A Note on Unit Root Tests with Infinite Variance Noise

In recent years, a number of authors have considered extensions of classical unit root tests to cases where the process is driven by infinite variance innovations, as well as considering their asymptotic properties. Unfortunately, these extensions are typically inefficient as they do not exploit the dynamics of the infinite variance process. In this article, we consider Dickey-Fuller-type tests based on M-estimators and develop the asymptotic theory for these estimators and resulting test statistics.