Polynomial Regression Channel (PRC) / Quadratic Regression

Solution
markos
@hockeycoachdoug
See if this is what you're looking for. I found it in the Thinkscript Cloud.
Code: 
# Quadratic Regression
# Robert Payne
# funwiththinkscript.com

input length = 20;
def n = length;
def bn = BarNumber();
def lastBar = HighestAll(if IsNaN(close) then 0 else bn);
def x = bn;
def y = close;

# calculate summation values

def startBar = lastBar - (n - 1);
def sumX = if bn < startBar then 0 else x + sumX[1];
def sumY = if bn < startBar then 0 else y + sumY[1];
def sumX2 = if bn < startBar then 0 else Power(x, 2) + sumX2[1];
def sumX3 = if bn < startBar then 0 else Power(x, 3) + sumX3[1];
def sumX4 = if bn < startBar then 0 else Power(x, 4) + sumX4[1];
def sumXY = if bn < startBar then 0 else x * y + sumXY[1];
def sumX2Y...
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H

hockeycoachdoug

Active member
2019 Donor
VIP
Does anyone have the TOS code to plot this? It would be a great first sort for prices near one of the extremes, then use the Ultimate Breakout indicator on a lower time frame and only take the buys when prices near bottom deviation and slope is positive and sells when at top deviation and negative slope.
 
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H

hockeycoachdoug

Active member
2019 Donor
VIP
@codydog- thanks for pointing me in a direction, I just couldn't find the direction you were pointing. I tried searching "growex" and "polynomial" on the onenote site I was familiar with with no luck. Can you point me a bit more specifically. Thanks in advance for your help.

Also, @RobertPayne- any chance of a discount to usethinkscript members for your indicators for sale on your site?
 
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markos

markos

Well-known member
VIP
@hockeycoachdoug
See if this is what you're looking for. I found it in the Thinkscript Cloud.
Code: 
# Quadratic Regression
# Robert Payne
# funwiththinkscript.com

input length = 20;
def n = length;
def bn = BarNumber();
def lastBar = HighestAll(if IsNaN(close) then 0 else bn);
def x = bn;
def y = close;

# calculate summation values

def startBar = lastBar - (n - 1);
def sumX = if bn < startBar then 0 else x + sumX[1];
def sumY = if bn < startBar then 0 else y + sumY[1];
def sumX2 = if bn < startBar then 0 else Power(x, 2) + sumX2[1];
def sumX3 = if bn < startBar then 0 else Power(x, 3) + sumX3[1];
def sumX4 = if bn < startBar then 0 else Power(x, 4) + sumX4[1];
def sumXY = if bn < startBar then 0 else x * y + sumXY[1];
def sumX2Y = if bn < startBar then 0 else Power(x, 2) * y + sumX2Y[1];

# intermediary calculations

def xx = sumX2 - Power(sumX, 2) / n;
def xy = sumXY - (sumX * sumY / n);
def xx2 = sumX3 - (sumX2 * sumX / n);
def x2y = sumX2Y - (sumX2 * sumY / n);
def x2x2 = sumX4 - (Power(sumX2, 2) / n);

# calculate coefficients for the quadratic equation

def a0 = (x2y * xx - xy * xx2) / (xx * x2x2 - Power(xx2, 2));
def b0 = (xy * x2x2 - x2y * xx2) / (xx * x2x2 - Power(xx2, 2));
def c0 = sumY / n - b0 * sumX / n - a0 * sumX2 / n;

# for a, b, and c use the final value on the last bar of the chart for all calculations

def a = GetValue(a0, bn - lastBar);
def b = GetValue(b0, bn - lastBar);
def c = GetValue(c0, bn - lastBar);

# calculate and plot the regression curve

plot theCurve = if bn < startBar then Double.NaN else a * Power(x, 2) + b * x + c;
#####

If it works, please post a picture here!
 
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Solution
J

Jonas99

Active member
VIP
Function Polynomial Regression For TradingView by RicardoSantos
https://www.tradingview.com/script/12M8Jqu6-Function-Polynomial-Regression/
This is the script from TV on PRC, would anyone be interested in port it to TOS?
a1.png

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

//@version=4
study(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
float _Xi = array.get(id=_X, index=_i)
float _Yi = array.get(id=_Y, index=_i)
_meanXY := _meanXY + (_Xi * _Yi)
_meanY2 := _meanY2 + pow(_Yi, 2)
_meanX2 := _meanX2 + pow(_Xi, 2)
_meanX3 := _meanX3 + pow(_Xi, 3)
_meanX4 := _meanX4 + pow(_Xi, 4)
_meanX2Y := _meanX2Y + pow(_Xi, 2) * _Yi
_meanXY := _meanXY / _sizeX
_meanY2 := _meanY2 / _sizeX
_meanX2 := _meanX2 / _sizeX
_meanX3 := _meanX3 / _sizeX
_meanX4 := _meanX4 / _sizeX
_meanX2Y := _meanX2Y / _sizeX
//-----------|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
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
if _diff < _min_dev
_min_dev := _diff
_stdev := _stdev + abs(_diff)
//| 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)
if pivothigh(2, 2)
e = array.pop(id=prices)
i = array.pop(id=indices)
array.insert(id=prices, index=0, value=high[2])
array.insert(id=indices, index=0, value=bar_index[2])
if pivotlow(2, 2)
e = array.pop(id=prices)
i = array.pop(id=indices)
array.insert(id=prices, index=0, value=low[2])
array.insert(id=indices, index=0, value=bar_index[2])


[P, Pmax, Pmin, Pstdev] = f_array_polyreg(indices, prices)

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

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))))))))))

int pr_fractions = 10
int pr_size = array.size(id=P)
int pr_step = 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)
 
Last edited by a moderator:
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J

Jonas99

Active member
VIP
MerryDay said:
@Jonas99 How is the TradingView version different from all the COGs, Hursts, and Polynomial Regression already written for ToS?
Given that these are the worst of the worst repainters, how do you use this in your strategy?
Click to expand...
I was looking for a PRC but not seeing one? Don Monkey made one but it's not shared. It's a fancy LRC that fits the price better. I am a mean reversion trader so I would use them for range estimates.
https://imgur.com/a/qIQhrpC
 
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V

vikram

New member
VIP
markos said:
@hockeycoachdoug
See if this is what you're looking for. I found it in the Thinkscript Cloud.
Code: 
# Quadratic Regression
# Robert Payne
# funwiththinkscript.com

input length = 20;
def n = length;
def bn = BarNumber();
def lastBar = HighestAll(if IsNaN(close) then 0 else bn);
def x = bn;
def y = close;

# calculate summation values

def startBar = lastBar - (n - 1);
def sumX = if bn < startBar then 0 else x + sumX[1];
def sumY = if bn < startBar then 0 else y + sumY[1];
def sumX2 = if bn < startBar then 0 else Power(x, 2) + sumX2[1];
def sumX3 = if bn < startBar then 0 else Power(x, 3) + sumX3[1];
def sumX4 = if bn < startBar then 0 else Power(x, 4) + sumX4[1];
def sumXY = if bn < startBar then 0 else x * y + sumXY[1];
def sumX2Y = if bn < startBar then 0 else Power(x, 2) * y + sumX2Y[1];

# intermediary calculations

def xx = sumX2 - Power(sumX, 2) / n;
def xy = sumXY - (sumX * sumY / n);
def xx2 = sumX3 - (sumX2 * sumX / n);
def x2y = sumX2Y - (sumX2 * sumY / n);
def x2x2 = sumX4 - (Power(sumX2, 2) / n);

# calculate coefficients for the quadratic equation

def a0 = (x2y * xx - xy * xx2) / (xx * x2x2 - Power(xx2, 2));
def b0 = (xy * x2x2 - x2y * xx2) / (xx * x2x2 - Power(xx2, 2));
def c0 = sumY / n - b0 * sumX / n - a0 * sumX2 / n;

# for a, b, and c use the final value on the last bar of the chart for all calculations

def a = GetValue(a0, bn - lastBar);
def b = GetValue(b0, bn - lastBar);
def c = GetValue(c0, bn - lastBar);

# calculate and plot the regression curve

plot theCurve = if bn < startBar then Double.NaN else a * Power(x, 2) + b * x + c;
#####

If it works, please post a picture here!
Click to expand...
@markos This Quad regression line looks impressive. Any idea how can to make two lines like a channel instead of single line ? higher line touching highs and lower line touching lows
 
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M

MountainKing333

Member
Alright so I **** at calculus and I'm even worse at coding. Can anyone find a way to expand this Quadratic Regression Line code into Cubic and or Quartic regression? I have absolutely no clue how to start, and I cant find any code online that can even be adapted to do this. Please if anyone can help, I think this would be a great option to have.


Code: 
# Quadratic Regression
# Robert Payne
# funwiththinkscript.com

input length = 20;
def n = length;
def bn = BarNumber();
def lastBar = HighestAll(if IsNaN(close) then 0 else bn);
def x = bn;
def y = close;

# calculate summation values

def startBar = lastBar - (n - 1);
def sumX = if bn < startBar then 0 else x + sumX[1];
def sumY = if bn < startBar then 0 else y + sumY[1];
def sumX2 = if bn < startBar then 0 else Power(x, 2) + sumX2[1];
def sumX3 = if bn < startBar then 0 else Power(x, 3) + sumX3[1];
def sumX4 = if bn < startBar then 0 else Power(x, 4) + sumX4[1];
def sumXY = if bn < startBar then 0 else x * y + sumXY[1];
def sumX2Y = if bn < startBar then 0 else Power(x, 2) * y + sumX2Y[1];

# intermediary calculations

def xx = sumX2 - Power(sumX, 2) / n;
def xy = sumXY - (sumX * sumY / n);
def xx2 = sumX3 - (sumX2 * sumX / n);
def x2y = sumX2Y - (sumX2 * sumY / n);
def x2x2 = sumX4 - (Power(sumX2, 2) / n);

# calculate coefficients for the quadratic equation

def a0 = (x2y * xx - xy * xx2) / (xx * x2x2 - Power(xx2, 2));
def b0 = (xy * x2x2 - x2y * xx2) / (xx * x2x2 - Power(xx2, 2));
def c0 = sumY / n - b0 * sumX / n - a0 * sumX2 / n;

# for a, b, and c use the final value on the last bar of the chart for all calculations

def a = GetValue(a0, bn - lastBar);
def b = GetValue(b0, bn - lastBar);
def c = GetValue(c0, bn - lastBar);

# calculate and plot the regression curve

plot theCurve = if bn < startBar then Double.NaN else a * Power(x, 2) + b * x + c;
#####
 
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T

thinkorswimmer22

New member
MountainKing333 said:
Alright so I **** at calculus and I'm even worse at coding. Can anyone find a way to expand this Quadratic Regression Line code into Cubic and or Quartic regression? I have absolutely no clue how to start, and I cant find any code online that can even be adapted to do this. Please if anyone can help, I think this would be a great option to have.


Code: 
# Quadratic Regression
# Robert Payne
# funwiththinkscript.com

input length = 20;
def n = length;
def bn = BarNumber();
def lastBar = HighestAll(if IsNaN(close) then 0 else bn);
def x = bn;
def y = close;

# calculate summation values

def startBar = lastBar - (n - 1);
def sumX = if bn < startBar then 0 else x + sumX[1];
def sumY = if bn < startBar then 0 else y + sumY[1];
def sumX2 = if bn < startBar then 0 else Power(x, 2) + sumX2[1];
def sumX3 = if bn < startBar then 0 else Power(x, 3) + sumX3[1];
def sumX4 = if bn < startBar then 0 else Power(x, 4) + sumX4[1];
def sumXY = if bn < startBar then 0 else x * y + sumXY[1];
def sumX2Y = if bn < startBar then 0 else Power(x, 2) * y + sumX2Y[1];

# intermediary calculations

def xx = sumX2 - Power(sumX, 2) / n;
def xy = sumXY - (sumX * sumY / n);
def xx2 = sumX3 - (sumX2 * sumX / n);
def x2y = sumX2Y - (sumX2 * sumY / n);
def x2x2 = sumX4 - (Power(sumX2, 2) / n);

# calculate coefficients for the quadratic equation

def a0 = (x2y * xx - xy * xx2) / (xx * x2x2 - Power(xx2, 2));
def b0 = (xy * x2x2 - x2y * xx2) / (xx * x2x2 - Power(xx2, 2));
def c0 = sumY / n - b0 * sumX / n - a0 * sumX2 / n;

# for a, b, and c use the final value on the last bar of the chart for all calculations

def a = GetValue(a0, bn - lastBar);
def b = GetValue(b0, bn - lastBar);
def c = GetValue(c0, bn - lastBar);

# calculate and plot the regression curve

plot theCurve = if bn < startBar then Double.NaN else a * Power(x, 2) + b * x + c;
#####
Click to expand...
Someone would have to code a design matrix from linear algebra. I don't know how to do that, but I tried.
 
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A

amalia

Member
## PolynomialQuadraticMA_JQ

## v01.10.2021 version 01 dated October 2021

## based on

## Polynomial Quadratic Moving Average

## Mobius

## V01.09.2021

## JQ adulterations;

## the Y from close to (close + vwap)/2

## added a label identifying Y and n

##

## use with SingleBar VWAP to visualize the single bar VWAP





## mobius' comments and header

#15:33 Mobius: Bored so fooling around with close to zero lag moving averages again.



# Polynomial Quadratic Moving Average

# Mobius

# V01.09.2021



input n = 20; # mobius default was 20



script E

{

input y = 1;

input n = 10;

def t = fold i = 0 to n

with s

do s + getValue(y, i);

plot output = t;

}

def y = (close + VWAP )/2; #mobius y = close

def x = compoundValue(1, x[1] + 1, 1);

def Ex = E(x, n);

def Ey = E(y, n);

def Ex2 = E(sqr(x), n);

def Ex3 = E(power(x, 3), n);

def Ex4 = E(power(x, 4), n);

def Exy = E(x*y, n);

def Ex2y = E(sqr(x)*Y, n);

def Exx = Ex2 - (sqr(Ex)/n);

def Ex_y = Exy - ((Ex * Ey)/n);

def Exx2 = Ex3 - ((Ex2 * Ex)/n);

def Ex2_y = Ex2y - ((Ex2 * Ey)/n);

def Ex2x2 = Ex4 - (sqr(Ex2)/n);

def a = ((Ex2_y * Exx) - (Ex_y * Exx2)) / ((Exx * Ex2x2) - sqr(Exx2));

def b = ((Ex_y * Ex2x2) - (Ex2_y * Exx2)) / ((Exx * Ex2x2) - Sqr(Exx2));

def c = (Ey / n) - (b * (Ex / n)) - (a * (Ex2 / n));

plot poly = (a*sqr(x)) + (b*x) + c;



#label by JQ

addlabel (1, "Polynomial Quadratic Moving Average y=(close +vwap)/2 n=" + n + " ", poly.takevaluecolor());

# End Code Polynomial Quadratic Moving Average
 
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