BUREAU OF THE CENSUS STATISTICAL RESEARCH DIVISION REPORT SERIES SRD Research Report Number: CENSUS/SRD/RR-88/20 CALCULATION OF THE VARIANCE OF POPULATION FORECASTS

In this paper we propose a recursive method for forecasting populations and calculating the uncertainty in the estimate. In a recent survey paper Land (1986) discusses three widely used classes of methods for national population forecasts. They are demographic accounting equations, statistical time series, and structural modeling methods. This paper combines the first two of these techniques. An advantage of the time series approach is that forecast variances can be derived. * In this paper we assume that time series methods have been use&to model and to forecast fertility, survival, and migration rates. Either univariate (Box and Jenkins, 1970) or multivariate (Tiao and Box, 1981) autoregressiic-integrated-moving average (ARIMA) time series models could tx employed. Assuming that means and vari.tnces have been calculated for future values of the fertility, mortality, and migration series this paper shows how to use the accounting equations to calculate the mean and the variance of future populations.