Weighted compositional functional data analysis for modeling and forecasting life‐table death counts

Abstract

Age‐specific life‐table death counts observed over time are examples of densities. Nonnegativity and summability are constraints that sometimes require modifications of standard linear statistical methods. The centered log‐ratio transformation presents a mapping from a constrained to a less constrained space. With a time series of densities, forecasts are more relevant to the recent data than the data from the distant past. We introduce a weighted compositional functional data analysis for modeling and forecasting life‐table death counts. Our extension assigns higher weights to more recent data and provides a modeling scheme easily adapted for constraints. We illustrate our method using age‐specific Swedish life‐table death counts from 1751 to 2020. Compared with their unweighted counterparts, the weighted compositional data analytic method improves short‐term point and interval forecast accuracies. The improved forecast accuracy could help actuaries improve the pricing of annuities and setting of reserves.