The cross-correlation analysis of multi property of stock markets based on MM-DFA

In this paper, we propose a new method called DH-MXA based on distribution histograms of Hurst surface and multiscale multifractal detrended fluctuation analysis. The method allows us to investigate the cross-correlation characteristics among multiple properties of different stock time series. It may provide a new way of measuring the nonlinearity of several signals. It also can provide a more stable and faithful description of cross-correlation of multiple properties of stocks. The DH-MXA helps us to present much richer information than multifractal detrented cross-correlation analysis and allows us to assess many universal and subtle cross-correlation characteristics of stock markets. We show DH-MXA by selecting four artificial data sets and five properties of four stock time series from different countries. The results show that our proposed method can be adapted to investigate the cross-correlation of stock markets. In general, the American stock markets are more mature and less volatile than the Chinese stock markets.