In this paper we consider several modified wild bootstrap methods that, additionally to heteroskedasticity, can take dependence into account. The modified wild bootstrap methods are shown to correctly replicate an invariance principle for multivariate time series that are characterized by general forms of unconditional heteroskedasticity, or nonstationary volatility, as well as dependence within and between different elements of the time series. The invariance principle is then applied to derive the asymptotic validity of the wild bootstrap methods for unit root testing in a multivariate setting. The resulting tests, which can also be interpreted as panel unit root tests, are valid under more general assumptions than most current tests used in the literature. A simulation study is performed to evaluate the small sample properties of the bootstrap unit root tests.
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