Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses

摘要: Abstract Perron [Perron, P., 1989. The great crash, the oil price shock and unit root hypothesis. Econometrica 57, 1361–1401] introduced a variety of tests that are valid when break in trend function time series is present. motivation was to devise testing procedures were invariant magnitude shift level and/or slope. In particular, if change present it allowed under both null alternative hypotheses. This analysis carried assumption known date. subsequent literature aimed case an unknown However, doing so, most and, particular commonly used test Zivot Andrews [Zivot, E., Andrews, D.W.K., 1992. Further evidence on Journal Business Economic Statistics 10, 251–270], assumed occurs, does so only hypothesis stationarity. undesirable since (a) imposes asymmetric treatment allowing for break, may reject noise integrated but changing; (b) present, this information not exploited improve power test. paper, we propose procedure addresses issues. It allows hypotheses limit distribution same as date, thereby increased while maintaining correct size. Simulation experiments confirm our offers improvement over methods small samples.