Bias-corrected bootstrap prediction regions for vector autoregression

This paper examines small sample properties of alternative bias-corrected bootstrap prediction regions for the vector autoregressive (VAR) model. Bias-corrected bootstrap prediction regions are constructed by combining bias-correction of VAR parameter estimators with the bootstrap procedure. The backward VAR model is used to bootstrap VAR forecasts conditionally on past observations. Bootstrap prediction regions based on asymptotic bias-correction are compared with those based on bootstrap bias-correction. Monte Carlo simulation results indicate that bootstrap prediction regions based on asymptotic bias-correction show better small sample properties than those based on bootstrap bias-correction for nearly all cases considered. The former provide accurate coverage properties in most cases, while the latter over-estimate the future uncertainty. Overall, the percentile-t bootstrap prediction region based on asymptotic bias-correction is found to provide highly desirable small sample properties, outperforming its alternatives in nearly all cases.