Forecasting fertility by age and birth order using time series from the Human Fertility Database

Han Lin Shang, Australian National University
Alessandra Carioli, University of Southampton
Guy J. Abel, Asian Demographic Research Institute

This article presents a comparison of two approaches in forecasting total fertility, age specific fertility, and birth order age specific fertility rates. We employ an auto-arima and a functional time series robust forecasting model to project fertility for 23 countries using the Human Fertility Database time series. The comparison of the two models aim at demonstrating the advantages of forecasting both age specific rates as opposed to the common practice of simply forecasting total rates. We use a functional principal components analysis to project smoothed age-specific fertility rates in the short run (15 years). We compare the empirical accuracy of the approach by Hyndman and Ullah (2007) to auto-arima forecasts and we validate our results through the one-step-ahead to 20-step-ahead forecast error measures (MFE and MAFE).