# Daily Hurst Exponent

I am trying to estimate daily Hurst exponent values of a stock returns (e.g. for each day to have also Hurst exponent - something like that: https://www.quandl.com/data/PE/CKEC_HURST-Hurst-Exponent-of-Carmike-Cinemas-Inc-Common-Stock-CKEC-NASDAQ).

I am using tis Python code (taken from https://www.quantstart.com/articles/Basics-of-Statistical-Mean-Reversion-Testing), but I do not how to accomodate it for daily Hurst values instead of just one value:

from numpy import cumsum, log, polyfit, sqrt, std, subtract

from numpy.random import randn

def hurst(ts):

"""Returns the Hurst Exponent of the time series vector ts"""
# Create the range of lag values
lags = range(2, 100)

# Calculate the array of the variances of the lagged differences
tau = [sqrt(std(subtract(ts[lag:], ts[:-lag]))) for lag in lags]

# Use a linear fit to estimate the Hurst Exponent
poly = polyfit(log(lags), log(tau), 1)

# Return the Hurst exponent from the polyfit output
return poly[0]*2.0

• you can call the function by modifying the input time serie (ts) each time : using a rolling window approach. Example : first call with ts = [1:200], second call with ts = [2:201] – Malick Dec 28 '15 at 18:59
• You can't compute a Hurst exponent from 1 daily observation, you need a range of many days. It is unclear how the chart you showed is computed, it must be over a certain number of past days, i.e. with a moving window that is moved forward each day. – noob2 Dec 28 '15 at 18:59
• If you dont mind using matlab, you can find a lot of implementations of the Hurst exponent here: prorum.com/index.php/2173/… Some of them calculates the Hurst Exponent over time (if I correctly understand it is what you are looking for): prorum.com/index.php/2173/… – DanielTheRocketMan Feb 9 '16 at 15:50
• @DanielTheRocketMan: Thank you, this is what I was looking for! – Marcus Feb 9 '16 at 17:51