Unit Root Tests and Heavy-Tailed Innovations

We evaluate the impact of heavy-tailed innovations on some popular unit root tests. In the context of a near-integrated series driven by linear process shocks, we demonstrate that their limiting distributions are altered under infinite variance vis-à-vis finite variance. Reassuringly, however, simulation results suggest that the impact of heavy-tailed innovations on these tests is relatively small. We use the framework of Amsler and Schmidt () whereby the innovations have local-to-finite variances being generated as a linear combination of draws from a thin-tailed distribution (in the domain of attraction of the Gaussian distribution) and a heavy-tailed distribution (in the normal domain of attraction of a stable law). We also explore the properties of augmented Dickey–Fuller tests that employ Eicker–White standard errors, demonstrating that these can yield significant power improvements over conventional tests.