Mortality Forecasting Using Stacked Regression Ensembles

There are many alternative approaches to selecting mortality models and forecasting mortality. The standard practice is to produce forecasts using a single model such as the Lee-Carter, the Cairns-Blake-Dowd, or the Age- Period-Cohort model, with model selection based on in-sample goodness of fit measures. However, increasingly cross-validation measures based on forecasts are used in mortality model selection, and model combination methods such as Bayesian Model Averaging and Model Confidence Set have been proposed as alternatives to using a single model. We present a stacked regression ensemble method that optimally combines different mortality models to reduce the mean squared errors of mortality rate forecasts and mitigate model selection risk. Stacked regression uses a supervised machine learning algorithm to approximate the horizon-specific weights by minimizing the cross-validation criterion for each forecasting horizon. The horizon-specific weights facilitate the development of a mortality model combination customized to each horizon. Unlike other model combination methods, stacked regression simultaneously solves model selection and estimates model combinations to improve model forecasts. We use 44 populations from the Human Mortality Database to compare the stacked regression mortality approach with other alternative methods. We show that using one-year-ahead to 15−year-ahead out-of-sample mean squared errors, the stacked regression ensemble approach improves mortality forecast accuracy by 13% - 49% and 19% - 90% for females over individual mortality models. The stacked regression ensemble has better predictive accuracy than other model combination methods, including Simple Model Averaging, Bayesian Model Averaging, and Model Confidence Set. We provide a user-friendly open-source R package, CoMoMo, that estimates models and provides mortality rate forecasts for different mortality model combination methods