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.

本文研究了用于死亡率建模和预测的高维向量自回归（VAR）模型。我们建议对适用于对数死亡率改进的稀疏VAR（SVAR）模型进行扩展，我们将其称为“空间惩罚平滑VAR”（SSVAR）。通过根据年龄之间的距离自适应地对系数进行惩罚，SSVAR不仅允许系数矩阵的数据驱动的稀疏性结构灵活，而且还确保了包括同类效应的可解释系数。此外，与现有的SVAR模型相比，通过纳入平滑度惩罚，可以大大减少邻近年龄的预测死亡率的差异。提出了一种使用加速近端梯度算法的新型估计方法，以有效地求解SSVAR。同样，我们建议使用空间惩罚图形化套索估计残差的精度矩阵，以进一步研究残差的依存结构。使用英国和法国的人口数据，我们证明了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型模型。最后，我们通过一个说明性示例讨论了SSVAR模型到多种群死亡率预测的扩展，该示例证明了其在预测中优于现有方法的优势。以及两个VAR型模型的预测准确性。最后，我们通过一个说明性示例讨论了SSVAR模型到多种群死亡率预测的扩展，该示例证明了其在预测中优于现有方法的优势。以及两个VAR型模型的预测准确性。最后，我们通过一个说明性示例讨论了SSVAR模型到多种群死亡率预测的扩展，该示例证明了其在预测中优于现有方法的优势。