Mortality forecasting using the four-way CANDECOMP/PARAFAC decomposition

To design appropriate pension or insurance plans it is crucial to understand mortality heterogeneity across demographic features, such as age, gender, and country. To this aim, we propose a coherent mortality forecasting methodology, which leverages the four-way CANDECOMP/PARAFAC and Vector-Error Correction models. We examine how age groups, years, countries, and gender impact target variables, namely log-centered mortality rates and compositional transformation of mortality data using the Human Mortality Database. The CANDECOMP/PARAFAC model synthesizes the behavior of the target variables through a few latent components and highlights the evolution of the temporal patterns. These patterns are employed to forecast future trajectories of mortality with Vector-Error Correction models, which account for the non-stationarity of the series. We carry out Monte Carlo simulations to obtain the distributions of the time component over the forecasted period 2001-2015, and we evaluate the goodness of the prediction by computing the Root Mean Square Error and the Mean Absolute Error. Our analysis underlines that understanding mortality dynamics in a high-dimensional framework is crucial for demographic assessments and could help design appropriate pension plans that mitigate the burden of increased longevity. The paper provides two steps further on methodological developments in the field of mortality analysis and forecasting in a high-dimensional space by (i) offering a comprehensive picture of mortality data through the four-way decomposition and (ii) designing appropriate forecasting of mortality data which relies on the projection of the temporal component through Vector-Error Correction models.