Confidence intervals: An empirical investigation of the series in the M-competition

Abstract

This paper empirically evaluates the uncertainty of forecasts. It does so using the 1001 series of the M-Competition. The study indicates that although, in model fitting the percentage of observations outside the confidence intervals is close to that postulated theoretically, this is not true for forecasting. In the latter case the percentage of observations outside the confidence intervals is much higher than that postulated theoretically. This is so for the great majority of series, forecasting horizonts, and methods. In addition to evaluating the extent of uncertainty, we provide tables to help users to construct more realistic confidence intervals for their forecasts.