Long Memory Regressors and Predictive Testing: A Two-stage Rebalancing Approach
提出两阶段再平衡方法解决长记忆回归变量导致的预测检验偏差，通过分数差分调整回归变量，模拟显示方法稳健且功效优于整数阶假设，并扩展至因变量也分数积分的情形。
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.