Hurst Exponent - Detrended Fluctuation Analysis - Indicators

This is the port to PRT of the nice balipour indicator from tradingview.

In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analyzing time series that appear to be long-memory processes and noise.

WARNING : this indicator will hit your CPU very hard. It was a test drive for me to test the limit of ProBuilder. I don’t recommend using it in real time.

For practical and intuitive indicators, you can have a look at my ProRealCode Market store.

//defparam calculateonlastbars = 2000

// Params
 len: 100
 bsc: 8
 msc: 2

//Log Return
r = log(close / close[1])

//Mean of Log Return
mean = average[len](r)

//Cumulative Sum
sum = 0
for i = 0 to len - 1 do
sum = (r[i] - mean) + sum
$csum[i] = sum
next

// Approximating log scale function (save sample size)
for i = 0 to 9 do
$fs[i] = round(bsc*pow(pow(len/(msc*bsc),0.1111111111),i))
next

for i = 0 to 9 do
//Average of Root Mean Sum Measured each block (Log Scale) ARMS
bar = $fs[i]
num = floor(len / bar)
sumr = 0
for j = 0 to num - 1 do
//Root Mean Sum (FLuctuation) function linear trend to calculate error between linear trend and cumulative sum
rms = 0
count = 0
N1 = j * bar
N  = bar

//Slicing the array into different segments
for k = 0 to N - 1 do
count = count + 1
$seq[k] = count
next

for k = N1 to N1 + N - 1 do
$y[k - N1] = $csum[k]
next

//Linear regression measuing trend (N/(N-1) for sample unbiased adjustedment)
ec = 0
for k = 0 to N - 1 do
ec = ec + $seq[k]
next
mc = ec / N

varx = 0
for k = 0 to N - 1 do
varx = varx + square($seq[k] - mc)
next
sdx = sqrt(varx/N) * sqrt(N/(N-1))

ey = 0
for k = 0 to N - 1 do
ey = ey + $y[k]
next
my = ey / N

vary = 0
for k = 0 to N - 1 do
vary = vary + square($y[k] - my)
next
sdy = sqrt(vary/N) * sqrt(N/(N-1))

esy = 0
for k = 0 to N - 1 do
esy = esy + $seq[k] * $y[k]
next
msy = esy / N

cov = (msy - mc * my) * (N/(N-1))

rr2 = pow(cov/(sdx*sdy), 2)
rms = sqrt(1 - rr2) * sdy

sumr = sumr + rms
next

$fluc[i] = log(sumr / num) / log(10)
next

//Set Ten Points of data scale along the X log axis
for i = 0 to 9 do
$scl[i] = log($fs[i]) / log(10)
next

// Slope Measured from RMS and scale on log log plot using linear regression
ssc = 0
for i = 0 to 9 do
ssc = ssc + $scl[i]
next
esc = ssc / 10

sfl = 0
for i = 0 to 9 do
sfl = sfl + $fluc[i]
next
efl = sfl / 10

sf = 0
for i = 0 to 9 do
sf = sf + ($scl[i] - esc) * ($fluc[i] - efl)
next
cov = sf / 10

ssq = 0
for i = 0 to 9 do
ssq = ssq + square($scl[i] - esc)
next
var = ssq / 10

hurst = cov / var

//Critical Value based on Confidence Interval (95% Confidence)
ci = 1.645 * (0.3912 / pow(len,0.3))
//Expected Value plus Crtical Value
cu = 0.5 + ci
cd = 0.5 - ci

if hurst > cu then
hr = 0
hg = 255
hb = 128
elsif hurst >= 0.5 then
hr = 0
hg = 255
hb = 255
elsif hurst < cd then
hr = 255
hg = 255
hb = 0
elsif hurst < 0.5 then
hr = 255
hg = 0
hb = 255
endif

smooth = (hurst + 2 * hurst[1] + 2 * hurst[2] + hurst[3]) / 6

return hurst coloured(hr, hg, hb) style(point, 3) as "Hurst Exponent", cu as "Up Confidence Interval", cd as "Down Confidence Interval", 0.5 as "Random Walk Threshold", smooth

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//defparam calculateonlastbars = 2000

// Params

len: 100

bsc: 8

msc: 2

//Log Return

r = log(close / close[1])

//Mean of Log Return

mean = average[len](r)

//Cumulative Sum

sum = 0

for i = 0 to len - 1 do

sum = (r[i] - mean) + sum

$csum[i] = sum

// Approximating log scale function (save sample size)

for i = 0 to 9 do

$fs[i] = round(bsc*pow(pow(len/(msc*bsc),0.1111111111),i))

for i = 0 to 9 do

//Average of Root Mean Sum Measured each block (Log Scale) ARMS

bar = $fs[i]

num = floor(len / bar)

sumr = 0

for j = 0 to num - 1 do

//Root Mean Sum (FLuctuation) function linear trend to calculate error between linear trend and cumulative sum

rms = 0

count = 0

N1 = j * bar

N = bar

//Slicing the array into different segments

for k = 0 to N - 1 do

count = count + 1

$seq[k] = count

for k = N1 to N1 + N - 1 do

$y[k - N1] = $csum[k]

//Linear regression measuing trend (N/(N-1) for sample unbiased adjustedment)

ec = 0

for k = 0 to N - 1 do

ec = ec + $seq[k]

mc = ec / N

varx = 0

for k = 0 to N - 1 do

varx = varx + square($seq[k] - mc)

sdx = sqrt(varx/N) * sqrt(N/(N-1))

ey = 0

for k = 0 to N - 1 do

ey = ey + $y[k]

my = ey / N

vary = 0

for k = 0 to N - 1 do

vary = vary + square($y[k] - my)

sdy = sqrt(vary/N) * sqrt(N/(N-1))

esy = 0

for k = 0 to N - 1 do

esy = esy + $seq[k] * $y[k]

msy = esy / N

cov = (msy - mc * my) * (N/(N-1))

rr2 = pow(cov/(sdx*sdy), 2)

rms = sqrt(1 - rr2) * sdy

sumr = sumr + rms

$fluc[i] = log(sumr / num) / log(10)

//Set Ten Points of data scale along the X log axis

for i = 0 to 9 do

$scl[i] = log($fs[i]) / log(10)

// Slope Measured from RMS and scale on log log plot using linear regression

ssc = 0

for i = 0 to 9 do

ssc = ssc + $scl[i]

esc = ssc / 10

sfl = 0

for i = 0 to 9 do

sfl = sfl + $fluc[i]

efl = sfl / 10

sf = 0

for i = 0 to 9 do

sf = sf + ($scl[i] - esc) * ($fluc[i] - efl)

cov = sf / 10

ssq = 0

for i = 0 to 9 do

ssq = ssq + square($scl[i] - esc)

var = ssq / 10

hurst = cov / var

//Critical Value based on Confidence Interval (95% Confidence)

ci = 1.645 * (0.3912 / pow(len,0.3))

//Expected Value plus Crtical Value

cu = 0.5 + ci

cd = 0.5 - ci

if hurst > cu then

hr = 0

hg = 255

hb = 128

elsif hurst >= 0.5 then

hr = 0

hg = 255

hb = 255

elsif hurst < cd then

hr = 255

hg = 255

hb = 0

elsif hurst < 0.5 then

hr = 255

hg = 0

hb = 255

endif

smooth = (hurst + 2 * hurst[1] + 2 * hurst[2] + hurst[3]) / 6

return hurst coloured(hr, hg, hb) style(point, 3) as "Hurst Exponent", cu as "Up Confidence Interval", cd as "Down Confidence Interval", 0.5 as "Random Walk Threshold", smooth

hurst

Risk disclosure:

No information on this site is investment advice or a solicitation to buy or sell any financial instrument. Past performance is not indicative of future results. Trading may expose you to risk of loss greater than your deposits and is only suitable for experienced investors who have sufficient financial means to bear such risk.

ProRealTime ITF files and other attachments :

Filename : download the ITF files

How to import ITF files into ProRealTime platform?

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jonpt88 • 10/13/2022 #
This is great! Such a job you did!. I do not really understand though how it works.
- Bruno Carnazzi • 10/13/2022 #
  Thank you, I’ve just realized that all links are missing in the description. You can find the original indicator and explanations here : https://www.tradingview.com/script/vTloluai-Hurst-Exponent-Detrended-Fluctuation-Analysis-pig/ and my store here : https://market.prorealcode.com/store/digital-filters-workshop/

Nicolas Sorry there was a small issue in the code, i have changed the attached itf file and updated ...

Mitchy14 Hi Nicholas, apologies, I am usually fairly good at implementing your creations (for which I...

Nicolas Are you using PRT version pre-v11? TIMEFRAME for indicators is possible since months for pro...

Nicolas Sorry I do not provide assistance for Tradestation code.

surfeur Bonjour, Je suis pas expert en PRT donc si qq'un peut m'expliquer un peu le code ? Par...

Nicolas src c'est bien le customclose en effet. ATR, si aucune série de données n'est spécifié, il u...

Hurst Exponent – Detrended Fluctuation Analysis

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