Abstract: Some preliminaries for set-valued multivariate time series were studied, which provides a theoretical basis for extending the classical multivariate time series models. First, this paper introduced the definitions of set-valued vectors and set-valued random vectors based on the set-valued random variable theory. The definitions of expectation vectors, cross covariance matrixes and cross correlation matrixes were also given in this paper. Then, the set-valued multivariate time series was defined and the stationary property, expectation vectors, cross covariance matrixes and cross correlation matrixes of set-valued multivariate time series were discussed. Furthermore, the optimal linear forecast of stationary set-valued multivariate time series was studied. Finally, the interval-valued multivariate time series were discussed based on set-valued multivariate time series, and the interval-valued vector autoregressive model was built. Simulation study and real data analysis show the efficiency of the proposed model and approach.