Comparing several methods to compute joint prediction regions for path forecasts generated by vector autoregressions

Path forecasts, defined as sequences of individual forecasts, generated by vector autoregressions are widely used in applied work. It has been recognized that a profound econometric analysis often requires, besides the path forecast, a joint prediction region that contains the whole future path with a prespecified coverage probability. The forecasting literature offers several different methods for computing joint prediction regions, where the existing methods are either bootstrap based or rely on asymptotic results. The aim of this paper is to investigate the finite-sample performance of three methods for constructing joint prediction regions in various scenarios via Monte Carlo simulations.