Precision, bias, and uncertainty for state population forecasts: an exploratory analysis of time series models

Abstract

Many researchers have used time series models to construct population forecasts and prediction intervals at the national level, but few have evaluated the accuracy of their forecasts or the out-of-sample validity of their prediction intervals. Fewer still have developed models for subnational areas. In this study, we develop and evaluate six ARIMA time series models for states in the United States. Using annual population estimates from 1900 to 2000 and a variety of launch years, base periods, and forecast horizons, we construct population forecasts for four states chosen to reflect a range of population size and growth rate characteristics. We compare these forecasts with population counts for the corresponding years and find precision, bias, and the width of prediction intervals to vary by state, launch year, model specification, base period, and forecast horizon. Furthermore, we find that prediction intervals based on some ARIMA models provide relatively accurate forecasts of the distribution of future population counts but prediction intervals based on other models do not. We conclude that there is some basis for optimism regarding the possibility that ARIMA models might be able to produce realistic prediction intervals to accompany population forecasts, but a great deal of work remains to be done before we can draw any firm conclusions.