Bootstrap prediction regions for multivariate autoregressive processes

Two new methods for improving prediction regions in the context of vector autoregressive (VAR) models are proposed. These methods, which are based on the bootstrap technique, take into account the uncertainty associated with the estimation of the model order and parameters. In particular, by exploiting an independence property of the prediction error, we will introduce a bootstrap procedure that allows for better estimates of the forecasting distribution, in the sense that the variability of its quantile estimators is substantially reduced, without requiring additional bootstrap replications. The proposed methods have a good performance even if the disturbances distribution is not Gaussian. An application to a real data set is presented.