Five different distributions for the Lee–Carter model of mortality forecasting: A comparison using GAS models

Abstract

This paper extends the well-known Lee–Carter model used for forecasting mortality rates by utilizing a new class of time series models, known as Generalized Autoregressive Score (GAS) or Dynamic Conditional Score (DCS) models. This framework can be used to derive a wide range of non-Gaussian time series models with time varying coefficients and has shown to be very successful in financial applications. In this paper we propose five probability models (Poisson, binomial, negative binomial, Gaussian and beta) based on the GAS framework to estimate the Lee–Carter parameters and dynamically forecast the mortality rates using a single unified step. The models are applied to the mortality rates time series for the male population of the United States, Sweden, Japan and the UK. Diagnostic tests are performed on quantile residuals, model selection is made via AIC and predictive accuracy of the models is compared using the Diebold–Mariano test. We conclude that, amongst the proposed models, the negative binomial extension of the Lee–Carter model is the most appropriate for forecasting mortality rates.