Improving the power of the Diebold–Mariano–West test for least squares predictions

We propose a more powerful version of the test of Diebold and Mariano (1995) and West (1996) for comparing least squares predictors based on non-nested models when the parameter being tested is the expected difference between the squared prediction errors. The proposed test improves the asymptotic power by using a more efficient estimator of the parameter being tested than that used in the literature. The estimator used by the standard version of the test depends on the individual predictions and realizations only through the observations on the prediction errors. However, the parameter being tested can also be expressed in terms of moments of the predictors and the predicted variable, some of which cannot be identified separately by the observations on the prediction errors alone. Parameterizing these moments in a GMM framework and drawing on the theory of West (1996), we devise more powerful versions of the test by exploiting a restriction that is maintained routinely under the null hypothesis by West (1996, Assumption 2b) and later studies. This restriction requires only finite second-order moments and covariance stationarity in order to ensure that the population linear projection exists. Simulation experiments show that the potential gains in power can be substantial.