This paper presents a generalized approach to the fractal analysis of self-similar random processes by short time series. Several stages of the fractal analysis are proposed. Preliminary time series analysis includes the removal of short-term dependence, the identification of true long-term dependence and hypothesis test on the existence of a self-similarity property. Methods of unbiased interval estimation of the Hurst exponent in cases of stationary and non-stationary time series are discussed. Methods of estimate refinement are proposed. This approach is applicable to the study of self-similar time series of different nature.


self-similar stochastic process; time series; Hurst exponent

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Published : 2018-02-28

Kirichenko, L., Radivilova, T., & Bulakh, V. (2018). GENERALIZED APPROACH TO HURST EXPONENT ESTIMATING BY TIME SERIES. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 8(1), 28-31.

Lyudmyla Kirichenko
Kharkiv National University of Radioelectronics, Deptartment of Applied Mathematics  Ukraine
Tamara Radivilova 
Kharkiv National University of Radioelectronics, Deptartment of Infocommunication Engineering  Ukraine
Vitalii Bulakh 
Kharkiv National University of Radioelectronics, Deptartment of Applied Mathematics  Ukraine