  The bootstrap procedure has emerged as a general framework to construct
prediction intervals for future observations in autoregressive time series
models. Such models with outlying data points are standard in real data
applications, especially in the field of econometrics. These outlying data
points tend to produce high forecast errors, which reduce the forecasting
performances of the existing bootstrap prediction intervals calculated based on
non-robust estimators. In the univariate and multivariate autoregressive time
series, we propose a robust bootstrap algorithm for constructing prediction
intervals and forecast regions. The proposed procedure is based on the weighted
likelihood estimates and weighted residuals. Its finite sample properties are
examined via a series of Monte Carlo studies and two empirical data examples.
