Clustering-based simultaneous forecasting of life expectancy time series through Long-Short Term Memory Neural Networks

In this paper, we apply a functional clustering method to the multivariate time series of life expectancy at birth of the female populations collected in the Human Mortality Database. We reconstruct the functional form of life expectancy from the available discrete observations and derive the curves through non-parametric smoothing. Once the clustering is realized, we perform the life expectancy simultaneous forecasting of the countries inside each cluster implementing a multivariate Long-Short Term Memory neural network. Although functional clustering has already been used in the actuarial literature, in this work it is applied for the first time to the study of life expectancy. The originality of the work also lies in the combination of a functional clustering approach with simultaneous forecasting obtained through the Long-Short Term Memory. We point out that such a combination provides a more informative outlook of the evolution of life expectancy, allowing us to depict country-specific longevity consistently with acknowledged mortality profiles. The results show that the evolution of developed countries follows a homogeneous pattern and supports the persisting homogeneity within the high longevity cluster over time. Moreover, we find a remarkable cross-country heterogeneity in the medium-low longevity cluster. By exploiting the cluster information, we improve the simultaneous forecasting of life expectancy time series using Long Short Term Memory neural networks and compare the error forecast of our approach with those of the classical VAR model, showing a better performance of the former when considering the cluster average errors.