On the choice of test for a unit root when the errors are conditionally heteroskedastic

It is well known that in the context of the classical regression model with heteroskedastic errors, while ordinary least squares (OLS) is not efficient, the weighted least squares (WLS) and quasi-maximum likelihood (QML) estimators that utilize the information contained in the heteroskedasticity are. In the context of unit root testing with conditional heteroskedasticity, while intuition suggests that a similar result should apply, the relative performance of the tests associated with the OLS, WLS and QML estimators is not well understood. In particular, while QML has been shown to be able to generate more powerful tests than OLS, not much is known regarding the relative performance of the WLS-based test. By providing an in-depth comparison of the tests, the current paper fills this gap in the literature.