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Although the analysis of human mortality has a well-established history, theattempt to accurately forecast future death-rate patterns for different agegroups and time horizons still attracts active research. Such a predictivefocus has motivated an increasing shift towards more flexible representationsof age-specific period mortality trajectories at the cost of reducedinterpretability. Although this perspective has led to successful predictivestrategies, the inclusion of interpretable structures in modeling of humanmortality can be, in fact, beneficial for improving forecasts. We pursue thisdirection via a novel B-spline process with locally-adaptive dynamiccoefficients. Such a process outperforms state-of-the-art forecastingstrategies by explicitly incorporating the core structures of period mortalitywithin an interpretable formulation which enables inference on age-specificmortality trends and the corresponding rates of change across time. This isobtained by modeling the age-specific death counts via a Poisson log-normalmodel parameterized through a linear combination of B-spline bases with dynamiccoefficients that characterize time changes in mortality rates via suitablestochastic differential equations. While flexible, the resulting formulationcan be accurately approximated by a Gaussian state-space model that facilitatesclosed-form Kalman filtering, smoothing and forecasting, for both the trends ofthe spline coefficients and the corresponding first derivatives, which measurerates of change in mortality for different ages. As illustrated in applicationsto mortality data from different countries, our model outperformsstate-of-the-art methods both in point forecasts and in calibration ofpredictive intervals. Moreover, it unveils substantial differences in mortalitypatterns across countries and ages, both in the past decades and during theCOVID-19 pandemic.

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