Background: For commonly used mortality models, the existing estimates change with the recalibration of new data. This issue is also known as the lack of the new-data-invariant property. Objective: We adapt the Lee–Carter, age-period-cohort, Renshaw–Haberman, and Li–Lee models to achieve the new-data-invariant property. The resulting fitted or forecast mortality indexes are tractable and comparable when more recent data are modelled. Methods: Illustrated by mortality rates of the England and Wales populations, we explore the tradeoff between goodness of fit and the new-data-invariant property. Using the adapted model and vector autoregressive framework, we explore the interdependencies of subregional mortality dynamics in the United Kingdom. Results: To compare the goodness of fit, we consider the four adapted models and the Cairns– Blake–Dowd model, which are invariant to new data without adaptation. The Renshaw– Haberman model is demonstrated to be the best-performing model. The in-sample and backtesting results show that the proposed adaptation introduces only a small cost of reduced model fitting, which is robust across sensitivity analyses. Conclusions: The adapted Renshaw–Haberman model is recommended to construct tractable mortality indexes. Contribution: From a methodological perspective, we adopt popular models to achieve a desirable newdata-invariant property. Our empirical results suggest that the adapted model can provide reliable forecast of mortality rates for use in demographic research.

中文翻译：

---

额外年份死亡率数据到来时的死亡率建模：校准和预测（作者：Kenny Kam Kuen Mok、Chong It Tan、Yanlin Shi、Jinhui Zhang）

背景：对于常用的死亡率模型，现有的估计会随着新数据的重新校准而变化。此问题也称为缺乏新数据不变属性。目标：我们采用 Lee-Carter、age-period-cohort、Renshaw-Haberman 和 Li-Lee 模型来实现新数据不变属性。当对更新的数据进行建模时，所得的拟合或预测死亡率指数易于处理且具有可比性。方法：以英格兰和威尔士人口的死亡率为例，我们探讨了拟合优度与新数据不变属性之间的权衡。使用适应的模型和向量自回归框架，我们探索了英国次区域死亡率动态的相互依赖性。结果：为了比较拟合优度，我们考虑了四种适应模型和 Cairns-Blake-Dowd 模型，它们在不适应的情况下对新数据具有不变性。 Renshaw-Haberman 模型被证明是性能最好的模型。样本内和回测结果表明，所提出的调整仅引入了减少模型拟合的很小成本，这在敏感性分析中是稳健的。结论：建议采用改编后的伦肖-哈伯曼模型来构建易于处理的死亡率指数。贡献：从方法论的角度来看，我们采用流行的模型来实现理想的新数据不变性。我们的实证结果表明，改编后的模型可以为人口研究中使用的死亡率提供可靠的预测。