A new tendency correlation coefficient for bivariate time series

Abstract

The correlation analysis of bivariate time series is a common problem in many fields. Based on the analysis of the changing range and the changing direction between any two time points on the bivariate time series, this paper proposes a new tendency correlation coefficient that is applicable for both stationary and non-stationary time series. It ranges from − 1 to 1, and the necessary and sufficient condition of the tendency correlation coefficient getting the extremum value is theoretically given. To measure the similarity of bivariate time series, the concept of congruence is proposed based on the normalization process, and the invariant character of the tendency correlation coefficient for the congruent bivariate time series is theoretically proved. Compared with other existing methods, experiment results of Monte Carlo simulations on both stationary series and non-stationary series with different degrees of intrinsic correlations, and real time series of oil-immersed transformers convince the advantages of the proposed tendency correlation coefficient on accuracy and stability.