Joint Hypothesis Tests for a Unit Root When There is a Break in the Innovation Variance

We develop extensions of the Dickey-Fuller F-statistics for the joint null hypothesis of a unit root that allows for a break in the innovation variance. Our statistics are based on the modified generalized least squares (GLS) strategy outlined in Kim, Leybourne and Newbold [Journal of Econometrics (2002) Vol. 109, pp. 365-387] that requires estimation of the break-date and corresponding pre-break and post-break variances. We derive the asymptotic distribution of the new F-statistics, tabulate their finite sample and asymptotic critical values, and present finite sample simulation evidence regarding their size and power. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.