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Title: Uniform Inference Via The Restricted Likelihood in Predictive Regression Models


The restricted likelihood is shown to provide a well-behaved likelihood ratio test in autoregressive models due to its low curvature. This fact is exploited to get valid inference in predictive regression models. Using the weighted least squares approximation to the restricted likelihood 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. There are numerous other applications of the Restricted Likelihood in Vector Autoregressive models.