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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. The aim is to provide tools for analysis of predictive accuracy and efficiency, and, more generally, of predictive ability. The paper allows for nonnested and nonlinear models, as well as for possible dependence of predictions and prediction errors on estimated regression parameters. Simulations indicate that the procedures can work well in samples of size typically available.