The power of unit root tests under local-to-finite variance errors

We study the power of four popular unit root tests in the presence of a local-to-finite variance DGP. We characterize the asymptotic distribution of these tests under a sequence of local alternatives, considering both stationary and explosive ones. We supplement the theoretical analysis with a small simulation study to assess the finite sample power of the tests. Our results suggest that the finite sample power is affected by the αα-stable component for low values of αα and that, in the presence of this component, the DW test has the highest power under stationary alternatives. We also document a rather peculiar behavior of the DW test whose power, under the explosive alternative, suddenly falls from 1 to zero for very small changes in the autoregressive parameter suggesting a discontinuity in the power function of the DW test.