Coupling Correlation Detrended Analysis for Multiple Nonstationary Series

Abstract Research on the temporal fluctuations of complex process is helpful to understand the underlying dynamical mechanisms. Here we propose a method called coupling correlation detrended analysis (CCDA) which allows us to rigorously and robustly test the long-range coupling properties of multivariate time series resulting from complex system. By introducing sign information of fluctuations, this new algorithm overcomes the limitation of existing CDFA method causing spurious coupling correlations. Efficiency of the method is showed on two artificial tests. Furthermore, a new R − statistic is proposed to explore the multifractal source of the coupling, which can quantify the contribution of every series to the system at different time scales and different fluctuations. We also apply the method on six air pollutant concentration series from different seasons in Beijing’s AQI system and uncover some interesting results.