Durbin Watson Test

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

//@version=4
study("Durbin Watson Test [pig]", "BA🐷 DWT", false, format.inherit, precision=2, resolution = "")

//Background Color
bgcolor(#000000c0)

//Inputs
src = input(close,"===== Source =====",     input.source)
len = input(   30,"Lookback",               input.integer, minval = 6, step   = 2)
tk  = input(    1,"--- Line Thickness ---", input.integer, options=[1,2,3])

//Linear Regression: Runs an Regression on barindex and log returns
y = log(src/src[1]) //Log returns
x = bar_index
sumy  = sum(y,len)
sumx  = sum(x,len)
sumxy = sum(x*y,len)
sumx2 = sum(pow(x,2),len)
sumy2 = sum(pow(y,2),len)

//slope
B = ((len*sumxy) - sumx*sumy)/((len*sumx2) - pow(sumx,2))

//Intercept
a = ((sumy - B*sumx)/len)

//Linear Regression Function
Y = B*x + a

//Residual Function: Substract the prediction result generated from linear regression from the data
f(n) =>
    y[n] - (B*(x-n) + a)

//Sum of squared of the first difference error terms
d = array.new_float(0)
for i = 0 to len - 2
    array.push(d, pow(f(i+1) - f(i),2))

sumd = array.sum(d)

//Sum of squared of all error terms
e = array.new_float(0)
for i = 0 to len - 1
    array.push(e,pow(f(i),2))

sume = array.sum(e)

//Durbin Watson Stats, Value between 0 and 4. 
dw = sumd /sume

//Significance level based on N of observation. 0.05 significance Durbin Watson Table below
//Between Lower and Upper Threshold means no significant first order autocorrelation, outside threshold means significant first order autocorrelation
l = 0.0
if len == 6
    l := 0.61
if len == 7
    l := 0.70
if len == 8
    l := 0.76
if len == 9
    l := 0.82
if len == 10
    l := 0.88
if len == 11
    l := 0.93
if len == 12
    l := 0.97
if len == 13
    l := 1.01
if len == 14
    l := 1.05
if len == 15
    l := 1.08
if len == 16
    l := 1.10
if len == 17
    l := 1.13
if len == 18
    l := 1.16
if len == 19
    l := 1.18
if len == 20
    l := 1.20
if len == 21
    l := 1.22
if len == 22
    l := 1.24
if len == 23
    l := 1.26
if len == 24
    l := 1.27
if len == 25
    l := 1.29
if len == 26
    l := 1.30
if len == 27
    l := 1.32
if len == 28
    l := 1.33
if len == 29
    l := 1.34
if len == 30
    l := 1.35
if len == 31
    l := 1.36
if len == 32
    l := 1.37
if len == 33
    l := 1.38
if len == 34
    l := 1.39
if len == 35
    l := 1.40
if len == 36
    l := 1.41
if len == 37
    l := 1.42
if len == 38
    l := 1.43
if len == 39
    l := 1.43
if len == 40
    l := 1.44
if len > 40 and len <= 45
    l := 1.48
if len > 45 and len <= 50
    l := 1.50
if len > 50 and len <= 55
    l := 1.53
if len > 55 and len <= 60
    l := 1.55
if len > 60 and len <= 65
    l := 1.57
if len > 65 and len <= 70
    l := 1.58
if len > 70 and len <= 75
    l := 1.60
if len > 75 and len <= 80
    l := 1.61
if len > 80 and len <= 85
    l := 1.62
if len > 85 and len <= 90
    l := 1.63
if len > 90 and len <= 95
    l := 1.64
if len > 95 and len <= 100
    l := 1.65
if len > 100 and len <= 150
    l := 1.72
if len > 150 and len <= 200
    l := 1.76
if len > 200 and len <= 250
    l := 1.79
if len > 250 and len <= 300
    l := 1.80
if len > 300
    l := 1.82

//Upper Threshold eqauls to 4 - lower threshold due to symmetry
ut = 4 - l

//Colors
c = dw > 2 ? color.white : dw < 2 ? color.orange : na

bgcolor(dw > ut ? color.aqua: na,75)
bgcolor(dw < l  ? color.red : na,70)

//Plots
plot(dw, "DWS", color = c, transp=0, linewidth=tk, style = plot.style_stepline)

hline(2, "Mid",             color.gray, hline.style_solid) //Above 2 -autocorrelation, Below 2 +autocorrelation
plot(l,  "Lower threshold", color.fuchsia, trackprice = true, show_last = 1, style = plot.style_linebr)
plot(ut, "Upper threshold", color.lime,    trackprice = true, show_last = 1, style = plot.style_linebr)