Regression-based tests of predictive ability

We develop regression-based tests of hypotheses about out of sample prediction errors. Representative tests include ones for zero mean and zero correlation between a prediction error and a vector of predictors. The relevant environments are ones in which predictions depend on estimated parameters. We show that standard regression statistics generally fail to account for errors introduced by estimation of these parameters. We propose computationally convenient test statistics that properly account for such errors. Simulations indicate that the procedures can work well in samples of size typically available, although there sometimes are substantial size distortions.