An infimum coefficient unit root test allowing for an unknown break in trend

In this paper we consider testing for a unit root in the possible presence of a trend break at an unknown time. Zivot and Andrews (1992) [Journal of Business and Economic Statistics 10, 251–270] proposed using the infimum of t-ratio Dickey–Fuller statistics across all candidate break points in a trimmed range, however this procedure can have an asymptotic size of one when a break occurs under the unit root null. We show that if the same approach is used, but instead with coefficient Dickey–Fuller statistics in an additive outlier framework, the test is asymptotically conservative when a break is present under the null, provided the degree of trimming is appropriately controlled. The test is also shown to have superior local asymptotic power to the t-ratio version.