GARCH, heteroscedasticity-consistent covariance matrix estimation and (non)linear unit root testing

In previous research it has been shown that while the Dickey--Fuller unit root test exhibits oversizing in the presence of GARCH, this is reduced via the application of White's heteroscedasticity-consistent covariance matrix (HCCM). These findings provide the motivation for the present study. It is shown that the application of White's HCCM to the Dickey--Fuller test results in a shift of the finite-sample distribution of the test thereby necessitating the use of HCCM-specific critical values. Re-examination of the impact of GARCH upon the Dickey--Fuller test shows the combination of White's HCCM and HCCM-specific critical values leads to a marked improvement in empirical size. A similar analysis is performed for an alternative nonlinear unit root test. The results obtained show that in comparison to the Dickey--Fuller test, the distribution of this test is more sensitive to the use of White's HCCM while it also exhibits greater oversizing in the presence of GARCH. However, use of White's HCCM and HCCM-specific critical values are found to correct the size of the test. The results presented illustrate the usefulness of White's HCCM and HCCM-specific critical values when examining the unit root hypothesis in time series exhibiting GARCH.