Empirical simultaneous prediction regions for path-forecasts

This paper investigates the problem of constructing prediction regions for forecast trajectories 1 to H periods into the future—a path forecast. When the null model is only approximative, or completely unavailable, one cannot either derive the usual analytic expressions or resample from the null model. In this context, this paper derives a method for constructing approximate rectangular regions for simultaneous probability coverage that correct for serial correlation in the case of elliptical distributions. In both Monte Carlo studies and an empirical application to the Greenbook path-forecasts of growth and inflation, the performance of this method is compared to the performances of the Bonferroni approach and the approach which ignores simultaneity.