Forecasting mortality rates with the adaptive spatial temporal autoregressive model

Accurate forecasts of mortality rates are essential to various types of demographic research such as population projection, and the pricing of insurance products such as pensions and annuities. Recent studies have considered a spatial temporal autoregressive (STAR) model for the mortality surface, where mortality rates for each age depend (temporally) on their historical values as well as (spatiality) on those of neighboring age cohorts. This model has sound statistical properties including cointegrated dependent variables and the existence of closed-form solutions. Despite its improved forecasting performance over the famous Lee–Carter (LC) model, the constraint that only the effects of the same and neighboring cohorts are significant can be too restrictive. In this study, we adopt a data-driven adaptive weighted structure and propose the adaptive STAR (ASTAR) model. Retaining all the desirable features of the STAR, our model uniformly outperforms the LC and STAR counterparts in terms of forecasting accuracy, when mortality data for ages 0–100 from the UK, France, Italy, Spain, and Japan over the period 1950–2016 are considered. Two sensitivity tests and additional simulation results also lead to robust conclusions. The proposed ASTAR model could therefore be a widely useful tool for modeling and forecasting mortality rates in other contexts, and may be extended to multipopulation modeling.