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.

中文翻译：

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自适应时空自回归模型预测死亡率

准确的死亡率预测对于各种类型的人口研究（例如人口预测）和保险产品（例如养老金和年金）的定价都是必不可少的。最近的研究已经考虑了死亡率表面的时空自回归（STAR）模型，其中每个年龄的死亡率（暂时）取决于其历史值，（空间）取决于相邻年龄组的死亡率。该模型具有良好的统计属性，包括协整因变量和闭式解的存在。尽管与著名的Lee-Carter（LC）模型相比，它的预测性能有所提高，但只有相同和相邻队列的影响显着的约束可能会过于严格。在这项研究中，我们采用数据驱动的自适应加权结构，并提出了自适应STAR（ASTAR）模型。在保留1950-2016年英国，法国，意大利，西班牙和日本0至100岁年龄段的死亡率数据的情况下，我们的模型保留了STAR的所有理想功能，在预测准确性方面始终优于LC和STAR。被考虑。两次敏感性测试和其他仿真结果也得出了可靠的结论。因此，建议的ASTAR模型可以是在其他情况下用于建模和预测死亡率的广泛有用的工具，并且可以扩展到多人口建模。考虑了1950-2016年期间的西班牙和日本。两次敏感性测试和其他仿真结果也得出了可靠的结论。因此，建议的ASTAR模型可以是在其他情况下用于建模和预测死亡率的广泛有用的工具，并且可以扩展到多人口建模。考虑了1950-2016年期间的西班牙和日本。两次敏感性测试和其他仿真结果也得出了可靠的结论。因此，建议的ASTAR模型可以是在其他情况下用于建模和预测死亡率的广泛有用的工具，并且可以扩展到多人口建模。