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.

双变量时间序列的相关性分析是许多领域中的常见问题。在分析双变量时间序列中任意两个时间点之间的变化范围和变化方向的基础上，提出了一种适用于平稳和非平稳时间序列的新趋势相关系数。从-1到1，从理论上给出了趋势相关系数获得极值的充要条件。为了度量双变量时间序列的相似性，在归一化过程的基础上提出了全同的概念，并从理论上证明了全双变量时间序列的趋势相关系数的不变性。与其他现有方法相比，