A Test for Superior Predictive Ability

We propose a new test for superior predictive ability. The new test compares favorably to the reality check (RC) for data snooping, because it is more powerful and less sensitive to poor and irrelevant alternatives. The improvements are achieved by two modifications of the RC. We use a studentized test statistic that reduces the influence of erratic forecasts and invoke a sample-dependent null distribution. The advantages of the new test are confirmed by Monte Carlo experiments and an empirical exercise in which we compare a large number of regression-based forecasts of annual U.S. inflation to a simple random-walk forecast. The random-walk forecast is found to be inferior to regression-based forecasts and, interestingly, the best sample performance is achieved by models that have a Phillips curve structure.