The Econometrics Journal 2000/1. [antikvár]

Behaviour of the standard and symmetric Dickey-Fuller-type tests when there is a break under the null hypothesis Stephen J. Leybourne and Paul Newbold Department of Economics, University of Nottingham, Nottingham NG7 2RD, UK E-mail: steve.leybourneSnottingham.ac.uk, paul.newboldOnottingham.ac.uk Received: January 1998 Summary We examine the behaviour of tests of the unit root null hypothesis when the true generating model is I (1) with a break. Asymptotic distributional results are derived predicting that the standard Dickey-Fuller test will in that case yield frequent rejections of the null for relatively early breaks. This phenomenon is most severe for lowest values of the break fraction under a break in level, and for a break in slope occurring about 15% of the way through the series. However, asymptotics predict that the phenomenon will not be present for a modified test based on a symmetric weighted estimator. The theoretical predictions are confirmed by simulation evidence. Keywords: Structural breaks, Unit root tests, Weighted symmetric estimator, Spurious stationarity. 1. INTRODUCTION Perron (1989) demonstrated that, when the true generating process of a time series is stationary around a broken trend, Dickey-Fuller tests can have very low power. Subsequently, many authors, including Perron (1989, 1993, 1994). Banerjee et al. (1992), Perron and Vogelsang (1992) and Zivot and Andrews (1992) have discussed methods for incorporating the possibility of a trend break, either exogenously or endogenously determined, into Dickey-Fuller-type tests of the null hypothesis that a generating process is I (1). However, such elaborations of the standard test are by no means invariably employed in practice, so that further exploration of the consequences of ignoring a break is desirable. Recently, Leybourne etal. (1998) have demonstrated by simulation the possibility of a 'converse Perron phenomenon': if the true generating process is I (1) but with a break, frequent spurious rejections of the null hypothesis can occur. One objective of the present paper is to provide a more elaborate asymptotic theoretical explanation of these Monté Carlo results. In fact, the occurrence or otherwise and the severity of this phenomenon depends on the location of the break. For example, if a standard Dickey-Fuller test is applied to an I (1) process with a break, then spurious rejections occur if the break is early but not late in the series. This asymmetry suggests that different conclusions would be reached if Dickey-Fuller-type tests were based on estimators that treated the data symmetrically, such as the Rj and /V2 statistics of Bharghava (1986), maximization of the exact Gaussian likelihood function (under stationarity), and the weighted symmetric estimator discussed by Pantula et al. (1994) and Park and Fuller (1995). In Section 3 of the paper, we analyse the last of these.