According to previous research, standard unit root tests are considered robust to stationary GARCH distortions. These conclusions are in fact correct when the number of observations is extraordinarily high. However, simulation experiments in this study, using more normal sample sizes, reveal that eight of the most commonly applied unit root tests exhibit considerable bias in the size in the presence of fairly moderate GARCH distortions. As a remedy for the disturbances from GARCH, this paper presents size-corrected unbiased critical values for all these examined tests. Nevertheless there is still reduced power in the presence of stationary GARCH distortions. As a solution, a completely new test is formulated which simultaneously models unit roots and the interconnected parameters of GARCH risk. For empirically relevant sample sizes, this new test exhibits superior size and power properties compared with all the traditional unit root tests in the presence of GARCH disturbances.

Currently, the theory of long-run purchasing power parity (PPP) attains its strongest support in more than thirty years. In this paper, the validity of the PPP revisionists’ scientific evidence supporting long-run PPP is questioned based on the replication of an influential review study that is considered by PPP revisionists to exhibit “some of the strongest evidence” in favour of the PPP theory. By simulation experiments it is demonstrated that the traditional PPP unit root tests are non-robust to the empirically identified (G)ARCH distortions. Due to (G)ARCH distortions, over-rejections for the traditional unit root tests are shown to be a problem that potentially misleads researchers to believe that long-run PPP holds under circumstances when it is in fact not valid. As a potential remedy to this problem, a new unit root test is introduced which is robust to conditional heteroscedasticity disturbances, and in contrast to traditional unit root tests, it exhibits no significant empirical support for the PPP theory. The study illustrates that the PPP revisionists’ unit root tests cannot reliably test the PPP hypothesis in the presence of (G)ARCH distortions, due to bad power and size properties. Perhaps it is time to conclude that, based on the currently existing research, it is virtually impossible to empirically come to a credible conclusion regarding whether long-run PPP holds or not.