The Hurst phenomenon and fractional Gaussian noise made easy

Koutsoyiannis, D., The Hurst phenomenon and fractional Gaussian noise made easy, Hydrological Sciences Journal, 47 (4), 573–595, 2002.



The Hurst phenomenon, which characterises hydrological and other geophysical time series, is formulated and studied in an easy manner in terms of the variance and autocorrelation of a stochastic process on multiple temporal scales. In addition, a simple explanation of the Hurst phenomenon based on the fluctuation of a hydrologic process upon different temporal scales is presented. The stochastic process that was devised to represent the Hurst phenomenon, i.e. the fractional Gaussian noise, is also studied on the same grounds. Based on its studied properties, three simple and fast methods to generate fractional Gaussian noise or good approximations of it are proposed.

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Alternative names for Hurst phenomenon are Hurst effect, Joseph effect, Long term persistence, Long range dependence, Scaling behaviour (in time), Multi-scale fluctuation, Hurst-Kolmogorov pragmaticity, etc.

Our works referenced by this work:

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Tagged under: Course bibliography: Stochastic methods, Hurst-Kolmogorov dynamics, Papers initially rejected, Stochastics