Modelling Monthly Births and Deaths Using Seasonal Forecasting Methods as an Input for Population Estimates

Abstract

Forecasts of monthly births and deaths are a critical input when computing monthly estimates of a resident population because they determine, together with international net migration, the dynamics of both the population size and its age distribution. Empirical time series data for births and deaths exhibits strong evidence of seasonality patterns at both national and subnational levels. In this paper, we evaluate the forecasting performance of alternative linear and non-linear time series methods (i.e., seasonal ARIMA, Holt-Winters, and State Space models) to death and birth monthly forecasting at the sub-national level. Additionally, we investigate how well the models perform, in terms of predicting the uncertainty of future monthly birth and death counts. We use the series of monthly death and birth data from 2000 to 2018, disaggregated by sex for the 25 Portuguese NUTS3 regions, to compare the model’s short-term (i.e., 1-year) forecasting accuracy, using a backtesting time series cross-validation approach. Our results provide valuable insights, regarding the forecasting performance of alternative time series models, in small population forecasting exercises and on the validity of using such models as predictors of population forecast uncertainty.