Accurate forecasts of weekly mortality are essential for public health and the insurance industry. We develop a forecasting framework that extends the Lee-Carter model with age- and region-specific seasonal effects and penalized distributed lag non-linear components that capture the delayed and non-linear effects of heat, cold, and influenza on mortality. The model accommodates overdispersed mortality rates via a negative binomial distribution. We model the temporal dynamics of the latent factors in the model using SARIMA processes and capture cross-regional dependencies through a copula-based approach. Using regional French mortality data (1990-2019), we demonstrate that the proposed framework yields well-calibrated forecast distributions and improves predictive accuracy relative to benchmark models. The results further show substantial heterogeneity in temperature- and influenza-related relative risks between ages and regions. These findings underscore the importance of incorporating exogenous drivers and dependence structures into a weekly mortality forecasting framework.

翻译：周死亡率的准确预测对公共卫生和保险行业至关重要。我们开发了一个预测框架，该框架扩展了Lee-Carter模型，包含年龄和区域特异性季节效应，以及惩罚性分布滞后非线性成分，以捕捉高温、寒冷和流感对死亡率的延迟及非线性影响。该模型通过负二项分布处理过度离散的死亡率数据。我们利用SARIMA过程对模型中潜因子的时间动态进行建模，并通过基于copula的方法捕捉跨区域依赖性。基于法国区域死亡率数据（1990-2019），我们证明所提出的框架能够生成校准良好的预测分布，并相比基准模型提高预测准确性。结果进一步显示，温度和流感相关相对风险在年龄和区域间存在显著异质性。这些发现强调了将外源驱动因素和依赖结构纳入周死亡率预测框架的重要性。