Stochastic Period and Cohort Effect State-Space Mortality Models Incorporating Demographic Factors via Probabilistic Robust Principal Components

Abstract

In this study we develop a multi-factor extension of the family of Lee-Carter stochastic mortality models. We build upon the time, period and cohort stochastic model structure to extend it to include exogenous observable demographic features that can be used as additional factors to improve model fit and forecasting accuracy. We develop a dimension reduction feature extraction framework which (a) employs projection based techniques of dimensionality reduction; in doing this we also develop (b) a robust feature extraction framework that is amenable to different structures of demographic data; (c) we analyse demographic data sets from the patterns of missingness and the impact of such missingness on the feature extraction, and (d) introduce a class of multi-factor stochastic mortality models incorporating time, period, cohort and demographic features, which we develop within a Bayesian state-space estimation framework; finally (e) we develop an efficient combined Markov chain and filtering framework for sampling the posterior and forecasting. We undertake a detailed case study on the Human Mortality Database demographic data from European countries and we use the extracted features to better explain the term structure of mortality in the UK over time for male and female populations when compared to a pure Lee-Carter stochastic mortality model, demonstrating our feature extraction framework and consequent multi-factor mortality model improves both in sample fit and importantly out-off sample mortality forecasts by a non-trivial gain in performance.

Keywords

• mortality modelling
• cohort models
• factor models
• state-space models
• Bayesian inference
• Markov chain Monte Carlo
• features extraction
• robust dimensionality reduction