A multilevel functional data method for forecasting population, with an application to the United Kingdom

Cohort component models are often used to model the evolution of an age-specific population, and are particularly useful for highlighting the demographic component that contributes the most to the population change. Recently, most of the attention has been devoted to the estimation of four specific demographic components, namely mortality, fertility, emigration and immigration. Many methods take a deterministic viewpoint, which can be quite restrictive in practice. The statistical method that we propose is a multilevel functional data method, where both mortality and migration are modelled and forecast jointly for females and males. The forecast uncertainty associated with each component is incorporated through parametric bootstrapping. Using the historical data for the United Kingdom from 1975 to 2009, we found that the proposed method shows a good in-sample forecast accuracy for the holdout data between 2001 and 2009. Moreover, we produce out-of-sample population forecasts from 2010 to 2030, and compare our forecasts with those produced by the Office for National Statistics.