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.