为线性回归 PineScript 计算 Pearson 的 R

Question

我在下面有一个 pinescript 策略，我试图在其中计算 Pearsons R 相关值。我从这里获取代码并对其进行了一些修改 (https://www.tradingview.com/script/CD7yUWRV-Linear-Regression-Trend-Channel/)。

他的代码不包括 Pearson 的 R 相关性，这对我尝试使用的交易策略非常重要，因为它表明趋势的强度和方向（向上或向下）。要查看 Pearson's R 的工作示例，请添加默认指标线性回归，它将是左下角的数字。我将附上屏幕截图作为示例。

我如何根据目前的代码计算 Pearson 的 R 值？

我已经在 pinescript 中寻找具有用于线性回归的 Pearson R 计算的样本 pine 脚本，但找不到任何东西。

strategy(title="Linear Regression Trend Channel Strategy", overlay=true,initial_capital=1000,commission_type=strategy.commission.percent,commission_value=0.26,default_qty_type=strategy.percent_of_equity,default_qty_value=100)
period     = input(     240, "Period"       , input.integer, minval=3)//288
deviations = input(    2.0, "Deviation(s)" , input.float  , minval=0.1, step=0.1)
extendType = input("Right", "Extend Method", input.string , options=["Right","None"])=="Right" ? extend.right : extend.none
periodMinusOne = period-1
Ex = 0.0, Ey = 0.0, Ex2 = 0.0, Exy = 0.0, for i=0 to periodMinusOne
    closeI = nz(close[i]), Ex := Ex + i, Ey := Ey + closeI, Ex2 := Ex2 + (i * i), Exy := Exy + (closeI * i)
ExEx = Ex * Ex, slope = Ex2==ExEx ? 0.0 : (period * Exy - Ex * Ey) / (period * Ex2 - ExEx)
linearRegression = (Ey - slope * Ex) / period
intercept = linearRegression + bar_index * slope
deviation = 0.0, for i=0 to periodMinusOne
    deviation := deviation + pow(nz(close[i]) - (intercept - slope * (bar_index[i])), 2.0)
deviation := deviations * sqrt(deviation / periodMinusOne)
startingPointY = linearRegression + slope * periodMinusOne
var line upperChannelLine = na  , var line medianChannelLine = na  , var line lowerChannelLine = na
line.delete(upperChannelLine[1]), line.delete(medianChannelLine[1]), line.delete(lowerChannelLine[1])
upperChannelLine  := line.new(bar_index - period + 1, startingPointY + deviation, bar_index, linearRegression + deviation, xloc.bar_index, extendType, color.new(#FF0000, 0), line.style_solid , 2)
medianChannelLine := line.new(bar_index - period + 1, startingPointY            , bar_index, linearRegression            , xloc.bar_index, extendType, color.new(#C0C000, 0), line.style_solid , 1)
lowerChannelLine  := line.new(bar_index - period + 1, startingPointY - deviation, bar_index, linearRegression - deviation, xloc.bar_index, extendType, color.new(#00FF00, 0), line.style_solid , 2)

if(crossunder(close,line.get_y2(lowerChannelLine)))
    strategy.entry("Long", strategy.long)

if(crossover(close,line.get_y2(upperChannelLine)))
    strategy.entry("Short", strategy.short)

Answer 1

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © x11joe
// Credit given to @midtownsk8rguy for original source code.  I simply modified to add Pearson's R

//@version=4
study("Linear Regression Trend Channel With Pearson's R", "LRTCWPR", true, format.inherit)
period     = input(     20, "Period"       , input.integer, minval=3)
deviations = input(    2.0, "Deviation(s)" , input.float  , minval=0.1, step=0.1)
extendType = input("Right", "Extend Method", input.string , options=["Right","None"])=="Right" ? extend.right : extend.none
periodMinusOne = period-1
Ex = 0.0, Ey = 0.0, Ex2 = 0.0,Ey2 =0.0, Exy = 0.0, for i=0 to periodMinusOne
    closeI = nz(close[i]), Ex := Ex + i, Ey := Ey + closeI, Ex2 := Ex2 + (i * i),Ey2 := Ey2 + (closeI * closeI), Exy := Exy + (closeI * i)
ExT2 = pow(Ex,2.0) //Sum of X THEN Squared
EyT2 = pow(Ey,2.0) //Sym of Y THEN Squared
PearsonsR = (Exy - ((Ex*Ey)/period))/(sqrt(Ex2-(ExT2/period))*sqrt(Ey2-(EyT2/period)))
ExEx = Ex * Ex, slope = Ex2==ExEx ? 0.0 : (period * Exy - Ex * Ey) / (period * Ex2 - ExEx)
linearRegression = (Ey - slope * Ex) / period
intercept = linearRegression + bar_index * slope
deviation = 0.0, for i=0 to periodMinusOne
    deviation := deviation + pow(nz(close[i]) - (intercept - slope * (bar_index[i])), 2.0)
deviation := deviations * sqrt(deviation / periodMinusOne)
startingPointY = linearRegression + slope * periodMinusOne
var label pearsonsRLabel = na
label.delete(pearsonsRLabel[1])
pearsonsRLabel := label.new(bar_index,startingPointY - deviation*2,text=tostring(PearsonsR), color=color.black,style=label.style_labeldown,textcolor=color.white,size=size.large)
var line upperChannelLine = na  , var line medianChannelLine = na  , var line lowerChannelLine = na
line.delete(upperChannelLine[1]), line.delete(medianChannelLine[1]), line.delete(lowerChannelLine[1])
upperChannelLine  := line.new(bar_index - period + 1, startingPointY + deviation, bar_index, linearRegression + deviation, xloc.bar_index, extendType, color.new(#FF0000, 0), line.style_solid , 2)
medianChannelLine := line.new(bar_index - period + 1, startingPointY            , bar_index, linearRegression            , xloc.bar_index, extendType, color.new(#C0C000, 0), line.style_solid , 1)
lowerChannelLine  := line.new(bar_index - period + 1, startingPointY - deviation, bar_index, linearRegression - deviation, xloc.bar_index, extendType, color.new(#00FF00, 0), line.style_solid , 2)

好的，所以我在下面发布了我的解决方案。多亏了这里的 youtube 视频，我有了这个想法，https://www.youtube.com/watch?v=2B_UW-RweSE

这真的帮助我弄清楚了公式。希望这对 tradingView 上需要它的其他人有所帮助！

Answer 2

我觉得这个

PearsonsR = (Exy - ((Ex*Ey)/period))/(sqrt(Ex2-(ExT2/period))*sqrt(Ey2-(EyT2/period)))

应该是 PearsonsR = (((Ex*Ey)/period)-Exy)/(sqrt(Ex2-(ExT2/period))*sqrt(Ey2-(EyT2/period)))

根据：https://it.wikipedia.org/wiki/Indice_di_correlazione_di_Pearson#/media/File:Correlation_coefficient.png

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