Hurst Exponent as a Part of Wavelet Decomposition Coefficients to Measure Long-term Memory Time Series Based on Multiresolution Analysis

Abstract

Processing and analysis of data sequences using wavelet-decomposition and subsequent analysis of the all relevant coefficients of such decomposition is one of strong methods to study various processes and phenomena. The key point of data sequence analysis lies in the concept of Hurst exponent. This is due to the fact that Hurst exponent gives an indication of the complexity and dynamics of the correlation structure of any given time series taking into consideration the importance of Hurst exponent estimation for such analysis. There are various methods and approaches to find the Hurst exponent estimation with varying degrees of accuracy and complexity. Therefore, in this paper we have made an attempt to prove the possibility of considering an estimation of Hurst exponent based on the properties of coefficients of wavelet decomposition of a given time series. The obtained results which mainly based on the properties of detailing coefficients of wavelet decomposition show that estimation is easy to calculate and comparable with classic estimation of Hurst exponent. Also ratios has been obtained, that allow to analyze the self-similarity of a given time series.