Optimal Versus Robust Inference in Nearly Integrated Non Gaussian Models

Elliott, Rothenberg and Stock (1996) derived a class of point-optimal unit root tests in a time series model with Gaussian errors. Other authors have proposed "robust" tests which 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 Elliott et al.'s (1996) tests as well as 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 tradeoff between robustness to unknown error distributions and optimality with respect to the trend coefficients.