The existence of long memory in mortality data improves the understandings of features of mortality data and provides a new approach for establishing mortality models. The findings of long-memory phenomena in mortality data motivate us to develop new mortality models by extending the Lee–Carter (LC) model to death counts and incorporating long-memory model structure. Furthermore, there are no identification issues arising in the proposed model class. Hence, the constraints which cause many computational issues in LC models are removed. The models are applied to analyse mortality death count data sets from three different countries divided according to genders. Bayesian inference with various selection criteria is applied to perform the model parameter estimation and mortality rate forecasting. Results show that multivariate long-memory mortality model with long-memory cohort effect model outperforms multivariate extended LC cohort model in both in-sample fitting and out-sample forecast. Increasing the accuracy of forecasting of mortality rates and improving the projection of life expectancy is an important consideration for insurance companies and governments since misleading predictions may result in insufficient funds for retirement and pension plans.

中文翻译：

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多元长记忆群组死亡率模型

死亡率数据中长记忆的存在增进了对死亡率数据特征的理解，并为建立死亡率模型提供了一种新方法。死亡率数据中长记忆现象的发现促使我们通过将Lee-Carter（LC）模型扩展到死亡计数并结合长记忆模型结构来开发新的死亡率模型。此外，在建议的模型类别中没有出现识别问题。因此，消除了导致LC模型中许多计算问题的约束。该模型用于分析来自三个不同国家（按性别划分）的死亡率死亡计数数据集。应用各种选择标准的贝叶斯推断来执行模型参数估计和死亡率预测。结果表明，在样本内拟合和样本外预测方面，具有长记忆群效应模型的多变量长记忆死亡率模型优于多元扩展LC群组模型。对于保险公司和政府而言，提高死亡率的预测准确性和改善预期寿命的预测是重要的考虑因素，因为误导性的预测可能会导致退休和养老金计划的资金不足。