MULTIFRACTAL CROSS-CORRELATION ANALYSIS BASED ON STATISTICAL MOMENTS

Abstract

We introduce a new method, multifractal cross-correlation analysis based on statistical moments (MFSMXA), to investigate the long-term cross-correlations and cross-multifractality between time series generated from complex system. Efficiency of this method is shown on multifractal series, comparing with the well-known multifractal detrended cross-correlation analysis (MFXDFA) and multifractal detrending moving average cross-correlation analysis (MFXDMA). We further apply this method on volatility time series of DJIA and NASDAQ indices, and find some interesting results. The MFSMXA has comparative performance with MFXDMA and sometimes perform slightly better than MFXDFA. Multifractal nature exists in volatility series. In addition, we find that the cross-multifractality of volatility series is mainly due to their cross-correlations, via comparing the MFSMXA results for original series with those for shuffled series.