Exact joint forecast regions for vector autoregressive models

Assume that a ii-element vector time series follows a vector autoregressive (VAR) model. Obtaining simultaneous forecasts of the k elements of the vector time series is an important problem. Based on the Bonferroni inequality, Lutkepohl (1991) derived the procedures which construct the conservative joint forecast regions for the VAR model. In this paper, we propose to use an exact method which provides shorter predict ion intervals than does the Bonferroni method. Three illustrative examples are given for comparison of the various VAR forecasting procedures.