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Testing for a unit root against ESTAR stationarity

Harvey, David I.; Leybourne, Stephen J.; Whitehouse, Emily J.


Emily J. Whitehouse


In this paper we examine the local power of unit root tests against globally stationary exponential smooth transition autoregressive [ESTAR] alternatives under two sources of uncertainty: the degree of nonlinearity in the ESTAR model, and the presence of a linear deterministic trend. First, we show that the Kapetanios, Shin and Snell (2003, Journal of Econometrics 112, 359.379) [KSS] test for nonlinear stationarity has local asymptotic power gains over standard Dickey-Fuller [DF] tests for certain degrees of nonlinearity in the ESTAR model, but that for other degrees of nonlinearity, the linear DF test has superior power. Second, we derive limiting distributions of demeaned, and demeaned and detrended KSS and DF tests under a local ESTAR alternative when a local trend is present in the DGP. We show that the power of the demeaned tests outperforms that of the detrended tests when no trend is present in the DGP, but deteriorates as the magnitude of the trend increases. We propose a union of rejections testing procedure that combines all four individual tests and show that this captures most of the power available from the individual tests across different degrees of nonlinearity and trend magnitudes. We also show that incorporating a trend detection procedure into this union testing strategy can result in higher power when a large trend is present in the DGP.


Harvey, D. I., Leybourne, S. J., & Whitehouse, E. J. (2018). Testing for a unit root against ESTAR stationarity. Studies in Nonlinear Dynamics and Econometrics, 22(1),

Journal Article Type Article
Acceptance Date May 27, 2017
Online Publication Date Jun 16, 2017
Publication Date 2018-02
Deposit Date May 23, 2017
Publicly Available Date Jun 16, 2017
Journal Studies in Nonlinear Dynamics and Econometrics
Electronic ISSN 1558-3708
Publisher De Gruyter
Peer Reviewed Peer Reviewed
Volume 22
Issue 1
Keywords Nonlinearity; Trend uncertainty; Union of rejections
Public URL
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