A bunch of models, a bunch of nulls and inference about predictive ability

Inference about predictive ability is usually carried-out in the form of pairwise comparisons between two forecasting methods. Nevertheless, some interesting questions are concerned with families of models and not just with a couple of forecasting strategies. For instance: Are time-series models more accurate than economic models to predict inflation? In this family wise context it is not clear if the methods developed to analyze two models will be useful. We address this problem by presenting a simple methodology to test the null hypothesis of equal predictive ability between two families of forecasting methods. Our approach builds on the reality check presented by White. We illustrate our results comparing the ability of two families of models to predict inflation in Chile, the US, Sweden and Mexico.