 Library "LinearRegressionLibrary" contains functions for fitting a regression line to the time series by means of different models, as well as functions for estimating the accuracy of the fit.

Linear regression algorithms:

RepeatedMedian(y, n, lastBar) applies repeated median regression (robust linear regression algorithm) to the input time series within the selected interval.
Parameters:
• y :: float series, source time series (e.g. close)
• n :: integer, the length of the selected time interval
• lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
Output:
• mSlope :: float, slope of the regression line
• mInter :: float, intercept of the regression line

TheilSen(y, n, lastBar) applies the Theil-Sen estimator (robust linear regression algorithm) to the input time series within the selected interval.
Parameters:
• y :: float series, source time series
• n :: integer, the length of the selected time interval
• lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
Output:
• tsSlope :: float, slope of the regression line
• tsInter :: float, intercept of the regression line

OrdinaryLeastSquares(y, n, lastBar) applies the ordinary least squares regression (non-robust) to the input time series within the selected interval.
Parameters:
• y :: float series, source time series
• n :: integer, the length of the selected time interval
• lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
Output:
• olsSlope :: float, slope of the regression line
• olsInter :: float, intercept of the regression line

Model performance metrics:

metricRMSE(y, n, lastBar, slope, intercept) returns the Root-Mean-Square Error (RMSE) of the regression. The better the model, the lower the RMSE.
Parameters:
• y :: float series, source time series (e.g. close)
• n :: integer, the length of the selected time interval
• lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
• slope :: float, slope of the evaluated linear regression line
• intercept :: float, intercept of the evaluated linear regression line
Output:
• rmse :: float, RMSE value

metricMAE(y, n, lastBar, slope, intercept) returns the Mean Absolute Error (MAE) of the regression. MAE is is similar to RMSE but is less sensitive to outliers. The better the model, the lower the MAE.
Parameters:
• y :: float series, source time series
• n :: integer, the length of the selected time interval
• lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
• slope :: float, slope of the evaluated linear regression line
• intercept :: float, intercept of the evaluated linear regression line
Output:
• mae :: float, MAE value

metricR2(y, n, lastBar, slope, intercept) returns the coefficient of determination (R squared) of the regression. The better the linear regression fits the data (compared to the sample mean), the closer the value of the R squared is to 1.
Parameters:
• y :: float series, source time series
• n :: integer, the length of the selected time interval
• lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
• slope :: float, slope of the evaluated linear regression line
• intercept :: float, intercept of the evaluated linear regression line
Output:
• Rsq :: float, R-sqared score

Usage example:

//@version=5
indicator('ExampleLinReg', overlay=true)
// import the library
import tbiktag/LinearRegressionLibrary/1 as linreg
// define the studied interval: last 100 bars
int Npoints = 100
int lastBar = bar_index
int firstBar = bar_index - Npoints
// apply repeated median regression to the closing price time series within the specified interval
{square bracket}slope, intercept{square bracket} = linreg.RepeatedMedian(close, Npoints, lastBar)
// calculate the root-mean-square error of the obtained linear fit
rmse = linreg.metricRMSE(close, Npoints, lastBar, slope, intercept)
// plot the line and print the RMSE value
float y1 = intercept
float y2 = intercept + slope * (Npoints - 1)
if barstate.islast
{indent} line.new(firstBar,y1, lastBar,y2)
{indent} label.new(lastBar,y2,text='RMSE = '+str.format("{0,number,#.#}", rmse))

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