Interval forecasts and parameter uncertainty

Forecast intervals generalize point forecasts to represent and incorporate uncertainty. Forecast intervals calculated from dynamic models typically sidestep the issue of parameter estimation. This paper shows how to construct asymptotic forecast intervals which incorporate the uncertainty due to parameter estimation. Our proposed solution is a simple proportional adjustment to the interval endpoints, the adjustment factor depending on the asymptotic variance of the interval estimates. Our analysis is in the context of a forecasting equation with an error independent of the forecasting variables but with unknown distribution. The methods are illustrated with a simulation experiment and an application to the US monthly unemployment rate.