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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

33 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 (20)

QUYNH BUI

Dear Mr. Tamaso Aste,

I would like to ask whether there is any restriction on the values of the series S. Are there any problems if my series contains both positive and negative values? It's quite strange in my case, as I calculate the spread between 2 stocks for the period of 1 year (252 observations), and I get the mH for this series = -0.00518, which confuses me. Could you please give some advice me on this issue?

cheng cheng

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.?

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

asd

Pjotr

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

M T

good function. THX

roger wang

Jiayi XIE

Milot

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

BOJING ZHU

good

Thomas

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

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

faruto

Lars

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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