Coupling correlation adaptive detrended analysis for multiple nonstationary series

The interaction among objects leads to the complexity observed in real-world systems. Investigating the coupling behavior between multiple variables provides an effective means of understanding the dynamic mechanisms within a complex system. In this paper, we introduce a novel method called coupling correlation adaptive detrended analysis (CCADA), which enables rigorous and robust assessment of the long-range coupling properties in nonstationary multivariate series resulting from complex systems. By combining adaptive fractal analysis and coupling correlation detrended analysis (CCDA), CCADA inherits the merits of CCDA in overcoming the limitations of existing methods that lead to spurious coupling correlations. Furthermore, CCADA offers improved accuracy in estimating the coupling exponent for both monofractal and multifractal systems. Extensive numerical tests and a real-world case study have confirmed the effectiveness and practicality of the proposed method. An in-depth discussion on the comparison of existing coupling correlation analysis methods demonstrates CCADA exhibits the highest levels of accuracy and robustness.