Mortality projection and forecasting of life expectancy are two important aspects of the study of demography and life insurance modelling. We demonstrate in this work the existence of long memory in mortality data. Furthermore, models incorporating long memory structure provide a new approach to enhance mortality forecasts in terms of accuracy and reliability, which can improve the understanding of mortality. Novel mortality models are developed by extending the Lee–Carter (LC) model for death counts to incorporate a long memory time series structure. To link our extensions to existing actuarial work, we detail the relationship between the classical models of death counts developed under a Generalised Linear Model (GLM) formulation and the extensions we propose that are developed under an extension to the GLM framework known in time series literature as the Generalised Linear Autoregressive Moving Average (GLARMA) regression models. Bayesian inference is applied to estimate the model parameters. The Deviance Information Criterion (DIC) is evaluated to select between different LC model extensions of our proposed models in terms of both in-sample fits and out-of-sample forecasts performance. Furthermore, we compare our new models against existing models structures proposed in the literature when applied to the analysis of death count data sets from 16 countries divided according to genders and age groups. Estimates of mortality rates are applied to calculate life expectancies when constructing life tables. By comparing different life expectancy estimates, results show the LC model without the long memory component may provide underestimates of life expectancy, while the long memory model structure extensions reduce this effect. In summary, it is valuable to investigate how the long memory feature in mortality influences life expectancies in the construction of life tables.

中文翻译：

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用于生命表估计的长记忆死亡率模型：综合分析

死亡率预测和预期寿命预测是人口学和人寿保险建模研究的两个重要方面。我们在这项工作中证明了死亡率数据中存在长记忆。此外，结合长记忆结构的模型为提高死亡率预测的准确性和可靠性提供了一种新方法，可以提高对死亡率的理解。通过扩展 Lee-Carter (LC) 死亡计数模型以结合长记忆时间序列结构，开发了新的死亡率模型。要将我们的扩展与现有的精算工作联系起来，我们详细介绍了在广义线性模型 (GLM) 公式下开发的经典死亡人数模型与我们提出的扩展之间的关系，这些扩展是在时间序列文献中称为广义线性自回归移动平均 (GARMA) 的 GLM 框架的扩展下开发的) 回归模型。贝叶斯推理用于估计模型参数。评估偏差信息准则 (DIC)，以根据样本内拟合和样本外预测性能在我们提出的模型的不同 LC 模型扩展之间进行选择。此外，我们将我们的新模型与文献中提出的现有模型结构进行比较，以分析根据性别和年龄组划分的 16 个国家的死亡人数数据集。在构建生命表时，应用死亡率估计值来计算预期寿命。通过比较不同的预期寿命估计，结果表明没有长记忆组件的 LC 模型可能会低估预期寿命，而长记忆模型结构扩展会降低这种影响。总之，研究死亡率中的长记忆特征如何影响生命表构建中的预期寿命是有价值的。