Multi-population mortality forecasting using tensor decomposition

Abstract

In this paper, weformulate the multi-population mortalityforecasting problem based on 3-way (age, year, and country/gender) decompositions. By applying the canonical polyadic decomposition (CPD) and the different forms of the Tucker decomposition to multi-population mortality data (10 European countries and 2 genders), we find that the out-of-sample forecasting performance is significantly improved both for individual populations and the aggregate population compared with using the single-population mortality model based on rank-1 singular value decomposition (SVD), or the Lee–Carter model. The results also shed lights on the similarity and difference of mortality among different countries. Additionally, we compare the variance-explained method and the out-of-sample validation method for rank (hyper-parameter) selection. Results show that the out-of-sample validation method is preferred for forecasting purposes.