An accurate algorithm to calculate the Hurst exponent of self-similar processes

Abstract In this paper, we introduce a new approach which generalizes the GM2 algorithm (introduced in Sanchez-Granero et al. (2008) [52] ) as well as fractal dimension algorithms (FD1, FD2 and FD3) (first appeared in Sanchez-Granero et al. (2012) [51] ), providing an accurate algorithm to calculate the Hurst exponent of self-similar processes. We prove that this algorithm performs properly in the case of short time series when fractional Brownian motions and Levy stable motions are considered. We conclude the paper with a dynamic study of the Hurst exponent evolution in the S&P500 index stocks.

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