Sampling Distributions of Post-Sample Forecasting Errors

Abstract

Forecasting errors fall in two clearly different categories: (a) the residual errors from fitting a model to the available data and (b) the post-sample forecasting errors. The emphasis of statistical theory and forecasting methodology has been on model fitting errors, even though the greatest concern in applied work should be with post-sample errors. The purpose of this paper is to investigate empirically sampling distributions of post-sample forecasting errors. The characteristics of such distributions are studied and compared with characteristics of distributions of model fitting errors. The discrepancies between characteristics of model fitting and post-sample errors are quite large and somewhat variable.