ZHONG Yu, LI Shoumei, ZHANG Lei. Set-valued and Interval-valued Multivariate Time Series[J]. Journal of Beijing University of Technology, 2020, 46(2): 208-216. DOI: 10.11936/bjutxb2019030021
    Citation: ZHONG Yu, LI Shoumei, ZHANG Lei. Set-valued and Interval-valued Multivariate Time Series[J]. Journal of Beijing University of Technology, 2020, 46(2): 208-216. DOI: 10.11936/bjutxb2019030021

    Set-valued and Interval-valued Multivariate Time Series

    • 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.
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