Multi-population modelling and forecasting life-table death counts

When modelling the age distribution of death counts for multiple populations, we should consider three features: (1) how to incorporate any possible correlation among multiple populations to improve point and interval forecast accuracy through multi-population joint modelling; (2) how to forecast age distribution of death counts so that the forecasts are non-negative and have a constrained integral; (3) how to construct a prediction interval that is well-calibrated in terms of coverage. Within the framework of compositional data analysis, we apply a log-ratio transform to transform a constrained space into an unconstrained space. We apply multivariate and multilevel functional time series methods to forecast period life-table death counts in the unconstrained space. Through the inverse log-ratio transformation, the forecast period life-table death counts are obtained. Using the age-specific period life-table death counts in England and Wales and Sweden obtained from the Human Mortality Database (2022), we investigate one-step-ahead to 30-step-ahead point and interval forecast accuracies of the proposed models and make our recommendations.