Multiscale temporal weighted coupling correlation detrended analysis for multivariate nonstationary series

Understanding coupling correlations in multivariate time series is crucial for analyzing the complex dynamics of real world systems, where interactions often vary across different time scales. In this paper, we propose two novel methods: temporal weighted coupling correlation detrended analysis and its multiscale extension and multiscale temporal weighted coupling correlation detrended analysis (MTWCCDA). These two methods improve the trend removal process by incorporating temporal weighting, leading to a more robust and accurate characterization of coupling correlation behavior. We evaluate the performance of the proposed methods using synthetic data from several perspectives: accuracy of scaling index estimation, robustness to trends, sensitivity to noise and various components, and the necessity of MTWCCDA for capturing coupling behavior across scales. Additionally, MTWCCDA is applied to study the coupling behaviors of six air pollutants in Hunan Province, China, at different time scales. A Q-statistic quantifies each pollutant's contribution to the system's multifractal coupling correlation across scales, while scaling indices are used for clustering 14 cities, revealing regional variations in coupling behavior. The results provide valuable insights into pollutant interdependencies, aiding in the development of targeted air quality management strategies. The proposed methods offer a robust framework for investigating dynamic coupling behaviors in complex, multiscale, and non-stationary multivariate time series.