Forecasting Fertility Rates: A Functional Principal Components Approach

Alessandra Carioli, Netherlands Interdisciplinary Demographic Institute (NIDI) and University of Groningen
Leo van Wissen, Netherlands Interdisciplinary Demographic Institute (NIDI) and University of Groningen

The present paper aims to forecast sub-national Spanish fertility time series using Functional Principal Component Analysis. The data used in the forecast are time series of age specific fertility rates obtained using Census and Municipal Register data for the 50 Spanish provinces. The approach applies Time Series Forecasting using Functional Principal Component Analysis (Hyndman and Ullah, 2007; Hyndman and Booth, 2008). Fertility schedules are smoothed using (Ediev, 2013) to apply the principal component decomposition, which is used for the forecasting. The final results consist of forecasted Age Specific Fertility Schedules, Total Fertility Rates 15 years into the future and of the basis funtionas and coefficients deriving from principal components decomposition, which provide useful insights on tempo-quantum effects. The forecast has been applied at national level Spain and to various regions and provinces. Heterogeneity is present across the sub-national level as some regions and provinces show a diverging increasing trend.