Abstract

The paper provides a general framework for investigating the effects of permanent changes in the variance of the errors of an autoregressive process on unit root tests. Such a framework — which is based on a novel asymptotic theory for integrated and near integrated processes with heteroskedastic errors — allows to evaluate how the variance dynamics affect the size and the power function of unit root tests. Contrary to previous studies, it is shown that under permanent variance shifts, the conventional critical values can lead both to oversized and undersized tests. The paper concludes by showing that the power function of the unit root tests is affected by non-constant variances as well.