Mortality Forecasting using Factor Models: Time-varying or Time-invariant Factor Loadings?

TL;DR

This paper introduces a time-varying factor model for mortality forecasting, extending classical models by allowing factor loadings to change over time, which improves prediction accuracy across different countries and horizons.

Contribution

The paper develops a novel time-varying factor model for mortality data, proposes two forecasting methods, and introduces a change point analysis for optimal short- and long-term predictions.

Findings

Time-varying factor model better captures empirical data features.

Improved mortality forecasting accuracy across countries.

Change point analysis effectively distinguishes short- and long-term horizons.

Abstract

Many existing mortality models follow the framework of classical factor models, such as the Lee-Carter model and its variants. Latent common factors in factor models are defined as time-related mortality indices (such as $\kappa_t$ in the Lee-Carter model). Factor loadings, which capture the linear relationship between age variables and latent common factors (such as $\beta_x$ in the Lee-Carter model), are assumed to be time-invariant in the classical framework. This assumption is usually too restrictive in reality as mortality datasets typically span a long period of time. Driving forces such as medical improvement of certain diseases, environmental changes and technological progress may significantly influence the relationship of different variables. In this paper, we first develop a factor model with time-varying factor loadings (time-varying factor model) as an extension of the classical factor model for mortality modelling. Two forecasting methods to extrapolate the factor loadings, the local regression method and the naive method, are proposed for the time-varying factor model. From the empirical data analysis, we find that the new model can capture the empirical feature of time-varying factor loadings and improve mortality forecasting over different horizons and countries. Further, we propose a novel approach based on change point analysis to estimate the optimal `boundary' between short-term and long-term forecasting, which is favoured by the local linear regression and naive method, respectively. Additionally, simulation studies are provided to show the performance of the time-varying factor model under various scenarios.