Model confidence sets and forecast combination: An application to age-specific mortality

Abstract: Model averaging combines forecasts obtained from a range of models, and it often produces more accurate forecasts than a forecast from a single model. The crucial part of forecast accuracy improvement in using the model averaging lies in the determination of optimal weights from a finite sample. If the weights are selected sub-optimally, this can affect the accuracy of the model-averaged forecasts. Instead of choosing the optimal weights, we consider trimming a set of models before equally averaging forecasts from the selected superior models. Motivated by Hansen, Lunde and Nason (2011), we apply and evaluate the model confidence set procedure when combining mortality forecasts. The proposed model averaging procedure is motivated by Samuels and Sekkel (2017) based on the concept of model confidence sets as proposed by Hansen et al. (2011) that incorporates the statistical significance of the forecasting performance. As the model confidence level increases, the set of superior models generally decreases. The proposed model averaging procedure is demonstrated via national and sub-national Japanese mortality for retirement ages between 60 and 100+. Illustrated by national and sub-national Japanese mortality for ages between 60 and 100+, the proposed model-average procedure gives the smallest interval forecast errors, especially for males. We find that robust out-of-sample point and interval forecasts may be obtained from the trimming method. By robust, we mean robustness against model misspecification.