A common feature in the modelling and extrapolation of the trends in mortality rates over time, based on fitted parametric structures, has tended to involve the treatment of a structured fitted main effects period component (with possibly a cohort component) as a random effects time series. In this paper, we follow the lead of Haberman and Renshaw (Insurance Math Econ 50:309–333, 2012) and other authors in modelling and forecasting mortality improvement rates over time, rather than mortality rates. In this context, we assume linear parametric structures for mortality improvement rates, and we examine the feasibility of modelling the main period effects (and possibly any cohort effects) as a random effect from the outset. We argue that this leads to a more unified approach to model fitting and extrapolation.

基于拟合的参数结构，对死亡率随时间的趋势进行建模和外推的一个共同特征是倾向于将结构化的拟合主效应期成分（可能包括队列成分）作为随机效应时间序列进行处理。在本文中，我们遵循Haberman和Renshaw（Insurance Math Econ 50：309–333，2012）和其他作者的模型，对随着时间推移而非死亡率的死亡率提高率进行建模和预测。在这种情况下，我们假设线性参数结构可提高死亡率，并从一开始就检验将主要时期效应（以及可能的任何队列效应）建模为随机效应的可行性。我们认为这导致了更统一的模型拟合和外推方法。