Short-term mortality fluctuations are traditionally estimated using Serfling models [2], which capture trend and seasonality through Fourier harmonic components. Recent studies have highlighted the importance of climate in explaining mortality dynamics. Robben et al. (2024) [1] show that climate variables significantly improve weekly mortality prediction using machine learning techniques. This evidence suggests that climate contains relevant information for seasonal mortality dynamics. However, many approaches impose rigid seasonal structures or rely on black-box models, limiting interpretability. Moreover, spatial mortality models typically require the explicit specification of geographic dependence through spatial weight matrices. Motivated by these considerations, we introduce an interpretable deep-learning extension of the Serfling model in which climate effects are structurally incorporated into the seasonal dynamics. Our framework allows spatial heterogeneity to emerge directly from the learning architecture without requiring external spatial regularization. Specifically, we introduce feedforward neural networks that dynamically model the amplitudes of seasonal oscillations as a function of climate variables. This extension preserves the interpretability of the baseline framework while enabling nonlinear climate modulation. We use weekly mortality data for NUTS3 regions in Europe; models are estimated over 2014–2022 and evaluated out-of-sample in 2023.
Across multiple evaluation metrics, these extensions reveal consistent improvements in predictive performance over the baseline, with gains observed in more than half of the analyzed regions. These findings confirm the models’ ability to capture spatial heterogeneity and demonstrate the robustness of the proposed specification. The framework therefore provides an interpretable advancement for climate-sensitive risk analysis in actuarial applications.

References

[1] Robben, J., Antonio, K., & Kleinow, T. (2025). The short-term association between environmental variables and mortality: evidence from Europe. Journal of the Royal Statistical Society Series A: Statistics in Society, qnaf052.

[2] Serfling, R. E. (1963). Methods for current statistical analysis of excess pneumonia-influenza deaths. Public health reports, 78(6), 494.