The Federal Reserve Bank of St. Louis has developed a novel and effective bootstrap method for simulating asymptotic critical values for tests of equal forecast accuracy and encompassing among many nested models.
The bootstrap, which combines elements of fixed regressor and wild bootstrap methods, is simple to use. Researchers of the Federal Reserve Bank of St. Louis first derived the asymptotic distributions of tests of equal forecast accuracy and encompassing applied to forecasts from multiple models that nest the benchmark model – that is, reality check tests applied to nested models.
They proved the validity of the bootstrap for these tests. Monte Carlo experiments indicate that the proposed bootstrap has better finite-sample size and power than other methods designed for comparison of non-nested models. They conclude with empirical applications to multiple-model forecasts of commodity prices and GDP growth.