Mortality Forecasting for Multiple Populations: An Augmented Common Factor Model with a Penalized Log-Likelihood

Abstract

Recently, the topic of multipopulation mortality forecasting has gained considerable attention among researchers and end-users. One of the most popular multipopulation mortality models is the augmented common factor (ACF) model. In spite of its popularity, the ACF model is subject to the limitation of producing mortality forecasts with a jagged pattern rather than a smooth relationship with age. In this article, we attempt to mitigate this problem by generalizing the work of Delwarde et al. [(2007). Smoothing the Lee–Carter and Poisson log-bilinear models for mortality forecasting a penalized log-likelihood approach. Statistical Modelling 7 (1), 29–48] to a multipopulation setting. The generalization involves smoothing parameters, one for the common trend and one for each of the np individual populations. The smoothing parameters are determined by using an extended leave-one-out cross-validation. We illustrate the proposed extension with real mortality data. It is found that compared to the original ACF model, the proposed extension produces mortality forecasts that are more reasonable, with less jagged patterns across ages.