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

TL;DR

This paper introduces a weighted compositional functional data analysis method for modeling and forecasting age-specific life-table death counts, emphasizing recent data to improve short-term forecast accuracy.

Contribution

It extends compositional functional data analysis by incorporating weights for recent data, enhancing forecasting accuracy for life-table death counts under constraints.

Findings

Weighted method outperforms unweighted in forecast accuracy

Improved short-term point and interval forecasts

Method applicable to constrained compositional data

Abstract

Age-specific life-table death counts observed over time are examples of densities. Non-negativity 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 to 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.