Evaluating the Goodness of Fit of Stochastic Mortality Models

This study sets out a framework to evaluate the goodness of fit of stochastic mortality models and applies it to six different models estimated using English & Welsh male mortality data. The methodology exploits the structure of each model to obtain various residual series that are predicted to be iid standard normal under the null hypothesis of model adequacy. Goodness of fit can then be assessed using conventional tests of the predictions of iid standard normality. 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, Currie's 2006 age-period-cohort model, which is a simplified version of the Renshaw-Haberman model, the Cairns-Blake-Dowd 2006 two-factor model and two generalised versions of the latter that allow for a cohort effect. For the data set considered, there are some notable differences amongst the different models, but none of the models performs well in all tests and no model clearly dominates the others