Hurst R/S Estimate

Problem

Estimate the Hurst exponent with a single-scale rescaled range. Subtract the mean and form cumulative deviations; let R be max minus min of that path and S the population standard deviation. Return log(R / S) / log(n).

Return 0.0 if n < 2, S is 0, or R is not positive.

Hint

H near 0.5 suggests a random walk; more persistent series score higher.

Test cases

case 1

in: [[1,2,3,4,5]]

expected: 0.46726791544928875

case 2

in: [[1,2,3,4,5,6,7,8]]

expected: 0.6012804295368734

case 3

in: [[5,5,5]]

expected: 0

case 4

in: [[1,5,2,4,3]]

expected: 0.2153382790366965

Starter codePython

import math
def hurst_rs(series):
    # Your code here
    pass

4 test cases · run your code against them in the editor