Methods for Estimating the Hurst Exponent of Stock Returns: A Note

9 Pages Posted: 16 Feb 2015 Last revised: 16 Apr 2015

Date Written: February 14, 2015


This note is a further commentary on a previous paper on the chaos theory of stock returns that derives from the alleged detection of persistence in time series data indicated by values of the Hurst exponent H that differs from the neutral value of H=0.5 implied by the efficient market hypothesis (EMH) (Munshi, 2014). A comparison of four different methods for estimating H is presented. Linear regression of log transformed values (OLS) is compared against a numerical approach using the generalized reduced gradient (GRG) method. These methods are applied to two different empirical models for the estimation of H. We find that the major source of error in the empirical estimation of H is the insertion of the extraneous constant C into the empirical model.

Keywords: finance, financial analysis, efficient market hypothesis, financial markets, chaos theory, stock markets, rescaled range analysis, Hurst constant, fractal theory of stock markets, stock price behavior, long term memory of stock returns, persistence in stock returns, OLS regression, least squares, li

Suggested Citation

Munshi, Jamal, Methods for Estimating the Hurst Exponent of Stock Returns: A Note (February 14, 2015). Available at SSRN: or

Jamal Munshi (Contact Author)

Sonoma State University ( email )

1801 East Cotati Avenue
Rohnert Park, CA 94928
United States

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