Spatio-Temporal Extensions of the Lee−Carter and Li−Lee Models

Several stochastic mortality forecasting techniques, such as the Lee-Carter and Li-Lee models, extract a time-dependent mortality index from logarithmic mortality rates, while producing a residual noise term. These models typically forecast the index while discarding the noise. However, residuals may contain significant temporal, spatial, and spatio-temporal autocorrelation, offering valuable patterns that can be leveraged to improve forecasts. In this study, we propose a machine learning methodology to incorporate this autocorrelation into the mortality index and its forecasts. We introduce two hyperparameters: one regulates the strength of the enhancement, and the other specifies the adjustment method for the mortality index. The adjusted index can then be forecasted using traditional methods such as random walk, ARIMA, and vector autoregression, or more advanced techniques like spatial dynamic panel linear models, eigenvector spatio-temporal filters, and spatio-temporal ARIMA models. Special care is taken to ensure coherence in forecasts across multiple populations, particularly for the Li-Lee model. We apply the proposed methods to data from several countries, testing them on both the Lee-Carter and Li-Lee models. By optimizing the hyperparameters through a train-test-validation split, we compare forecasts with and without incorporating autocorrelational patterns. The results demonstrate that traditional models can be significantly improved by including this additional information. These refined forecasts offer substantial benefits for applications such as life insurance, annuities, pensions, and other areas dealing with longevity risk.