Long Memory Regressors and Predictive Testing: A Two-stage Rebalancing Approach

Predictability tests with long memory regressors may entail both size distortion and incompatibility between the orders of integration of the dependent and independent variables. Addressing both problems simultaneously, this paper proposes a two-step procedure that rebalances the predictive regression by fractionally differencing the predictor based on a first-stage estimation of the memory parameter. Extensive simulations indicate that our procedure has good size, is robust to estimation error in the first stage, and can yield improved power over cases in which an integer order is assumed for the regressor. We also extend our approach beyond the standard predictive regression context to cases in which the dependent variable is also fractionally integrated, but not cointegrated with the regressor. We use our procedure to provide a valid test of forward rate unbiasedness that allows for a long memory forward premium.