Asymptotic behaviour of tests for a unit root against an explosive alternative

We compare the asymptotic local power of upper-tail unit root tests against an explosive alternative based on ordinary least squares (OLS) and quasi-di erenced (QD) demeaning/detrending. We nd that under an asymptotically negligible initialization, the QD-based tests are near asymptotically e cient and generally o er superior power to OLS-based approaches; however, the power gains are much more modest than in the lower-tail testing context. We also nd that asymptotically non-negligible initial conditions do not a ect the power ranking in the same way as they do for lower-tail tests, with the QD-based tests retaining a power advantage in such cases.