Bootstrap prediction intervals for single period regression forecasts

The prediction interval formula for the forecast of a regression-dependent variable conditional upon known future values for the independent variables and normally distributed disturbances is commonly taught and used. This pedagogic note illustrates how badly this standard formula can fail when the disturbances are nonnormal, with the degree of failure increasing rather than decreasing with sample size. A small Monte Carlo experiment emphasizes the point for some asymmetric distributions and some seldom-tried symmetric distributions and shows how poorly the standard formula performs, even in large samples. Bootstrap prediction intervals based on either the percentile principle or the percentile-t principle perform substantially better.