A new centered Copula function based method suitable for clustering of time series with general dependency structure is proposed. In light of the centered Copula function can capture the dependency structure between two variables, the centered Copula process is used to capture the dynamic dependency structure of the time series. Using the Cramér-von Mises statistics of the centered Copula process, a new similarity measure of time series is constructed, and a consistent nonparametric estimator with its equivalent form which is easy to calculate are given. Hierarchical clustering algorithm simulation studies show that the proposed similarity measure of time series is not only suitable for nonlinear time series data, but also has higher clustering quality for time series data with linearly dependency structures, and the practice data: GDP data in domestic provinces.

similarity measure; centered Copula; nonlinear time series; independence; dynamic dependent structure