Multiscale multifractal detrended cross-correlation analysis of financial time series

• Discuss the cross-correlation between two stock markets in both multiscale and multifractal view.
• Expend J. Gieraltowski’s MMA method to two time series and apply the new process to financial time series for the first time.
• Discuss the influence of the length of series to the multiscale and multifractal results.
• Using the artificial time series to proving the efficiency of our multiscale multifractal detrended cross-correlation analysis.

In this paper, we introduce a method called multiscale multifractal detrended cross-correlation analysis (MM-DCCA). The method allows us to extend the description of the cross-correlation properties between two time series. MM-DCCA may provide new ways of measuring the nonlinearity of two signals, and it helps to present much richer information than multifractal detrended cross-correlation analysis (MF-DCCA) by sweeping all the range of scale at which the multifractal structures of complex system are discussed. Moreover, to illustrate the advantages of this approach we make use of the MM-DCCA to analyze the cross-correlation properties between financial time series. We show that this new method can be adapted to investigate stock markets under investigation. It can provide a more faithful and more interpretable description of the dynamic mechanism between financial time series than traditional MF-DCCA. We also propose to reduce the scale ranges to analyze short time series, and some inherent properties which remain hidden when a wide range is used may exhibit perfectly in this way.