Testing for a unit root against ESTAR stationarity

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

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.

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

• 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
• DOI: https://doi.org/10.1515/snde-2016-0076
• Keywords: Nonlinearity; Trend uncertainty; Union of rejections
• Public URL: https://nottingham-repository.worktribe.com/output/866570
• Publisher URL: https://www.degruyter.com/view/j/snde.ahead-of-print/snde-2016-0076/snde-2016-0076.xml