Improved Cross-Correlation Coefficient: Quantifying the Cross-Correlation Level between Fluctuant Amplitude Ranges in Two Non-Stationary Time Series

Abstract

In this study, the cross-correlation coefficient [Formula: see text] is improved to quantify the cross-correlation level between fluctuant amplitude ranges in two non-stationary time series on various temporal scales. The proposed method is based on the de-trended cross-correlation analysis, de-trended fluctuation analysis, Kendall correlation analysis, and Gaussian kernel density estimation technique. The implementation of the improved cross-correlation coefficient is illustrated in computer-generated and empirical datasets. The results demonstrate that small–small and large–large fluctuation amplitude ranges in synchronous records of wind speed and PM2.5 are cross-correlated. The [Formula: see text] coefficient can be used as an appropriate practical measure for obtaining the cross-correlation level between the fluctuation amplitude ranges in two non-stationary time series. This finding enables a better understanding of the cross-correlation behavior between two non-stationary time series.