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

2025-10-27

AI Summary

This paper addresses the modeling and forecasting of age-specific life table death counts—nonnegative, additive, and temporally structured density data. Methodologically, it proposes a weighted compositional functional data analysis framework: first, the centered log-ratio (clr) transformation maps the constrained density data into an unconstrained Euclidean space; second, a time-decay weighting scheme is introduced to emphasize recent observations in both functional principal component analysis and weighted least-squares fitting, yielding a tunable, time-aware modeling pipeline. Evaluated on Swedish mortality data from 1751 to 2020, the framework significantly improves short-term point forecast accuracy and predictive interval coverage compared to conventional unweighted approaches. By delivering more robust density manifold forecasts, it enhances actuarial applications such as annuity pricing and reserve valuation.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Feature Construction/Reformulation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Modeling life-table death counts with compositional constraints
• Forecasting mortality using weighted recent data
• Improving accuracy for annuity pricing and reserves

Innovation

• Weighted compositional functional data analysis
• Assigns higher weights to recent data
• Centered log-ratio transformation handles constraints