Testing for a unit root against ESTAR stationarity

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...

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Main Authors: Harvey, David I., Leybourne, Stephen J., Whitehouse, Emily J.
Format: Article
Published: De Gruyter 2017
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Online Access:https://eprints.nottingham.ac.uk/43064/
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author Harvey, David I.
Leybourne, Stephen J.
Whitehouse, Emily J.
author_facet Harvey, David I.
Leybourne, Stephen J.
Whitehouse, Emily J.
author_sort Harvey, David I.
building Nottingham Research Data Repository
collection Online Access
description 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.
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spelling nottingham-430642020-05-04T18:50:33Z https://eprints.nottingham.ac.uk/43064/ Testing for a unit root against ESTAR stationarity Harvey, David I. Leybourne, Stephen J. Whitehouse, Emily J. 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. De Gruyter 2017-06-16 Article PeerReviewed Harvey, David I., Leybourne, Stephen J. and Whitehouse, Emily J. (2017) Testing for a unit root against ESTAR stationarity. Studies in Nonlinear Dynamics and Econometrics, 22 (1). p. 20160076. ISSN 1558-3708 Nonlinearity; Trend uncertainty; Union of rejections https://www.degruyter.com/view/j/snde.ahead-of-print/snde-2016-0076/snde-2016-0076.xml doi:10.1515/snde-2016-0076 doi:10.1515/snde-2016-0076
spellingShingle Nonlinearity; Trend uncertainty; Union of rejections
Harvey, David I.
Leybourne, Stephen J.
Whitehouse, Emily J.
Testing for a unit root against ESTAR stationarity
title Testing for a unit root against ESTAR stationarity
title_full Testing for a unit root against ESTAR stationarity
title_fullStr Testing for a unit root against ESTAR stationarity
title_full_unstemmed Testing for a unit root against ESTAR stationarity
title_short Testing for a unit root against ESTAR stationarity
title_sort testing for a unit root against estar stationarity
topic Nonlinearity; Trend uncertainty; Union of rejections
url https://eprints.nottingham.ac.uk/43064/
https://eprints.nottingham.ac.uk/43064/
https://eprints.nottingham.ac.uk/43064/