Multiscale multifractal detrended partial cross-correlation analysis of Chinese and American stock markets

Abstract

• We analyzed multifractal binomial measures contaminated with strong white noises. • We investigated the cross correlations between stock markets using MM DPXA methods. • New conclusions regarding multiscale correlation structures were obtained. • We studied the effect of financial crisis on the cross correlations of stock markets. In this paper, a new method called multiscale multifractal detrended partial cross-correlation analysis (MM-DPXA) method is proposed, which combines multifractal detrended partial cross-correlation analysis (MF-DPXA) with multiscale multifractal analysis (MMA). To demonstrate the advantages of this method, we analyze multifractal binomial measures contaminated with strong white noises and compare the performance of MM-DPXA method to traditional cross-correlation techniques. It is found that MM-DPXA method can not only eliminate the influence of other variables, but also provide more valuable information from multiscale perspective. Moreover, this method is able to characterize monofractality or multifractality of the time series in a wide range of scales simultaneously and without assuming any presumed time scale. To further show the utility of MM-DPXA method in complex systems, we provide new evidence on the financial time series. By comparing Hurst surfaces before and after removing common influences, we conclude that cross-correlations and intrinsic cross-correlations show different properties in different scales. Furthermore, we also study the effect of financial crisis on the cross-correlations between Chinese and American stock markets using MF-DCCA and MF-DPXA methods.