A new test for simultaneous estimation of unit roots and GARCH risk in the presence of stationary conditional heteroscedasticity disturbances

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 article 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.