This article deals with the interplay of explosive behaviour and long memory. We conduct Monte Carlo simulations and study the finite‐sample properties of the popular unit root test by Phillips et al. (2011) against explosive alternatives. This test exhibits severe upward size distortions under the presence of strongly autocorrelated residuals. We propose the usage of a set of adjusted critical values which leads to a size‐controlled test with increased power. As a complement, we consider the Lagrange Multiplier test against long memory by Tanaka (1999). We study European government bond yield spreads during the financial crisis.