It is well known that accurate forecasts of mortality rates are essential to various demographic research topics, such as population projections and the pricing of insurance products such as pensions and annuities. In this study, we argue that including the lagged rates of neighbouring ages cannot further improve mortality forecasting after allowing for autocorrelations. This is because the sample cross-correlation function cannot exhibit meaningful and statistically significant correlations. In other words, rates of neighbouring ages are usually not leading indicators in mortality forecasting. Therefore, multivariate stochastic mortality models like the classic Lee–Carter may not necessarily lead to more accurate forecasts, compared with sophisticated univariate models. Using Australian mortality data, simulation and empirical studies employing the Lee–Carter, Functional Data, Vector Autoregression, Autoregression-Autoregressive Conditional Heteroskedasticity and exponential smoothing (ETS) state space models are performed. Results suggest that ETS models consistently outperform the others in terms of forecasting accuracy. This conclusion holds for both female and male mortality data with different empirical features across various forecasting error measurements. Hence, ETS can be a widely useful tool to model and forecast mortality rates in actuarial practice.

中文翻译：

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预测死亡率：多变量或单变量模型？

众所周知，准确的死亡率预测对于各种人口统计学研究主题都是至关重要的，例如人口预测和养老金和年金等保险产品的定价。在这项研究中，我们认为，考虑到自相关后，包括邻近年龄的滞后率不能进一步改善死亡率预测。这是因为样本互相关函数无法显示有意义且统计上显着的相关。换句话说，邻近年龄的比率通常不是死亡率预测的主要指标。因此，与复杂的单变量模型相比，经典的Lee-Carter等多变量随机死亡率模型不一定会导致更准确的预测。利用澳大利亚的死亡率数据，使用Lee-Carter进行模拟和经验研究，功能数据，矢量自回归，自回归-自回归条件异方差和指数平滑（ETS）状态空间模型。结果表明，ETS模型在预测准确性方面始终优于其他模型。这一结论适用于在各种预测误差测量中具有不同经验特征的男女死亡率数据。因此，ETS可以成为在精算实践中建模和预测死亡率的广泛有用的工具。这一结论适用于在各种预测误差测量中具有不同经验特征的男女死亡率数据。因此，ETS可以成为在精算实践中建模和预测死亡率的广泛有用的工具。这一结论适用于在各种预测误差测量中具有不同经验特征的男女死亡率数据。因此，ETS可以成为在精算实践中建模和预测死亡率的广泛有用的工具。