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Testing for a unit root against ESTAR stationarity

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

Authors

Emily J. Whitehouse



Abstract

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.

Journal Article Type Article
Publication Date 2018-02
Journal Studies in Nonlinear Dynamics and Econometrics
Electronic ISSN 1558-3708
Publisher De Gruyter
Peer Reviewed Peer Reviewed
Volume 22
Issue 1
APA6 Citation 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), https://doi.org/10.1515/snde-2016-0076
DOI https://doi.org/10.1515/snde-2016-0076
Keywords Nonlinearity; Trend uncertainty; Union of rejections
Publisher URL https://www.degruyter.com/view/j/snde.ahead-of-print/snde-2016-0076/snde-2016-0076.xml
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf


union_kssdf.pdf (1.1 Mb)
PDF

Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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