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

In this paper, we introduce a new approach which generalizes the GM2 algorithm (introduced in Sánchez-Granero et al. (2008) [52]) as well as fractal dimension algorithms (FD1, FD2 and FD3) (first appeared in Sánchez-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 Lévy stable motions are considered. We conclude the paper with a dynamic study of the Hurst exponent evolution in the S&P500 index stocks. •We provide a new approach to properly calculate the Hurst exponent.•This generalizes FD algorithms and GM2, introduced previously by the authors.•This method (FD4) results especially appropriate for short time series.•FD4 may be used in both unifractal and multifractal contexts.•As an empirical application, we show that S&P500 stocks improved their efficiency.