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Generalized Hurst exponent

version 1.2.0.0 (2.08 KB) by Tomaso Aste
Generalized Hurst exponent of a stochastic variable

32 Downloads

Updated 31 Jan 2013

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Calculates the generalized Hurst exponent H(q) of a stochastic variable x(t) (a time series) from the scaling of the renormalized q-moments of the distribution

<|x(t+r)-x(t)|^q>/<x(t)^q> ~ r^[qH(q)]

The value of H(q) give indication about the fractal nature of the signal. H(q) = 0.5 corresponds to a Brownian motion, deviations form 0.5 and dependency on q are indications of multi-fractality and time-correlations.

Comments and Ratings (18)

Pankaj Dey

Dear Tamaso Aste

I want to know that whether I should use cumsum(data) to the function instead of raw data to get the value of Hurst Exponent.

Thank you very much for sharing the code to enitre community.

Regards,

Pankaj

Vincent Hary

asd

Pjotr

Pjotr (view profile)

I found this very useful. I translated the implementation into Python, with a reference to this FileExchange: https://github.com/PTRRupprecht/GenHurst

M T

M T (view profile)

good function. THX

roger wang

Jiayi XIE

Milot

Milot (view profile)

igor skachkov

a little biased on a pure random walk. is it possible to add corrections/

BOJING ZHU

good

Thomas

Thomas (view profile)

xinxing

Tomaso Aste

The Hurst exponent for a random walk is indeed 0.5. The Hurst exponent for a random variable is instead 0. If you apply the genhurst to cumsum(randn) and you will get numbers close to 0.5.

Sandro

Sandro (view profile)

I tried your file with a random time series (both rand and randn) and this values of obtained is close to 0 (although it should be close to 0.5 right?). Can you explain it?

WARR

WARR (view profile)

faruto

faruto (view profile)

Lars

Lars (view profile)

Updates

1.2.0.0

minor changes

1.1.0.0

Minor changes.

MATLAB Release Compatibility
Created with R2011a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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