This paper investigates a high-dimensional vector-autoregressive (VAR) model in mortality modeling and forecasting. We propose an extension of the sparse VAR (SVAR) model fitted on the log-mortality improvements, which we name “spatially penalized smoothed VAR” (SSVAR). By adaptively penalizing the coefficients based on the distances between ages, SSVAR not only allows a flexible data-driven sparsity structure of the coefficient matrix but simultaneously ensures interpretable coefficients including cohort effects. Moreover, by incorporating the smoothness penalties, divergence in forecast mortality rates of neighboring ages is largely reduced, compared with the existing SVAR model. A novel estimation approach that uses the accelerated proximal gradient algorithm is proposed to solve SSVAR efficiently. Similarly, we propose estimating the precision matrix of the residuals using a spatially penalized graphical Lasso to further study the dependency structure of the residuals. Using the UK and France population data, we demonstrate that the SSVAR model consistently outperforms the famous Lee–Carter, Hyndman–Ullah, and two VAR-type models in forecasting accuracy. Finally, we discuss the extension of the SSVAR model to multi-population mortality forecasting with an illustrative example that demonstrates its superiority in forecasting over existing approaches.

中文翻译：

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使用空间惩罚平滑 VAR 模型的死亡率预测

本文研究了死亡率建模和预测中的高维向量自回归 (VAR) 模型。我们提出了对数死亡率改进拟合的稀疏 VAR（SVAR）模型的扩展，我们将其命名为“空间惩罚平滑 VAR”（SSVAR）。通过基于年龄之间的距离自适应地惩罚系数，SSVAR 不仅允许系数矩阵的灵活的数据驱动稀疏结构，而且同时确保可解释的系数，包括队列效应。此外，与现有的 SVAR 模型相比，通过结合平滑惩罚，相邻年龄预测死亡率的差异大大减少。提出了一种使用加速近端梯度算法的新估计方法来有效地求解SSVAR。相似地，我们建议使用空间惩罚图形 Lasso 估计残差的精度矩阵，以进一步研究残差的依赖结构。使用英国和法国的人口数据，我们证明 SSVAR 模型在预测准确性方面始终优于著名的 Lee-Carter、Hyndman-Ullah 和两个 VAR 类型模型。最后，我们通过一个说明性示例讨论了 SSVAR 模型对多人口死亡率预测的扩展，该示例证明了其在预测方面优于现有方法。以及预测准确性的两个 VAR 类型模型。最后，我们通过一个说明性示例讨论了 SSVAR 模型对多人口死亡率预测的扩展，该示例证明了其在预测方面优于现有方法。以及预测准确性的两个 VAR 类型模型。最后，我们通过一个说明性示例讨论了 SSVAR 模型对多人口死亡率预测的扩展，该示例证明了其在预测方面优于现有方法。