Multifractal Detrending Moving Average Cross-correlation Analysis
There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. The MultiFractal Detrended Cross-Correlation Analysis (MF-DCCA) approaches can be used to quantify such cross-correlations, such as the MF-DCCA based on Detrended Fluctuation Analysis (MF-X-DFA) method. The authors develop in this paper a class of MF-DCCA algorithms based on the detrending moving average analysis, called MF-X-DMA. The performances of the MF-X-DMA algorithms are compared with the MF-X-DFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated moving average processes and binomial measures, which have theoretical expressions of the multifractal nature.