Learning and forecasting of age-specific period mortality via B-spline processes with locally-adaptive dynamic coefficients

The overarching focus on predictive accuracy in mortality forecasting has motivated an increasing shift towards more flexible representations of age-specific period mortality trajectories at the cost of reduced interpretability. While this perspective has led to successful predictive strategies, the inclusion of interpretable structures in modeling of human mortality can be, in fact, beneficial in improving forecasts. We pursue this direction via a novel B-spline process with locally-adaptive dynamic coefficients that outperforms state-of-the-art forecasting strategies by explicitly incorporating core structures of period mortality trajectories within an interpretable formulation that facilitates efficient computation via closed-form Kalman filters and allows direct inference not only on age-specific mortality trends but also on the associated rates of change across times. This is obtained by modelling the age-specific death counts via an over-dispersed Poisson log-normal model parameterized with a combination of B-spline bases having dynamic coefficients that characterize time changes in mortality rates through a set of carefully-defined stochastic differential equations. Such a representation yields high flexibility, but also preserves tractability in inference on dynamic changes of mortality patterns for different age profiles, while accounting for shocks. As illustrated in applications to mortality data from different countries, the proposed model yields more accurate forecasts than state-of-the-art competitors and unveils substantial differences across countries and age groups in mortality patterns, both in the past decades and during the recent covid-19 pandemic.