State space models for estimating and forecasting fertility

Abstract

We introduce multivariate State-Space Models to estimate and forecast fertility rates that are dynamic alternatives to logistic representations for fixed time points. Strategies for Kalman filter initialization and convergence of likelihood optimization are provided. The broad impact of the new methodology in practice is proven using data series from Spain, Sweden and Australia and comparing the results with a recent approach based on Functional Data analysis and with official forecasts. Very satisfactory short and medium term forecasts are obtained. Besides, the new modeling proposal provides practitioners with several suitable interpretative tools and this application is one interesting example that shows the usefulness of the State-Space representation to model a real multivariate process.