Optimal Versus Robust Inference In Nearly Integrated Non-Gaussian Models

Elliott, Rothenberg, and Stock (1996, Econometrica 64, 813–836) derive a class of point-optimal unit root tests in a time series model with Gaussian errors. Other authors have proposed “robust” tests that are not optimal for any model but perform well when the error distribution has thick tails. I derive a class of point-optimal tests for models with non-Gaussian errors. When the true error distribution is known and has thick tails, the point-optimal tests are generally more powerful than the tests of Elliott et al. (1996) and also than the robust tests. However, when the true error distribution is unknown and asymmetric, the point-optimal tests can behave very badly. Thus there is a trade-off between robustness to unknown error distributions and optimality with respect to the trend coefficients.This paper could not have been written without the encouragement of Thomas Rothenberg. This is based on my dissertation, which he supervised. I also thank Don Andrews, Jack Porter, Jim Stock, and seminar participants at the University of Pennsylvania, the University of Toronto, the University of Montreal, Princeton University, and the meetings of the Econometric Society in UCLA. Comments of three anonymous referees greatly improved the exposition of the paper. I owe special thanks to Gary Chamberlain for helping me to understand these results.