Ridge estimation of uncertain vector autoregressive model with imprecise data

Uncertain vector autoregressive model (UVAR) is used to describe the variational relationship between multivariable time series. Based on the imprecise observations, the issue of predicting the future data accurately attracts more and more scholars attentions. This paper takes the ridge estimation into consideration and applies it into uncertain vector autoregressive model. In order to determine the shrinkage parameter, we use the cross-validation to solve this problem. On this basis, we conduct the residual analysis. A point estimation and a confidence interval are given to predict the future value. Finally, two numerical examples are applyied to clarify the feasibility and validity of the ridge estimation, compared with the least square estimation.