Abstract: Estimating of the Hurst exponent for experimental data playas a very important role in research of processes which show properties of self-affinity. There are many methods for estimating the Hurst exponent using time series. The aim of this work is to carry out the comparative analysis of statistical properties of estimates of the Hurst exponent obtained by different methods using short length model fractal time series (the number of values less than 4000). In the work the most common used methods for estimating the Hurst exponent are researched. They are: R / S -analysis, variance-time analysis, detrended fluctuation analysis (DFA) and wavelet-based estimation. The fractal Brownian motion that is constructed using biorthogonal wavelets has been chosen as a model random process which exhibit fractal properties. In the work the results of a numerical experiment are represented where the fractal Brown motion was modelled for the specified values of the exponent H. The values of Hurst exponent for the model realizations were varied within the whole interval of possible values 0 < H < 1.The lengths of the realizations were defined as 500, 1000, 2000 and 4000 values. The estimates of H were calculated for each generated time series using the methods mentioned above. Samples of estimates of the exponent H were obtained for each value of H and their statistical characteristics were researched. The results of the analysis have shown that the estimates of the Hurst exponent, which were obtained for the realisations of short length using the considered methods, are biased normal random variables. For each method the bias depends on the true value of degree of self-similarity of a process and a length of time series. Those estimates which are obtained by the DFA method and the wavelet transform have the minimal bias. Standard deviations of the estimates depend on the estimation method and decrease while the length of the series increases. Those estimates which are obtained by using the wavelet analysis have the minimal standard deviation.

Keywords: Hurst exponent, estimate of the Hurst exponent, self-similar stochastic process, time series, methods for estimating the Hurst exponent

ACM Classification Keywords: G.3 Probability and statistics - Time series analysis , Stochastic processes, G.1 Numerical analysis, G.1.2 Approximation - Wavelets and fractals

Link:

COMPARATIVE ANALYSIS OF STATISTICAL PROPERTIES OF THE HURST EXPONENT ESTIMATES OBTAINED BY DIFFERENT METHODS

Ludmila Kirichenko, Tamara Radivilova

http://foibg.com/ibs_isc/ibs-19/ibs-19-p56.pdf