Existing literature argues that the mortality rate of a specific age is affected not only by its own lags but by the lags of neighbouring ages, known as cohort effects. Although these effects are assumed constant in most studies, they can be dynamic over a long timespan. Consequently, popular mortality models with time-invariant age-dependent coefficients, including the Lee-Carter (LC) and vector autoregression (VAR) models, are incapable of modelling these dynamic cohort effects. To capture such dynamic patterns, we propose a time-varying coefficient spatial-temporal autoregressive (TVSTAR) model that allows for flexible time-dependent parameters. The proposed TVSTAR model is compatible with multi-population modelling and enjoys sound statistical properties. Using empirical results of mortality data from the United Kingdom (UK) and France over the period 1950–2016, we show that the TVSTAR model consistently outperforms the LC (Li-Lee, or LL) and the original STAR model under the single-population (multi-population) modelling framework. Finally, our empirical results suggest that cohort effects strengthen over time for very old ages in both the UK and France. Using simulation evidence, we argue that this observed upward trend can be caused by the overall advancement in the mortality evolution of the same cohort.

中文翻译：

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死亡率的动态建模和连贯预测：时变系数时空自回归方法

现有文献认为，特定年龄的死亡率不仅受其自身滞后的影响，还受到邻近年龄滞后的影响，称为队列效应。尽管在大多数研究中假设这些影响是恒定的，但它们在很长一段时间内可能是动态的。因此，具有时间不变的年龄相关系数的流行死亡率模型，包括 Lee-Carter (LC) 和向量自回归 (VAR) 模型，无法对这些动态队列效应进行建模。为了捕捉这种动态模式，我们提出了一种时变系数时空自回归 (TVSTAR) 模型，该模型允许灵活的时间相关参数。提议的 TVSTAR 模型与多群体建模兼容，并具有良好的统计特性。使用 1950 年至 2016 年期间英国（英国）和法国死亡率数据的实证结果，我们表明 TVSTAR 模型在单一人群下始终优于 LC（Li-Lee，或 LL）和原始 STAR 模型（多群体）建模框架。最后，我们的实证结果表明，英国和法国的高龄人群的队列效应会随着时间的推移而增强。使用模拟证据，我们认为这种观察到的上升趋势可能是由同一队列死亡率演变的整体进步引起的。我们的实证结果表明，英国和法国的高龄人群的队列效应会随着时间的推移而增强。使用模拟证据，我们认为这种观察到的上升趋势可能是由同一队列死亡率演变的整体进步引起的。我们的实证结果表明，英国和法国的高龄人群的队列效应会随着时间的推移而增强。使用模拟证据，我们认为这种观察到的上升趋势可能是由同一队列死亡率演变的整体进步引起的。