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GLS Detrending, Efficient Unit Root Tests and Structural Change

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Author Info
PERRON, Pierre
RODRIGUEZ, Gabriel

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Abstract

We extend the class of M-tests for a unit root analyzed by Perron and Ng (1996) and Ng and Perron (1997) to the case where a change in the trend function is allowed to occur at an unknown time. These tests M(GLS) adopt the GLS detrending approach of Dufour and King (1991) and Elliott, Rothenberg and Stock (1996) (ERS). Following Perron (1989), we consider two models : one allowing for a change in slope and the other for both a change in intercept and slope. We derive the asymptotic distribution of the tests as well as that of the feasible point optimal tests PT(GLS) suggested by ERS. The asymptotic critical values of the tests are tabulated. Also, we compute the non-centrality parameter used for the local GLS detrending that permits the tests to have 50% asymptotic power at that value. We show that the M(GLS) and PT(GLS) tests have an asymptotic power function close to the power envelope. An extensive simulation study analyzes the size and power in finite samples under various methods to select the truncation lag for the autoregressive spectral density estimator. An empirical application is also provided.

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Publisher Info
Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 9809.

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Length: 45 pages
Date of creation: 1998
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Handle: RePEc:mtl:montde:9809

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Related research
Keywords: unit root test; GLS detrending; structural change; truncation lag; information criteria;

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Find related papers by JEL classification:
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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  1. Giuseppe Cavaliere & David I. Harvey & Stephen J. Leybourne & A.M. Robert Taylor, 2008. "Testing for Unit Roots in the Presence of a Possible Break in Trend and Non-Stationary Volatility," CREATES Research Papers 2008-62, School of Economics and Management, University of Aarhus. [Downloadable!]
  2. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000. [Downloadable!]
    Other versions:
  3. Serge Coulombe, 2000. "New Evidence of Convergence Across Canadian Provinces: The Role of Urbanization," Regional Studies, Taylor and Francis Journals, vol. 34(8), pages 713-725, November. [Downloadable!] (restricted)
    Other versions:
  4. Vicente Esteve & Francisco Requena, 2006. "A Cointegration Analysis of Car Advertising and Sales Data in the Presence of Structural Change," International Journal of the Economics of Business, Taylor and Francis Journals, vol. 13(1), pages 111-128, February. [Downloadable!] (restricted)
  5. Gabriel Rodríguez & Yiagadeesen Samy, 2003. "Analysing the effects of labour standards on US export performance. A time series approach with structural change," Applied Economics, Taylor and Francis Journals, vol. 35(9), pages 1043-1051, January. [Downloadable!] (restricted)
  6. Olivier Darné & Amélie Charles, 2009. "Large shocks in U.S. macroeconomic time series: 1860–1988," Working Papers hal-00422502_v1, HAL. [Downloadable!]
  7. Heejoon Kang, 2006. "Inappropriate Detrending and Spurious Cointegration," Working Papers 2006-14, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy. [Downloadable!]
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  8. Gawon Yoon, 2003. "The time series behaviour of Brazilian inflation rate: new evidence from unit root tests with good size and power," Applied Economics Letters, Taylor and Francis Journals, vol. 10(10), pages 627-631, August. [Downloadable!] (restricted)
  9. Vicente Esteve, . "Política fiscal y productividad del trabajo en la economía española: Un análisis de series temporales," Studies on the Spanish Economy 156, FEDEA. [Downloadable!]
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  10. Juan Carlos Cuestas & Paulo Jose Regis, 2008. "Nonlinearities and the order of integration of oil prices," Working Papers 2008/15, Nottingham Trent University, Nottingham Business School, Economics Division. [Downloadable!]
  11. Juan Carlos Cuestas & Paulo Jose Regis, 2008. "Testing for PPP in Australia: evidence from unit root tests against nonlinear trend stationarity alternatives," Working Papers 2008/3, Nottingham Trent University, Nottingham Business School, Economics Division. [Downloadable!]
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  12. Daiki Maki, 2006. "Variance ratio tests for a unit root in the presence of a mean shift: small sample properties and an application to purchasing power parity," Applied Financial Economics, Taylor and Francis Journals, vol. 16(8), pages 607-615, May. [Downloadable!] (restricted)
  13. Joseph P. Byrne & Roger Perman, 2006. "Unit Roots and Structural Breaks: A Survey of the Literature," Working Papers 2006_10, Department of Economics, University of Glasgow. [Downloadable!]
  14. Josep Lluís Carrion-i-Silvestre & Dukpa Kim & Pierre Perron, 2007. "GLS-based unit root tests with multiple structural breaks both under the null and the alternative hypotheses," Boston University - Department of Economics - Working Papers Series wp2008-019, Boston University - Department of Economics. [Downloadable!]
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