The Practical Specification of the Expected Error of Population Forecasts
Abstract: Forecasts of future population are uncertain, but the language of probability theory can be used to give the forecast users a realistic indication of their ex ante uncertainty. Knowing the magnitude of the expected error allows the users to prepare for contingencies they might otherwise neglect. The commonly offered high and low forecast variants fail to do the same because the users have no idea of how extreme they are. The purpose of this article is to review the central concepts needed in the analysis of uncertainty, and to present some approaches that are now available for the practical computation of the prediction intervals. Methods of constructing prediction intervals include the application of formal timeseries methods to past data, data analytic methods such as naive forecasting, analysis of ex post error of past forecasts, and subjective or judgmental analysis of error. Examples of each are given. In particular, we will comment on the compatibility of the results with our prior knowledge of the vital processes. In the probabilistic handling of the ex ante error we must be able to combine nonlinearly the different sources of error without making unrealistic correlational assumptions, such as the (implicit) perfect correlation assumption of most national forecasts. These propagation of error calculations can be carried out either using analytic Taylorseries approximations or via simulation. We present empirical data on the forecast errors of mortality and fertility to motivate a simplified model that is suited to the programming of these vital rates and their errors with the presentday computational resources. Keywords: Demography; forecasting; population projections; propagation of error.
