This paper develops procedures for inference about the moments of smooth functions of out of sample predictions and prediction errors, when there is a long time series of predictions and realizations, and each prediction is based on regression parameters estimated from a long time series. The aim is to provide tools for inference about predictive accuracy and efficiency, and, more generally, about predictive ability. The paper allows for nonlinear models and estimators, as well as for possible dependence of predictions and prediction errors on estimated regression parameters. Simulations indicate that the procedures work well.
