  We introduce a new approach for comparing the predictive accuracy of two
nested models that bypasses the difficulties caused by the degeneracy of the
asymptotic variance of forecast error loss differentials used in the
construction of commonly used predictive comparison statistics. Our approach
continues to rely on the out of sample MSE loss differentials between the two
competing models, leads to nuisance parameter free Gaussian asymptotics and is
shown to remain valid under flexible assumptions that can accommodate
heteroskedasticity and the presence of mixed predictors (e.g. stationary and
local to unit root). A local power analysis also establishes its ability to
detect departures from the null in both stationary and persistent settings.
Simulations calibrated to common economic and financial applications indicate
that our methods have strong power with good size control across commonly
encountered sample sizes.
