Abstract: In this works we propose an integrated approach to the analysis of self-similar properties of stochastic processes for time series of short length. The sequence of steps of the fractal analysis was given. These steps are: preliminary analysis, including the removal of short-term dependence and revealing the true long-term dependency; hypothesis testing of a self-similarity; unbiased interval estimation of the Hurst exponent in cases of stationary and non-stationary time series by several methods; correction of the resulting estimate of the Hurst exponent. Keywords: self-similar stochastic process, time series, Hurst exponent, 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:

КОМПЛЕКСНЫЙ ПОДХОД К ИССЛЕДОВАНИЮ ФРАКТАЛЬНЫХ ВРЕМЕННЫХ РЯДОВ (Integrated Approach to the Study of Fractal Time Series)

Людмила Кириченко, Лариса Чалая

http://www.foibg.com/ijitk/ijitk-vol08/ijitk08-01-p03.pdf