hurst_exponent

Builtin index · Signal processing

result = hurst_exponent(x)

Input: x · Output: result

What it is

x: a length-N real vector.

Overloads

One call shape — this function is not overloaded.

Code	Input	Output	Description
`result = hurst_exponent(x)`	`x` vectornot documented yet	`result` number	Returns a single number: 0.5 is a random walk, above that persistent, below it mean-reverting — long-range dependence.

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

fs = 1000
n = 0:1:511
t = n / fs
x = sin(2*pi*20*t) + 0.2*randn(512, seed=4)

r = acf(x, max_lag=50)
below = find_peaks(-abs(r - 1/e))
print("acf[0] = {r[0]}, acf drops below 1/e near lag {below[0]}")

h_tone = hurst_exponent(x)
h_walk = hurst_exponent(cumsum(randn(512, seed=5)))
print("hurst (periodic+noise) = {h_tone}, hurst (random walk) = {h_walk}")

output

acf[0] = 1, acf drops below 1/e near lag 9
hurst (periodic+noise) = 0.71599, hurst (random walk) = 0.998318

from signal-processing

How it works

hurst_exponent(x) — see the free function's own doc comment for the R/S-analysis algorithm and how to read the result (persistent/random-walk/anti-persistent).

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.