Long Memory Regressors and Predictive Regressions: A two-stage rebalancing approach

Alex Maynard, Aaron Smallwood and Mark E. Wohar

Predictability tests with long memory regressors entail both size distortion and potential regression imbalance. 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. A full set of asymptotic results are provided. The second-stage t-statistic used to test predictability has a standard normal limiting distribution. 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 use our procedure to provide a valid test of forward rate unbiasedness that allows for a long memory forward premium.