Stochastic population forecasting using functional data methods: the case of France

Heather Booth, Australian National University
Sophie Pennec, Institut National d'Études Démographiques (INED)
Rob Hyndman, Monash University

A probabilistic age-sex-specific population forecast for France is derived through stochastic population renewal using forecasts of mortality, fertility and net migration. Functional data models with time series coefficients are used to model age-specific mortality and fertility rates; the coefficients are forecast using time series methods. In the absence of reliable migration data, age-sex-specific net migration is estimated using the demographic growth-balance equation. This estimate, which includes error, is similarly modelled and forecast. Uncertainty is estimated from each model, with an adjustment to ensure that the one-step-forecast variances are equal to those obtained with historical data. The three models are then used in a Monte Carlo simulation of future fertility, mortality and net migration, which are combined using the cohort-component method to obtain age-specific forecasts of the population by sex. The distribution of the forecasts provides probabilistic prediction intervals. The results are compared with official population projections based on scenarios.