Abstract:

We consider the performance of Ibragimov & Mueller’s (2010) subsample HAR tests in a prediction setting. In particular, we analyze multi-step prediction with a persistent regressor, whose innovations may be correlated with the regression errors. This aligns with the prediction of equity returns using dividend yields. We model the regressor’s persistence as local-to-unity to capture the finite-sample bias of the subsample estimates in an asymptotic framework. This mirrors the bias results of Stambaugh (1999). We show that, asymptotically, the size of tests using the subsample HAR estimator approaches unity. We illustrate these properties in Monte Carlo simulations. These limitations are not shared by many orthogonal series estimators; in particular, an equal-weighted periodogram estimator of the long-run variance retains accurate size and approaches an optimal size-power frontier.