State space models for estimating and forecasting fertility

We introduce multivariate state space models for estimating and forecasting fertility rates that are dynamic alternatives to logistic representations for fixed time points. Strategies are provided for the Kalman filter and for quasi-Newton algorithm initialization, that assure the convergence of the iterative fitting process. The broad impact of the new methodology in practice is shown using data series from Spain, Sweden and Australia, and by comparing the results with a recent approach based on functional data analysis and also with official forecasts. Very satisfactory short- and medium-term forecasts are obtained. Besides this, the new modeling proposal provides practitioners with several suitable interpretative tools, and the application here is an interesting example of the usefulness of the state space representation in modelling real multivariate processes.