Multiple unit root tests under uncertainty over the initial condition: some powerful modifications

We modify the union-of-rejection unit root test of Harvey et al. "Unit Root Testing in Practice: Dealing with Uncertainty over the Trend and Initial Condition" (Harvey, Econom Theory 25:587-636, 2009). This test rejects if either of two different unit root tests rejects but controls the inherent multiple testing issue by suitably modifying the critical values to ensure the desired null rejection probability. We evaluate the new tests' power relative to existing ones' and to the Gaussian asymptotic power envelope. An empirical application illustrates the usefulness of the new statistics.