library or any scripts derived from it. wSma(source, weight, length)   Weighted Simple Moving Average (linear kernel).   Parameters:      source (float) : series float Data to average.      weight (float) : series float Weight series.      length (int) : series int Look-back length ≥ 1.   Returns: series float Linear-kernel weighted mean; falls back to the arithmetic mean if Σweight = 0. wEma(source, weight, length)   Weighted EMA (exponential kernel).   Parameters:      source (float) : series float Data to average.      weight (float) : series float Weight series.      length (simple int) : simple int Look-back length ≥ 1.   Returns: series float Exponential-kernel weighted mean; falls back to classic EMA if Σweight = 0. wWma(source, weight, length)   Weighted WMA (linear kernel).   Parameters:      source (float) : series float Data to average.      weight (float) : series float Weight series.      length (int) : series int Look-back length ≥ 1.   Returns: series float Linear-kernel weighted mean; falls back to classic WMA if Σweight = 0. wRma(source, weight, length)   Weighted RMA (Wilder kernel, α = 1/len).   Parameters:      source (float) : series float Data to average.      weight (float) : series float Weight series.      length (simple int) : simple int Look-back length ≥ 1.   Returns: series float Wilder-kernel weighted mean; falls back to classic RMA if Σweight = 0. wHma(source, weight, length)   Weighted HMA (linear kernel).   Parameters:      source (float) : series float Data to average.      weight (float) : series float Weight series.      length (int) : series int Look-back length ≥ 1.   Returns: series float Linear-kernel weighted mean; falls back to classic HMA if Σweight = 0. wRsi(source, weight, length)   Weighted Relative Strength Index.   Parameters:      source (float) : series float Price series.      weight (float) : series float Weight series.      length (simple int) : simple int Look-back length ≥ 1.   Returns: series float Weighted RSI; uniform if Σw = 0. wAtr(tr, weight, length)   Weighted ATR (Average True Range). Implemented as WRMA on *true range*.   Parameters:      tr (float) : series float True Range series.      weight (float) : series float Weight series.      length (simple int) : simple int Look-back length ≥ 1.   Returns: series float Weighted ATR; uniform weights if Σw = 0. wTr(tr, weight, length)   Weighted True Range over a window.   Parameters:      tr (float) : series float True Range series.      weight (float) : series float Weight series.      length (int) : series int Look-back length ≥ 1.   Returns: series float Weighted mean of TR; uniform if Σw = 0. wR(r, weight, length)   Weighted High-Low Range over a window.   Parameters:      r (float) : series float High-Low per bar.      weight (float) : series float Weight series.      length (int) : series int Look-back length ≥ 1.   Returns: series float Weighted mean of range; uniform if Σw = 0. wBtwVar(source, weight, length, biased)   Weighted Between Variance (biased/unbiased).   Parameters:      source (float) : series float Data series.      weight (float) : series float Weight series.      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population (biased); false → sample.   Returns: variance series float The calculated between-bar variance (σ²btw), either biased or unbiased. sumW series float The sum of weights over the lookback period (Σw). sumW2 series float The sum of squared weights over the lookback period (Σw²). wBtwStdDev(source, weight, length, biased)   Weighted Between Standard Deviation.   Parameters:      source (float) : series float Data series.      weight (float) : series float Weight series.      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population (biased); false → sample.   Returns: series float σbtw uniform if Σw = 0. wBtwStdErr(source, weight, length, biased)   Weighted Between Standard Error.   Parameters:      source (float) : series float Data series.      weight (float) : series float Weight series.      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population (biased); false → sample.   Returns: series float √(σ²btw / N_eff) uniform if Σw = 0. wTotVar(mu, sigma, weight, length, biased)   Weighted Total Variance (= between-group + within-group). Useful when each bar represents an aggregate with its own mean* and pre-estimated σ (e.g., second-level ranges inside a 1-minute bar). Assumes the *weight* series applies to both the group means and their σ estimates.   Parameters:      mu (float) : series float Group means (e.g., HL2 of 1-second bars).      sigma (float) : series float Pre-estimated σ of each group (same basis).      weight (float) : series float Weight series (volume, ticks, …).      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population (biased); false → sample.   Returns: varBtw series float The between-bar variance component (σ²btw). varWtn series float The within-bar variance component (σ²wtn). sumW series float The sum of weights over the lookback period (Σw). sumW2 series float The sum of squared weights over the lookback period (Σw²). wTotStdDev(mu, sigma, weight, length, biased)   Weighted Total Standard Deviation.   Parameters:      mu (float) : series float Group means (e.g., HL2 of 1-second bars).      sigma (float) : series float Pre-estimated σ of each group (same basis).      weight (float) : series float Weight series (volume, ticks, …).      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population (biased); false → sample.   Returns: series float σtot. wTotStdErr(mu, sigma, weight, length, biased)   Weighted Total Standard Error. SE = √( total variance / N_eff ) with the same effective sample size logic as `wster()`.   Parameters:      mu (float) : series float Group means (e.g., HL2 of 1-second bars).      sigma (float) : series float Pre-estimated σ of each group (same basis).      weight (float) : series float Weight series (volume, ticks, …).      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population (biased); false → sample.   Returns: series float √(σ²tot / N_eff). wLinReg(source, weight, length)   Weighted Linear Regression.   Parameters:      source (float) : series float Data series.      weight (float) : series float Weight series.      length (int) : series int Look-back length ≥ 2.   Returns: mid series float The estimated value of the regression line at the most recent bar. slope series float The slope of the regression line. intercept series float The intercept of the regression line. wResVar(source, weight, midLine, slope, length, biased)   Weighted Residual Variance. linear regression – optionally biased (population) or unbiased (sample).   Parameters:      source (float) : series float Data series.      weight (float) : series float Weighting series (volume, etc.).      midLine (float) : series float Regression value at the last bar.      slope (float) : series float Slope per bar.      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population variance (σ²_P), denominator ≈ N_eff. false → sample variance (σ²_S), denominator ≈ N_eff - 2. (Adjusts for 2 degrees of freedom lost to the regression).   Returns: variance series float The calculated residual variance (σ²res), either biased or unbiased. sumW series float The sum of weights over the lookback period (Σw). sumW2 series float The sum of squared weights over the lookback period (Σw²). wResStdDev(source, weight, midLine, slope, length, biased)   Weighted Residual Standard Deviation.   Parameters:      source (float) : series float Data series.      weight (float) : series float Weight series.      midLine (float) : series float Regression value at the last bar.      slope (float) : series float Slope per bar.      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population (biased); false → sample.   Returns: series float σres; uniform if Σw = 0. wResStdErr(source, weight, midLine, slope, length, biased)   Weighted Residual Standard Error.   Parameters:      source (float) : series float Data series.      weight (float) : series float Weight series.      midLine (float) : series float Regression value at the last bar.      slope (float) : series float Slope per bar.      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population (biased); false → sample.   Returns: series float √(σ²res / N_eff); uniform if Σw = 0. wLRTotVar(mu, sigma, weight, midLine, slope, length, biased)   Weighted Linear-Regression Total Variance **around the window’s weighted mean μ**. σ²_tot = E_w ⟶ *within-group variance* + Var_w ⟶ *residual variance* + Var_w ⟶ *trend variance* where each bar i in the look-back window contributes m_i = *mean* (e.g. 1-sec HL2) σ_i = *sigma* (pre-estimated intrabar σ) w_i = *weight* (volume, ticks, …) ŷ_i = b₀ + b₁·x (value of the weighted LR line) r_i = m_i − ŷ_i (orthogonal residual)   Parameters:      mu (float) : series float Per-bar mean m_i.      sigma (float) : series float Pre-estimated σ_i of each bar.      weight (float) : series float Weight series w_i (≥ 0).      midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).      slope (float) : series float Slope b₁ of the regression line.      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population; false → sample.   Returns: varRes series float The residual variance component (σ²res). varWtn series float The within-bar variance component (σ²wtn). varTrd series float The trend variance component (σ²trd), explained by the linear regression. sumW series float The sum of weights over the lookback period (Σw). sumW2 series float The sum of squared weights over the lookback period (Σw²). wLRTotStdDev(mu, sigma, weight, midLine, slope, length, biased)   Weighted Linear-Regression Total Standard Deviation.   Parameters:      mu (float) : series float Per-bar mean m_i.      sigma (float) : series float Pre-estimated σ_i of each bar.      weight (float) : series float Weight series w_i (≥ 0).      midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).      slope (float) : series float Slope b₁ of the regression line.      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population; false → sample.   Returns: series float √(σ²tot). wLRTotStdErr(mu, sigma, weight, midLine, slope, length, biased)   Weighted Linear-Regression Total Standard Error. SE = √( σ²_tot / N_eff ) with N_eff = Σw² / Σw² (like in wster()).   Parameters:      mu (float) : series float Per-bar mean m_i.      sigma (float) : series float Pre-estimated σ_i of each bar.      weight (float) : series float Weight series w_i (≥ 0).      midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).      slope (float) : series float Slope b₁ of the regression line.      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population; false → sample.   Returns: series float √((σ²res, σ²wtn, σ²trd) / N_eff). wLRLocTotStdDev(mu, sigma, weight, midLine, slope, length, biased)   Weighted Linear-Regression Local Total Standard Deviation. Measures the total "noise" (within-bar + residual) around the trend.   Parameters:      mu (float) : series float Per-bar mean m_i.      sigma (float) : series float Pre-estimated σ_i of each bar.      weight (float) : series float Weight series w_i (≥ 0).      midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).      slope (float) : series float Slope b₁ of the regression line.      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population; false → sample.   Returns: series float √(σ²wtn + σ²res). wLRLocTotStdErr(mu, sigma, weight, midLine, slope, length, biased)   Weighted Linear-Regression Local Total Standard Error.   Parameters:      mu (float) : series float Per-bar mean m_i.      sigma (float) : series float Pre-estimated σ_i of each bar.      weight (float) : series float Weight series w_i (≥ 0).      midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).      slope (float) : series float Slope b₁ of the regression line.      length (int) : series int Look-back length ≥ 2.      biased (bool) : series bool true → population; false → sample.   Returns: series float √((σ²wtn + σ²res) / N_eff). wLSma(source, weight, length)   Weighted Least Square Moving Average.   Parameters:      source (float) : series float Data series.      weight (float) : series float Weight series.      length (int) : series int Look-back length ≥ 2.   Returns: series float Least square weighted mean. Falls back to unweighted regression if Σw = 0.
Pine Script® library
by AustrianTradingMachine
TrendLibrary "Trend" calculateSlopeTrend(source, length, thresholdMultiplier)   Parameters:      source (float)      length (int)      thresholdMultiplier (float) Purpose: The primary goal of this function is to determine the short-term trend direction of a given data series (like closing prices). It does this by calculating the slope of the data over a specified period and then comparing that slope against a dynamic threshold based on the data's recent volatility. It classifies the trend into one of three states: Upward, Downward, or Flat. Parameters: `source` (Type: `series float`): This is the input data series you want to analyze. It expects a series of floating-point numbers, typically price data like `close`, `open`, `hl2` (high+low)/2, etc. `length` (Type: `int`): This integer defines the lookback period. The function will analyze the `source` data over the last `length` bars to calculate the slope and standard deviation. `thresholdMultiplier` (Type: `float`, Default: `0.1`): This is a sensitivity factor. It's multiplied by the standard deviation to determine how steep the slope needs to be before it's considered a true upward or downward trend. A smaller value makes it more sensitive (detects trends earlier, potentially more false signals), while a larger value makes it less sensitive (requires a stronger move to confirm a trend). Calculation Steps: Linear Regression: It first calculates the value of a linear regression line fitted to the `source` data over the specified `length` (`ta.linreg(source, length, 0)`). Linear regression finds the "best fit" straight line through the data points. Slope Calculation: It then determines the slope of this linear regression line. Since `ta.linreg` gives the *value* of the line on the current bar, the slope is calculated as the difference between the current bar's linear regression value (`linRegValue`) and the previous bar's value (`linRegValue `). A positive difference means an upward slope, negative means downward. Volatility Measurement: It calculates the standard deviation (`ta.stdev(source, length)`) of the `source` data over the same `length`. Standard deviation is a measure of how spread out the data is, essentially quantifying its recent volatility. Adaptive Threshold: An adaptive threshold (`threshold`) is calculated by multiplying the standard deviation (`stdDev`) by the `thresholdMultiplier`. This is crucial because it means the definition of a "flat" trend adapts to the market's volatility. In volatile times, the threshold will be wider, requiring a larger slope to signal a trend. In quiet times, the threshold will be narrower. Trend Determination: Finally, it compares the calculated `slope` to the adaptive `threshold`: If the `slope` is greater than the positive `threshold`, the trend is considered **Upward**, and the function returns `1`. If the `slope` is less than the negative `threshold` (`-threshold`), the trend is considered **Downward**, and the function returns `-1`. If the `slope` falls between `-threshold` and `+threshold` (inclusive of 0), the trend is considered **Flat**, and the function returns `0`. Return Value: The function returns an integer representing the determined trend direction: `1`: Upward trend `-1`: Downward trend `0`: Flat trend In essence, this library function provides a way to gauge trend direction using linear regression, but with a smart filter (the adaptive threshold) to avoid classifying minor noise or low-volatility periods as significant trends.
Pine Script® library
by jabez4jc
LinearRegressionLibrary "LinearRegression" Calculates a variety of linear regression and deviation types, with optional emphasis weighting. Additionally, multiple of slope and Pearson’s R calculations. calcSlope(_src, _len, _condition)   Calculates the slope of a linear regression over the specified length.   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The length of the lookback period for the linear regression.      _condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast for efficiency.   Returns: (float) The slope of the linear regression. calcReg(_src, _len, _condition)   Calculates a basic linear regression, returning y1, y2, slope, and average.   Parameters:      _src (float) : (float) The source data series.      _len (int) : (int) The length of the lookback period.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: (float ) An array of 4 values: . calcRegStandard(_src, _len, _emphasis, _condition)   Calculates an Standard linear regression with optional emphasis.   Parameters:      _src (float) : (series float) The source data series.      _len (int) : (int) The length of the lookback period.      _emphasis (float) : (float) The emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: (float ) . calcRegRidge(_src, _len, lambda, _emphasis, _condition)   Calculates a ridge regression with optional emphasis.   Parameters:      _src (float) : (float) The source data series.      _len (int) : (int) The length of the lookback period.      lambda (float) : (float) The ridge regularization parameter.      _emphasis (float) : (float) The emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: (float ) . calcRegLasso(_src, _len, lambda, _emphasis, _condition)   Calculates a Lasso regression with optional emphasis.   Parameters:      _src (float) : (float) The source data series.      _len (int) : (int) The length of the lookback period.      lambda (float) : (float) The Lasso regularization parameter.      _emphasis (float) : (float) The emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: (float ) . calcElasticNetLinReg(_src, _len, lambda1, lambda2, _emphasis, _condition)   Calculates an Elastic Net regression with optional emphasis.   Parameters:      _src (float) : (float) The source data series.      _len (int) : (int) The length of the lookback period.      lambda1 (float) : (float) L1 regularization parameter (Lasso).      lambda2 (float) : (float) L2 regularization parameter (Ridge).      _emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: (float ) . calcRegHuber(_src, _len, delta, iterations, _emphasis, _condition)   Calculates a Huber regression using Iteratively Reweighted Least Squares (IRLS).   Parameters:      _src (float) : (float) The source data series.      _len (int) : (int) The length of the lookback period.      delta (float) : (float) Huber threshold parameter.      iterations (int) : (int) Number of IRLS iterations.      _emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: (float ) . calcRegLAD(_src, _len, iterations, _emphasis, _condition)   Calculates a Least Absolute Deviations (LAD) regression via IRLS.   Parameters:      _src (float) : (float) The source data series.      _len (int) : (int) The length of the lookback period.      iterations (int) : (int) Number of IRLS iterations for LAD.      _emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: (float ) . calcRegBayesian(_src, _len, priorMean, priorSpan, sigma, _emphasis, _condition)   Calculates a Bayesian linear regression with optional emphasis.   Parameters:      _src (float) : (float) The source data series.      _len (int) : (int) The length of the lookback period.      priorMean (float) : (float) The prior mean for the slope.      priorSpan (float) : (float) The prior variance (or span) for the slope.      sigma (float) : (float) The assumed standard deviation of residuals.      _emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: (float ) . calcRFromLinReg(_src, _len, _slope, _average, _y1, _condition)   Calculates the Pearson correlation coefficient (R) based on linear regression parameters.   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The length of the lookback period.      _slope (float) : (float) The slope of the linear regression.      _average (float) : (float) The average value of the source data series.      _y1 (float) : (float) The starting point (y-intercept of the oldest bar) for the linear regression.      _condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast for efficiency.   Returns: (float) The Pearson correlation coefficient (R) adjusted for the direction of the slope. calcRFromSource(_src, _len, _condition)   Calculates the correlation coefficient (R) using a specified length and source data.   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The length of the lookback period.      _condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast for efficiency.   Returns: (float) The correlation coefficient (R). calcSlopeLengthZero(_src, _len, _minLen, _step, _condition)   Identifies the length at which the slope is flattest (closest to zero).   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The maximum lookback length to consider (minimum of 2).      _minLen (int) : (int) The minimum length to start from (cannot exceed the max length).      _step (int) : (int) The increment step for lengths.      _condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.   Returns: (int) The length at which the slope is flattest. calcSlopeLengthHighest(_src, _len, _minLen, _step, _condition)   Identifies the length at which the slope is highest.   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The maximum lookback length (minimum of 2).      _minLen (int) : (int) The minimum length to start from.      _step (int) : (int) The step for incrementing lengths.      _condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.   Returns: (int) The length at which the slope is highest. calcSlopeLengthLowest(_src, _len, _minLen, _step, _condition)   Identifies the length at which the slope is lowest.   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The maximum lookback length (minimum of 2).      _minLen (int) : (int) The minimum length to start from.      _step (int) : (int) The step for incrementing lengths.      _condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.   Returns: (int) The length at which the slope is lowest. calcSlopeLengthAbsolute(_src, _len, _minLen, _step, _condition)   Identifies the length at which the absolute slope value is highest.   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The maximum lookback length (minimum of 2).      _minLen (int) : (int) The minimum length to start from.      _step (int) : (int) The step for incrementing lengths.      _condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.   Returns: (int) The length at which the absolute slope value is highest. calcRLengthZero(_src, _len, _minLen, _step, _condition)   Identifies the length with the lowest absolute R value.   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The maximum lookback length (minimum of 2).      _minLen (int) : (int) The minimum length to start from.      _step (int) : (int) The step for incrementing lengths.      _condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.   Returns: (int) The length with the lowest absolute R value. calcRLengthHighest(_src, _len, _minLen, _step, _condition)   Identifies the length with the highest R value.   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The maximum lookback length (minimum of 2).      _minLen (int) : (int) The minimum length to start from.      _step (int) : (int) The step for incrementing lengths.      _condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.   Returns: (int) The length with the highest R value. calcRLengthLowest(_src, _len, _minLen, _step, _condition)   Identifies the length with the lowest R value.   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The maximum lookback length (minimum of 2).      _minLen (int) : (int) The minimum length to start from.      _step (int) : (int) The step for incrementing lengths.      _condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.   Returns: (int) The length with the lowest R value. calcRLengthAbsolute(_src, _len, _minLen, _step, _condition)   Identifies the length with the highest absolute R value.   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The maximum lookback length (minimum of 2).      _minLen (int) : (int) The minimum length to start from.      _step (int) : (int) The step for incrementing lengths.      _condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.   Returns: (int) The length with the highest absolute R value. calcDevReverse(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)   Calculates the regressive linear deviation in reverse order, with optional emphasis on recent data.   Parameters:      _src (float) : (float) The source data.      _len (int) : (int) The length of the lookback period.      _slope (float) : (float) The slope of the linear regression.      _y1 (float) : (float) The y-intercept (oldest bar) of the linear regression.      _inputDev (float) : (float) The input deviation multiplier.      _emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: A 2-element tuple: . calcDevForward(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)   Calculates the progressive linear deviation in forward order (oldest to most recent bar), with optional emphasis.   Parameters:      _src (float) : (float) The source data array, where _src is oldest and _src is most recent.      _len (int) : (int) The length of the lookback period.      _slope (float) : (float) The slope of the linear regression.      _y1 (float) : (float) The y-intercept of the linear regression (value at the most recent bar, adjusted by slope).      _inputDev (float) : (float) The input deviation multiplier.      _emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: A 2-element tuple: . calcDevBalanced(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)   Calculates the balanced linear deviation with optional emphasis on recent or older data.   Parameters:      _src (float) : (float) Source data array, where _src is the most recent and _src is the oldest.      _len (int) : (int) The length of the lookback period.      _slope (float) : (float) The slope of the linear regression.      _y1 (float) : (float) The y-intercept of the linear regression (value at the oldest bar).      _inputDev (float) : (float) The input deviation multiplier.      _emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: A 2-element tuple: . calcDevMean(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)   Calculates the mean absolute deviation from a forward-applied linear trend (oldest to most recent), with optional emphasis.   Parameters:      _src (float) : (float) The source data array, where _src is the most recent and _src is the oldest.      _len (int) : (int) The length of the lookback period.      _slope (float) : (float) The slope of the linear regression.      _y1 (float) : (float) The y-intercept (oldest bar) of the linear regression.      _inputDev (float) : (float) The input deviation multiplier.      _emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: A 2-element tuple: . calcDevMedian(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)   Calculates the median absolute deviation with optional emphasis on recent data.   Parameters:      _src (float) : (float) The source data array (index 0 = oldest, index _len - 1 = most recent).      _len (int) : (int) The length of the lookback period.      _slope (float) : (float) The slope of the linear regression.      _y1 (float) : (float) The y-intercept (oldest bar) of the linear regression.      _inputDev (float) : (float) The deviation multiplier.      _emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: calcDevPercent(_y1, _inputDev, _condition)   Calculates the percent deviation from a given value and a specified percentage.   Parameters:      _y1 (float) : (float) The base value from which to calculate deviation.      _inputDev (float) : (float) The deviation percentage.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: A 2-element tuple: . calcDevFitted(_len, _slope, _y1, _emphasis, _condition)   Calculates the weighted fitted deviation based on high and low series data, showing max deviation, with optional emphasis.   Parameters:      _len (int) : (int) The length of the lookback period.      _slope (float) : (float) The slope of the linear regression.      _y1 (float) : (float) The Y-intercept (oldest bar) of the linear regression.      _emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: A 2-element tuple: . calcDevATR(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)   Calculates an ATR-style deviation with optional emphasis on recent data.   Parameters:      _src (float) : (float) The source data (typically close).      _len (int) : (int) The length of the lookback period.      _slope (float) : (float) The slope of the linear regression.      _y1 (float) : (float) The Y-intercept (oldest bar) of the linear regression.      _inputDev (float) : (float) The input deviation multiplier.      _emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.      _condition (bool) : (bool) Flag to enable calculation (true = calculate).   Returns: A 2-element tuple: . calcPricePositionPercent(_top, _bot, _src)   Calculates the percent position of a price within a linear regression channel. Top=100%, Bottom=0%.   Parameters:      _top (float) : (float) The top (positive) deviation, corresponding to 100%.      _bot (float) : (float) The bottom (negative) deviation, corresponding to 0%.      _src (float) : (float) The source price.   Returns: (float) The percent position within the channel. plotLinReg(_len, _y1, _y2, _slope, _devTop, _devBot, _scaleTypeLog, _lineWidth, _extendLines, _channelStyle, _colorFill, _colUpLine, _colDnLine, _colUpFill, _colDnFill)   Plots the linear regression line and its deviations, with configurable styles and fill.   Parameters:      _len (int) : (int) The lookback period for the linear regression.      _y1 (float) : (float) The starting y-value of the regression line.      _y2 (float) : (float) The ending y-value of the regression line.      _slope (float) : (float) The slope of the regression line (used to determine line color).      _devTop (float) : (float) The top deviation to add to the line.      _devBot (float) : (float) The bottom deviation to subtract from the line.      _scaleTypeLog (bool) : (bool) Use a log scale if true; otherwise, linear scale.      _lineWidth (int) : (int) The width of the plotted lines.      _extendLines (string) : (string) How lines should extend (none, left, right, both).      _channelStyle (string) : (string) The style of the channel lines (solid, dashed, dotted).      _colorFill (bool) : (bool) Whether to fill the space between the top and bottom deviation lines.      _colUpLine (color) : (color) Line color when slope is positive.      _colDnLine (color) : (color) Line color when slope is negative.      _colUpFill (color) : (color) Fill color when slope is positive.      _colDnFill (color) : (color) Fill color when slope is negative.
Pine Script® library
by TanHef
2
regressionsLibrary "regressions" This library computes least square regression models for polynomials of any form for a given data set of x and y values. fit(X, y, reg_type, degrees)   Takes a list of X and y values and the degrees of the polynomial and returns a least square regression for the given polynomial on the dataset.   Parameters:      X (array) : (float ) X inputs for regression fit.      y (array) : (float ) y outputs for regression fit.      reg_type (string) : (string) The type of regression. If passing value for degrees use reg.type_custom      degrees (array) : (int ) The degrees of the polynomial which will be fit to the data. ex: passing array.from(0, 3) would be a polynomial of form c1x^0 + c2x^3 where c2 and c1 will be coefficients of the best fitting polynomial.   Returns: (regression) returns a regression with the best fitting coefficients for the selecected polynomial regress(reg, x)   Regress one x input.   Parameters:      reg (regression) : (regression) The fitted regression which the y_pred will be calulated with.      x (float) : (float) The input value cooresponding to the y_pred.   Returns: (float) The best fit y value for the given x input and regression. predict(reg, X)   Predict a new set of X values with a fitted regression. -1 is one bar ahead of the realtime   Parameters:      reg (regression) : (regression) The fitted regression which the y_pred will be calulated with.      X (array)   Returns: (float ) The best fit y values for the given x input and regression. generate_points(reg, x, y, left_index, right_index)   Takes a regression object and creates chart points which can be used for plotting visuals like lines and labels.   Parameters:      reg (regression) : (regression) Regression which has been fitted to a data set.      x (array) : (float ) x values which coorispond to passed y values      y (array) : (float ) y values which coorispond to passed x values      left_index (int) : (int) The offset of the bar farthest to the realtime bar should be larger than left_index value.      right_index (int) : (int) The offset of the bar closest to the realtime bar should be less than right_index value.   Returns: (chart.point ) Returns an array of chart points plot_reg(reg, x, y, left_index, right_index, curved, close, line_color, line_width)   Simple plotting function for regression for more custom plotting use generate_points() to create points then create your own plotting function.   Parameters:      reg (regression) : (regression) Regression which has been fitted to a data set.      x (array)      y (array)      left_index (int) : (int) The offset of the bar farthest to the realtime bar should be larger than left_index value.      right_index (int) : (int) The offset of the bar closest to the realtime bar should be less than right_index value.      curved (bool) : (bool) If the polyline is curved or not.      close (bool) : (bool) If true the polyline will be closed.      line_color (color) : (color) The color of the line.      line_width (int) : (int) The width of the line.   Returns: (polyline) The polyline for the regression. series_to_list(src, left_index, right_index)   Convert a series to a list. Creates a list of all the cooresponding source values from left_index to right_index. This should be called at the highest scope for consistency.   Parameters:      src (float) : (float ) The source the list will be comprised of.      left_index (int) : (float ) The left most bar (farthest back historical bar) which the cooresponding source value will be taken for.      right_index (int) : (float ) The right most bar closest to the realtime bar which the cooresponding source value will be taken for.   Returns: (float ) An array of size left_index-right_index range_list(start, stop, step)   Creates an from the start value to the stop value.   Parameters:      start (int) : (float ) The true y values.      stop (int) : (float ) The predicted y values.      step (int) : (int) Positive integer. The spacing between the values. ex: start=1, stop=6, step=2:   Returns: (float ) An array of size stop-start regression   Fields:      coeffs (array__float)      degrees (array__float)      type_linear (series__string)      type_quadratic (series__string)      type_cubic (series__string)      type_custom (series__string)      _squared_error (series__float)      X (array__float)
Pine Script® library
by fluxchart
3
KernelFunctionsFiltersLibrary "KernelFunctionsFilters" This library provides filters for non-repainting kernel functions for Nadaraya-Watson estimator implementations made by @jdehorty. Filters include a smoothing formula and zero lag formula. You can find examples in the code. For more information check out the original library KernelFunctions. rationalQuadratic(_src, _lookback, _relativeWeight, startAtBar, _filter)   Parameters:      _src (float)      _lookback (simple int)      _relativeWeight (simple float)      startAtBar (simple int)      _filter (simple string) gaussian(_src, _lookback, startAtBar, _filter)   Parameters:      _src (float)      _lookback (simple int)      startAtBar (simple int)      _filter (simple string) periodic(_src, _lookback, _period, startAtBar, _filter)   Parameters:      _src (float)      _lookback (simple int)      _period (simple int)      startAtBar (simple int)      _filter (simple string) locallyPeriodic(_src, _lookback, _period, startAtBar, _filter)   Parameters:      _src (float)      _lookback (simple int)      _period (simple int)      startAtBar (simple int)      _filter (simple string) j(line1, line2)   Parameters:      line1 (float)      line2 (float)
Pine Script® library
by veryfid
6
KernelFunctionsLibrary "KernelFunctions" This library provides non-repainting kernel functions for Nadaraya-Watson estimator implementations. This allows for easy substitution/comparison of different kernel functions for one another in indicators. Furthermore, kernels can easily be combined with other kernels to create newer, more customized kernels. Compared to Moving Averages (which are really just simple kernels themselves), these kernel functions are more adaptive and afford the user an unprecedented degree of customization and flexibility. rationalQuadratic(_src, _lookback, _relativeWeight, _startAtBar)   Rational Quadratic Kernel - An infinite sum of Gaussian Kernels of different length scales.   Parameters:      _src : The source series.      _lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.      _relativeWeight : Relative weighting of time frames. Smaller values result in a more stretched-out curve, and larger values will result in a more wiggly curve. As this value approaches zero, the longer time frames will exert more influence on the estimation. As this value approaches infinity, the behavior of the Rational Quadratic Kernel will become identical to the Gaussian kernel.      _startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.   Returns: yhat The estimated values according to the Rational Quadratic Kernel. gaussian(_src, _lookback, _startAtBar)   Gaussian Kernel - A weighted average of the source series. The weights are determined by the Radial Basis Function (RBF).   Parameters:      _src : The source series.      _lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.      _startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.   Returns: yhat The estimated values according to the Gaussian Kernel. periodic(_src, _lookback, _period, _startAtBar)   Periodic Kernel - The periodic kernel (derived by David Mackay) allows one to model functions that repeat themselves exactly.   Parameters:      _src : The source series.      _lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.      _period : The distance between repititions of the function.      _startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.   Returns: yhat The estimated values according to the Periodic Kernel. locallyPeriodic(_src, _lookback, _period, _startAtBar)   Locally Periodic Kernel - The locally periodic kernel is a periodic function that slowly varies with time. It is the product of the Periodic Kernel and the Gaussian Kernel.   Parameters:      _src : The source series.      _lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.      _period : The distance between repititions of the function.      _startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.   Returns: yhat The estimated values according to the Locally Periodic Kernel.
Pine Script® library
by jdehorty
11
FunctionPolynomialFitLibrary "FunctionPolynomialFit" Performs Polynomial Regression fit to data. In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. reference: en.wikipedia.org www.bragitoff.com gauss_elimination(A, m, n) Perform Gauss-Elimination and returns the Upper triangular matrix and solution of equations.   Parameters:      A : float matrix, data samples.      m : int, defval=na, number of rows.      n : int, defval=na, number of columns.   Returns: float array with coefficients. polyfit(X, Y, degree) Fits a polynomial of a degree to (x, y) points.   Parameters:      X : float array, data sample x point.      Y : float array, data sample y point.      degree : int, defval=2, degree of the polynomial.   Returns: float array with coefficients. note: p(x) = p * x**deg + ... + p interpolate(coeffs, x) interpolate the y position at the provided x.   Parameters:      coeffs : float array, coefficients of the polynomial.      x : float, position x to estimate y.   Returns: float.
Pine Script® library
by RicardoSantos
10
regressLibrary "regress" produces the slope (beta), y-intercept (alpha) and coefficient of determination for a linear regression regress(x, y, len) regress: computes alpha, beta, and r^2 for a linear regression of y on x   Parameters:      x : the explaining (independent) variable      y : the dependent variable      len : use the most recent "len" values of x and y   Returns: : alpha is the x-intercept, beta is the slope, an r2 is the coefficient of determination Note: the chart does not show anything, use the return values to compute model values in your own application, if you wish.
Pine Script® library
by taylor_o
FunctionPolynomialRegressionLibrary "FunctionPolynomialRegression" TODO: polyreg(sample_x, sample_y) Method to return a polynomial regression channel using (X,Y) sample points.   Parameters:      sample_x : float array, sample data X points.      sample_y : float array, sample data Y points.   Returns: tuple with: _predictions: Array with adjusted Y values. _max_dev: Max deviation from the mean. _min_dev: Min deviation from the mean. _stdev/_sizeX: Average deviation from the mean. draw(sample_x, sample_y, extend, mid_color, mid_style, mid_width, std_color, std_style, std_width, max_color, max_style, max_width) Method for drawing the Polynomial Regression into chart.   Parameters:      sample_x : float array, sample point X value.      sample_y : float array, sample point Y value.      extend : string, default=extend.none, extend lines.      mid_color : color, default=color.blue, middle line color.      mid_style : string, default=line.style_solid, middle line style.      mid_width : int, default=2, middle line width.      std_color : color, default=color.aqua, standard deviation line color.      std_style : string, default=line.style_dashed, standard deviation line style.      std_width : int, default=1, standard deviation line width.      max_color : color, default=color.purple, max range line color.      max_style : string, default=line.style_dotted, max line style.      max_width : int, default=1, max line width.   Returns: line array.
Pine Script® library
by RicardoSantos
1