Improving the Forecast of Longevity by Combining Models

Mortality is a dynamic process whose future evolution over time poses important challenges for life insurance, pension funds, public policy, and fiscal planning. In this paper, we propose two contributions: (1) a new dynamic corrective methodology of the predictive accuracy of the existing mortality projection models, by modeling a measure of their fitting errors as a Cox-Ingersoll-Ross process and; (2) various out-of-sample validation methods. Besides the usual static method, we develop a dynamic one allowing us to catch the change in behavior of the underlying data. For our numerical application, we choose the Cairns-Blake-Dowd (or M5) model. Using the Italian and French females mortality data and implementing the backtesting procedure, we empirically test the ex-post forecasting performance of the CBD model both for itself (CBD) and corrected by the CIR process (mCBD). We focus on age 65, but we show results for a wide range of ages, also much younger, and for cohort data. On the basis of average measures of forecasting errors and information criteria, we show that the mCBD model is parsimonious and provides better results in terms of predictive accuracy than the CBD model itself.