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Testing for a unit root against ESTAR stationarity

Lookup NU author(s): Dr Emily Whitehouse



This is the authors' accepted manuscript of an article that has been published in its final definitive form by De Gruyter, 2017.

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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 KSS test (Kapetanios, G., Y. Shin, and A. Snell. 2003. “Testing for a Unit Root in the Nonlinear STAR Framework.” Journal of Econometrics 112: 359–379) 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.

Publication metadata

Author(s): Harvey DI, Leybourne SJ, Whitehouse EJ

Publication type: Article

Publication status: Published

Journal: Studies in Nonlinear Dynamics and Econometrics

Year: 2017

Volume: 22

Issue: 1

Print publication date: 01/02/2018

Online publication date: 16/06/2017

Acceptance date: 22/05/2017

Date deposited: 05/07/2018

ISSN (print): 1081-1826

ISSN (electronic): 1558-3708

Publisher: De Gruyter


DOI: 10.1515/snde-2016-0076


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