Uniform Inference in Predictive Regression Models

The restricted likelihood has been found to provide a well-behaved likelihood ratio test in the predictive regression model even when the regressor variable exhibits almost unit root behavior. Using the weighted least squares approximation to the restricted likelihood obtained in Chen and Deo, we provide a quasi restricted likelihood ratio test (QRLRT), obtain its asymptotic distribution as the nuisance persistence parameter varies, and show that this distribution varies very slightly. Consequently, the resulting sup bound QRLRT is shown to maintain size uniformly over the parameter space without sacrificing power. In simulations, the QRLRT is found to deliver uniformly higher power than competing procedures with power gains that are substantial.