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

Abstract. 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.