4.7 Article

Simultaneous estimation of the parameters of the Hurst-Kolmogorov stochastic process

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Publisher

SPRINGER
DOI: 10.1007/s00477-010-0408-x

Keywords

Hurst phenomenon; Hurst-Kolmogorov behaviour; Long term persistence; Hydrological statistics; Hydrological estimation; Hurst parameter estimators

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Various methods for estimating the self-similarity parameter (Hurst parameter, H) of a Hurst-Kolmogorov stochastic process (HKp) from a time series are available. Most of them rely on some asymptotic properties of processes with Hurst-Kolmogorov behaviour and only estimate the self-similarity parameter. Here we show that the estimation of the Hurst parameter affects the estimation of the standard deviation, a fact that was not given appropriate attention in the literature. We propose the least squares based on variance estimator, and we investigate numerically its performance, which we compare to the least squares based on standard deviation estimator, as well as the maximum likelihood estimator after appropriate streamlining of the latter. These three estimators rely on the structure of the HKp and estimate simultaneously its Hurst parameter and standard deviation. In addition, we test the performance of the three methods for a range of sample sizes and H values, through a simulation study and we compare it with other estimators of the literature.

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