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Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce

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Volume 22, Issue 1

Issues

Testing for a unit root against ESTAR stationarity

David I. Harvey
  • School of Economics, University of Nottingham, Nottingham, NG7 2RD, United Kingdom of Great Britain and Northern Ireland
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/ Stephen J. Leybourne
  • School of Economics, University of Nottingham, Nottingham, NG7 2RD, United Kingdom of Great Britain and Northern Ireland
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  • De Gruyter OnlineGoogle Scholar
/ Emily J. Whitehouse
  • Corresponding author
  • School of Economics, University of Nottingham, Nottingham, NG7 2RD, United Kingdom of Great Britain and Northern Ireland
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Published Online: 2017-06-16 | DOI: https://doi.org/10.1515/snde-2016-0076

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 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.

This article offers supplementary material which is provided at the end of the article.

Keywords: nonlinearity; trend uncertainty; union of rejections

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About the article

Published Online: 2017-06-16


Citation Information: Studies in Nonlinear Dynamics & Econometrics, Volume 22, Issue 1, 20160076, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826, DOI: https://doi.org/10.1515/snde-2016-0076.

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