Validation, probability-weighted priors, and information in stochastic forecasts
This paper addresses issues that arise in evaluating, making, and using stochastic forecasts of future fertility in the United States. We begin with Lee's ARMA model which leads to prediction intervals that are more realistic and informative than point-wise forecasts or traditional scenario methods. The roles of historical information and expert judgment are analyzed in terms of their effects upon prediction uncertainty. Validation experiments suggest that the model performs well in characterizing the uncertainty of the US fertility experience. We argue that the long-run average of fertility, a key assumption of the model, operates on a time scale not probed by time-series methods and we use Bayesian priors to quantify the additional prediction uncertainty that comes from making the long-run fertility assumption.