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Estimating of the Hurst exponent for experimental data plays a very important role in the research of processes which show properties of self-similarity. There are many methods for estimating the Hurst exponent using time series. The aim of this research is to carry out the comparative analysis of the statistical properties of the Hurst exponent estimators obtained by different methods using model stationary and nonstationary fractal time series. In this paper the most commonly used methods for estimating the Hurst exponents are examined. There are:/RS-analysis, variance-time analysis, detrended fluctuation analysis (DFA) and wavelet-based estimation. The fractal Brownian motion that is constructed using biorthogonal wavelets have been chosen as a model random process which exhibit fractal properties.

In this paper, 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 the 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. For the nonstationary case model time series are presented by the sum of fractional noise and the trend component, which are a polynomial in varying degrees, irrational, transcendental and periodic functions. The estimates of H were calculated for each generated time series using the methods mentioned above. Samples of the exponent H estimates were obtained for each value of H and their statistical characteristics were researched.