Function Polynomial Regression: Free TradingView Indicator (Pine Script)

Add It to Your TradingView Chart

1Copy the scriptPress Copy script above, or the copy button on the code below.
2Open the Pine EditorOpen a TradingView chart and choose Pine Editor at the bottom of the screen.
3Paste over the templateCreate a new indicator, select all of the template text and paste. Press Save and give it a name.
4Add it to the chartPress Add to chart, then adjust the settings with the gear icon next to its name.

Source Code

197 lines of Pine Script v5 from beta/libs/v4_to_v5_conversions/Function - Polynomial Regression.pinescript, published under MPL-2.0 (file header). Keep the author's credit and licence lines when you reuse it.

Function - Polynomial Regression.pinescript

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © RicardoSantos

//@version=5
indicator(title='Function Polynomial Regression', overlay=true)

f_array_polyreg(_X, _Y) =>
//{
//| Returns a polynomial regression channel using (X,Y) vector points.
//| Resources:
//|     language D: https://rosettacode.org/wiki/Polynomial_regression
    int _sizeY = array.size(id=_Y)
    int _sizeX = array.size(id=_X)
    //
    float _meanX = array.sum(id=_X) / _sizeX
    float _meanY = array.sum(id=_Y) / _sizeX
    float _meanXY = 0.0
    float _meanY2 = 0.0
    float _meanX2 = 0.0
    float _meanX3 = 0.0
    float _meanX4 = 0.0
    float _meanX2Y = 0.0
    if _sizeY == _sizeX
        for _i = 0 to _sizeY - 1 by 1
            float _Xi = array.get(id=_X, index=_i)
            float _Yi = array.get(id=_Y, index=_i)
            _meanXY := _meanXY + _Xi * _Yi
            _meanY2 := _meanY2 + math.pow(_Yi, 2)
            _meanX2 := _meanX2 + math.pow(_Xi, 2)
            _meanX3 := _meanX3 + math.pow(_Xi, 3)
            _meanX4 := _meanX4 + math.pow(_Xi, 4)
            _meanX2Y := _meanX2Y + math.pow(_Xi, 2) * _Yi
            _meanX2Y
        _meanXY := _meanXY / _sizeX
        _meanY2 := _meanY2 / _sizeX
        _meanX2 := _meanX2 / _sizeX
        _meanX3 := _meanX3 / _sizeX
        _meanX4 := _meanX4 / _sizeX
        _meanX2Y := _meanX2Y / _sizeX
        _meanX2Y
    //-----------|covs
    float _sXX = _meanX2 - _meanX * _meanX
    float _sXY = _meanXY - _meanX * _meanY
    float _sXX2 = _meanX3 - _meanX * _meanX2
    float _sX2X2 = _meanX4 - _meanX2 * _meanX2
    float _sX2Y = _meanX2Y - _meanX2 * _meanY
    //-----------|
    float _b = (_sXY * _sX2X2 - _sX2Y * _sXX2) / (_sXX * _sX2X2 - _sXX2 * _sXX2)
    float _c = (_sX2Y * _sXX - _sXY * _sXX2) / (_sXX * _sX2X2 - _sXX2 * _sXX2)
    float _a = _meanY - _b * _meanX - _c * _meanX2
    //-----------|
    float[] _predictions = array.new_float(size=0, initial_value=0.0)
    float _max_dev = 0.0
    float _min_dev = 0.0
    float _stdev = 0.0
    for _i = 0 to _sizeX - 1 by 1
        float _Xi = array.get(id=_X, index=_i)
        float _vector = _a + _b * _Xi + _c * _Xi * _Xi
        array.push(id=_predictions, value=_vector)
        //
        float _Yi = array.get(id=_Y, index=_i)
        float _diff = _Yi - _vector
        if _diff > _max_dev
            _max_dev := _diff
            _max_dev
        if _diff < _min_dev
            _min_dev := _diff
            _min_dev
        _stdev := _stdev + math.abs(_diff)
        _stdev
//| Output:
//|     _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.
//}
    [_predictions, _max_dev, _min_dev, _stdev / _sizeX]



int length = input(10)
var float[] prices = array.new_float(size=length, initial_value=open)
var int[] indices = array.new_int(size=length, initial_value=0)
int fractal_size = input(2)
if ta.pivothigh(fractal_size, fractal_size)
    e = array.pop(id=prices)
    i = array.pop(id=indices)
    array.insert(id=prices, index=0, value=high[fractal_size])
    array.insert(id=indices, index=0, value=bar_index[fractal_size])
if ta.pivotlow(fractal_size, fractal_size)
    e = array.pop(id=prices)
    i = array.pop(id=indices)
    array.insert(id=prices, index=0, value=low[fractal_size])
    array.insert(id=indices, index=0, value=bar_index[fractal_size])


    //|----------------------------------------------------------------------------||
    //|----------------------------------------------------------------------------||
    //|----------------------------------------------------------------------------||
    //|----------------------------------------------------------------------------||
    //|----------------------------------------------------------------------------||
    //|----------------------------------------------------------------------------||

color _pr_mid_col = input(color.blue)
color _pr_std_col = input(color.aqua)
color _pr_max_col = input(color.purple)

f_init_mid() =>
    line.new(x1=bar_index, y1=0.0, x2=bar_index, y2=0.0, color=_pr_mid_col, style=line.style_solid, width=2)
f_init_std() =>
    line.new(x1=bar_index, y1=0.0, x2=bar_index, y2=0.0, color=_pr_std_col, style=line.style_dashed, width=1)
f_init_max() =>
    line.new(x1=bar_index, y1=0.0, x2=bar_index, y2=0.0, color=_pr_max_col, style=line.style_dotted, width=1)

var line pr_mid00 = f_init_mid()
var line pr_min00 = f_init_max()
var line pr_max00 = f_init_max()
var line pr_mid01 = f_init_mid()
var line pr_min01 = f_init_max()
var line pr_max01 = f_init_max()
var line pr_mid02 = f_init_mid()
var line pr_min02 = f_init_max()
var line pr_max02 = f_init_max()
var line pr_mid03 = f_init_mid()
var line pr_min03 = f_init_max()
var line pr_max03 = f_init_max()
var line pr_mid04 = f_init_mid()
var line pr_min04 = f_init_max()
var line pr_max04 = f_init_max()
var line pr_mid05 = f_init_mid()
var line pr_min05 = f_init_max()
var line pr_max05 = f_init_max()
var line pr_mid06 = f_init_mid()
var line pr_min06 = f_init_max()
var line pr_max06 = f_init_max()
var line pr_mid07 = f_init_mid()
var line pr_min07 = f_init_max()
var line pr_max07 = f_init_max()
var line pr_mid08 = f_init_mid()
var line pr_min08 = f_init_max()
var line pr_max08 = f_init_max()
var line pr_mid09 = f_init_mid()
var line pr_min09 = f_init_max()
var line pr_max09 = f_init_max()

var line pr_lower00 = f_init_std()
var line pr_upper00 = f_init_std()
var line pr_lower01 = f_init_std()
var line pr_upper01 = f_init_std()
var line pr_lower02 = f_init_std()
var line pr_upper02 = f_init_std()
var line pr_lower03 = f_init_std()
var line pr_upper03 = f_init_std()
var line pr_lower04 = f_init_std()
var line pr_upper04 = f_init_std()
var line pr_lower05 = f_init_std()
var line pr_upper05 = f_init_std()
var line pr_lower06 = f_init_std()
var line pr_upper06 = f_init_std()
var line pr_lower07 = f_init_std()
var line pr_upper07 = f_init_std()
var line pr_lower08 = f_init_std()
var line pr_upper08 = f_init_std()
var line pr_lower09 = f_init_std()
var line pr_upper09 = f_init_std()

f_pr_mid_line_selector(_i) =>
    _i == 0 ? pr_mid00 : _i == 1 ? pr_mid01 : _i == 2 ? pr_mid02 : _i == 3 ? pr_mid03 : _i == 4 ? pr_mid04 : _i == 5 ? pr_mid05 : _i == 6 ? pr_mid06 : _i == 7 ? pr_mid07 : _i == 8 ? pr_mid08 : _i == 9 ? pr_mid09 : pr_mid00
f_pr_max_line_selector(_i) =>
    _i == 0 ? pr_max00 : _i == 1 ? pr_max01 : _i == 2 ? pr_max02 : _i == 3 ? pr_max03 : _i == 4 ? pr_max04 : _i == 5 ? pr_max05 : _i == 6 ? pr_max06 : _i == 7 ? pr_max07 : _i == 8 ? pr_max08 : _i == 9 ? pr_max09 : pr_max00
f_pr_min_line_selector(_i) =>
    _i == 0 ? pr_min00 : _i == 1 ? pr_min01 : _i == 2 ? pr_min02 : _i == 3 ? pr_min03 : _i == 4 ? pr_min04 : _i == 5 ? pr_min05 : _i == 6 ? pr_min06 : _i == 7 ? pr_min07 : _i == 8 ? pr_min08 : _i == 9 ? pr_min09 : pr_min00
f_pr_upper_line_selector(_i) =>
    _i == 0 ? pr_upper00 : _i == 1 ? pr_upper01 : _i == 2 ? pr_upper02 : _i == 3 ? pr_upper03 : _i == 4 ? pr_upper04 : _i == 5 ? pr_upper05 : _i == 6 ? pr_upper06 : _i == 7 ? pr_upper07 : _i == 8 ? pr_upper08 : _i == 9 ? pr_upper09 : pr_upper00
f_pr_lower_line_selector(_i) =>
    _i == 0 ? pr_lower00 : _i == 1 ? pr_lower01 : _i == 2 ? pr_lower02 : _i == 3 ? pr_lower03 : _i == 4 ? pr_lower04 : _i == 5 ? pr_lower05 : _i == 6 ? pr_lower06 : _i == 7 ? pr_lower07 : _i == 8 ? pr_lower08 : _i == 9 ? pr_lower09 : pr_lower00

if barstate.ishistory[1] and (barstate.isrealtime or barstate.isconfirmed)
    [P, Pmax, Pmin, Pstdev] = f_array_polyreg(indices, prices)

    int pr_fractions = 10
    int pr_size = array.size(id=P)
    int pr_step = math.max(pr_size / pr_fractions, 1)
    for _i = 0 to pr_size - pr_step - 1 by pr_step
        int _next_step_index = _i + pr_step
        int _line = _i / pr_step

        line.set_xy1(id=f_pr_mid_line_selector(_line), x=array.get(id=indices, index=_i), y=array.get(id=P, index=_i))
        line.set_xy2(id=f_pr_mid_line_selector(_line), x=array.get(id=indices, index=_i + pr_step), y=array.get(id=P, index=_i + pr_step))
        line.set_xy1(id=f_pr_max_line_selector(_line), x=array.get(id=indices, index=_i), y=array.get(id=P, index=_i) + Pmax)
        line.set_xy2(id=f_pr_max_line_selector(_line), x=array.get(id=indices, index=_i + pr_step), y=array.get(id=P, index=_i + pr_step) + Pmax)
        line.set_xy1(id=f_pr_min_line_selector(_line), x=array.get(id=indices, index=_i), y=array.get(id=P, index=_i) + Pmin)
        line.set_xy2(id=f_pr_min_line_selector(_line), x=array.get(id=indices, index=_i + pr_step), y=array.get(id=P, index=_i + pr_step) + Pmin)
        line.set_xy1(id=f_pr_upper_line_selector(_line), x=array.get(id=indices, index=_i), y=array.get(id=P, index=_i) + Pstdev)
        line.set_xy2(id=f_pr_upper_line_selector(_line), x=array.get(id=indices, index=_i + pr_step), y=array.get(id=P, index=_i + pr_step) + Pstdev)
        line.set_xy1(id=f_pr_lower_line_selector(_line), x=array.get(id=indices, index=_i), y=array.get(id=P, index=_i) - Pstdev)
        line.set_xy2(id=f_pr_lower_line_selector(_line), x=array.get(id=indices, index=_i + pr_step), y=array.get(id=P, index=_i + pr_step) - Pstdev)

Overview

A reusable function returns fitted values plus maximum, minimum, and average absolute deviations from the curve. The length setting controls how many pivot samples stay in the rolling window, and fractal size sets how many bars confirm a pivot. Separate colors mark the midline, average-deviation band, and extreme deviation band.

Quadratic polynomial regression function
Rolling window of fractal pivot points
Maximum, minimum, and average deviation outputs
Adjustable sample length and fractal size
Separate colors for mid, deviation, and extreme bands

Details

Published by

ricardosantos79 on GitHub

Code credit

RicardoSantos, as written in the script's header

Type

Indicator, Pine Script v5

Draws

On the price chart

Markets

Any symbol

Timeframes

Any timeframe

Risk Notes

No repainting, lookahead or stacked entries were found in its code or README. That says nothing about how well it works: test it first.

File

beta/libs/v4_to_v5_conversions/Function - Polynomial Regression.pinescript

Repository

github.com/ricardosantos79/pinescript. See its other scripts in the library

Settings

The inputs you can change from the gear icon on the chart. Defaults are the author's.

Setting	Type	Default	Variable
length	`int`	`10`	`length`
fractal_size	`int`	`2`	`fractal_size`
_pr_mid_col	`color`	`color.blue`	`_pr_mid_col`
_pr_std_col	`color`	`color.aqua`	`_pr_std_col`
_pr_max_col	`color`	`color.purple`	`_pr_max_col`

Third-party code. ForexR did not write, test or endorse this script, and the summary above was generated automatically from its code and README. Indicators describe the past, and a strategy's backtest can look better than live trading, especially when a script repaints. Check it in the Strategy Tester and on a demo account before you rely on it.

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