Multi-affine visible height correlation analysis for revealing rich structures of fractal time series

Abstract

In this work we propose a novel algorithm, the multi-affine visible height correlation analysis (MA-VHCA), to analyze long-term correlations in fractal time series. Our method incorporates visible operator into the multi-affine height correlation analysis (MA-HCA). Besides the original power-law exponent obtained by MA-HCA, MA-VHCA can produce two more exponents. These three exponents, together with a newly proposed quantity (the average probability of two visible points P(L)), allow us to uncover rich structures of fractal time series. Some classical examples and analytical tools are used to test our method. In addition, our method may be used to distinguish chaotic series from random ones. As a case study, we apply the proposed MA-VHCA into electricity price series of the California power crisis. Our interesting findings show that there are significant differences between the price characteristics before and during the power crisis, which helps us better understand the price dynamics of the California power market.