Backtesting Stochastic Mortality Models : An Ex-Post Evaluation of Multi-Period Ahead-Density Forecasts

This study sets out a backtesting framework applicable to the multi-period-ahead forecasts from stochastic mortality models and uses it to evaluate the forecasting performance of six different stochastic mortality models applied to English & Welsh male mortality data. The models considered are: Lee-Carter's 1992 one-factor model; a version of Renshaw-Haberman's 2006 extension of the Lee-Carter model to allow for a cohort effect; the age-period-cohort model of Currie (2006), which is a simplified version of Renshaw-Haberman; Cairns, Blake and Dowd's 2006 two-factor model; and two generalised versions of the latter with an added cohort effect. For the data set used herein the results from applying this methodology suggest that the models perform adequately by most backtests, and that there is little difference between the performances of five of the models. The remaining model, however, shows forecast instability. The study also finds that density forecasts that allow for uncertainty in the parameters of the mortality model are more plausible than forecasts that do not allow for such uncertainty