Random cohort effects and smooth structures for mortality modelling and forecasting: A mixed-effects Gaussian process time series approach

The issue of population ageing has become a critical challenge for many developed nations in recent decades, and urgent action is needed to address this concern. Despite numerous efforts have been made to tackle the risks associated with increased longevity, the problem remains unresolved. The Cairns-Blake-Dowd (CBD) model, widely recognised as a leading approach for mortality modelling at older ages, incorporates cohort effects parameters into its parsimonious design. This article proposes a new mixed-effects Gaussian process time series approach that not only considers random cohort effects but also ensures smoothness across age ranges. By adopting Gaussian process, this novelty allows the proposed method naturally accounts for all uncertainties of the estimated parameters without requiring any pre-specified constraints and provides more accurate results. Through two empirical applications using male and female mortality data, we demonstrate the exceptional capabilities of our approach, which outperforms the CBD models with cohorts in short-, mid-, and long-term forecasting of mortality rates from various developed countries. Our proposed approach offers a significant improvement in forecast accuracy and shows a valuable contribution to the field of cohort mortality modelling.