Detrended moving average partial cross-correlation analysis on financial time series

Cross-correlations between nonlinear time series widely exist in complex systems. It is of great importance to accurately measure the correlations between time series. In this work, we suggest a combination methodology of Detrended Moving Average Processing and Partial Cross-correlation Analysis to quantify the correlations between different time series, which we call as Detrended Moving Average Partial Cross-correlation Analysis (DMPCCA). This novel approach combines the advantages of Detrended Moving Average Processing and Partial Cross-correlation Analysis, not only exploring power-law cross-correlations between two signals but removing underlying impacts of other signals on those two signals. To demonstrate the advantages of this approach, we carry out experiments with synthetic data generated by correlated processes and compare the performance of this measurement to traditional cross-correlation techniques. It is found that this method can reveal the real cross-correlations between systems even when the indirect cross-correlations established by other common factors exist. Then we go further study into the application of DMPCCA to financial time series in order to report its performance in stock markets and investigate cross-correlations between different stock indices. Furthermore, the rolling windows method is used in conjunction with DMPCCA to capture the changes of cross-correlations between stock indices as time goes on. We notice that there is a special period when DMPCCA coefficients between stock indices are obviously different from those of other periods.