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GLS-based unit root tests with multiple structural breaks both under the null and the alternative hypotheses

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Author Info

  • Josep Lluís Carrion-i-Silvestre

    ()
    (AQR Research Group, Departament of Econometrics, Statistics and Spanish Economy, University of Barcelona)

  • Dukpa Kim

    ()
    (Department of Economics, University of Virginia)

  • Pierre Perron

    ()
    (Department of Economics, Boston University)

Abstract

Perron (1989) introduced unit root tests valid when a break at a known date in the trend function of a time series is present, which are invariant to the magnitude of the shift in level and/or slope and to allow them under both the null and alternative hypotheses. The subsequent literature devised procedures valid in the case of an unknown break date. However, in doing so most, in particular the commonly used test of Zivot and Andrews (1992), assumed that if a break occurs it does so only under the alternative hypothesis of stationarity. This is undesirable for several reasons. Kim and Perron (2007) developed a methodology that allows a break at an unknown time under both the null and alternative hypotheses. When a break is present, the limit distribution of the test is the same as in the case of a known break date allowing increased power while maintaining the correct size. We extend their work in several directions: 1) we allow for an arbitrary number of changes in both the level and slope of the trend function; 2) we adopt the quasi-GLS detrending method advocated by Elliott et al. (1996) which permits tests that have local asymptotic power functions close to the local asymptotic Gaussian power envelope; 3) we consider a variety of tests, in particular the class of M-tests introduced in Stock (1999) and analyzed in Ng and Perron (2001).

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number wp2008-019.

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Length: 40
Date of creation: Sep 2007
Date of revision:
Handle: RePEc:bos:wpaper:wp2008-019

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Keywords: multiple structural breaks; unit root; GLS detrending;

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References

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  1. David Harris & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2007. "Testing for a unit root in the presence of a possible break in trend," Discussion Papers 07/04, University of Nottingham, Granger Centre for Time Series Econometrics.
  2. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Testing for Shifts in Trend With an Integrated or Stationary Noise Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 369-396.
  3. BAI, Jushan & PERRON, Pierre, 1998. "Computation and Analysis of Multiple Structural-Change Models," Cahiers de recherche 9807, Universite de Montreal, Departement de sciences economiques.
  4. PERRON, Pierre & RODRIGUEZ, Gabriel, 1998. "GLS Detrending, Efficient Unit Root Tests and Structural Change," Cahiers de recherche 9809, Universite de Montreal, Departement de sciences economiques.
  5. Perron, Pierre & Vogelsang, Timothy J, 1992. "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 301-20, July.
  6. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
  7. Leybourne, Stephen J. & C. Mills, Terence & Newbold, Paul, 1998. "Spurious rejections by Dickey-Fuller tests in the presence of a break under the null," Journal of Econometrics, Elsevier, vol. 87(1), pages 191-203, August.
  8. Perron, Pierre & Qu, Zhongjun, 2007. "A simple modification to improve the finite sample properties of Ng and Perron's unit root tests," Economics Letters, Elsevier, vol. 94(1), pages 12-19, January.
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Citations

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Cited by:
  1. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Unit root testing under a local break in trend," Journal of Econometrics, Elsevier, vol. 167(1), pages 140-167.
  2. 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.
  3. Mohitosh Kejriwal & Pierre Perron, 2010. "A sequential procedure to determine the number of breaks in trend with an integrated or stationary noise component," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 305-328, 09.
  4. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," PSE Working Papers halshs-00564897, HAL.
  5. jair Ojeda Joya, 2009. "Purchasing Power Parity and Breaking Trend Functions in the Real Exchange Rate," BORRADORES DE ECONOMIA 005521, BANCO DE LA REPÚBLICA.
  6. Mohitosh Kejriwal & Claude Lopez, 2009. "Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation," Purdue University Economics Working Papers 1227, Purdue University, Department of Economics.
  7. Ghoshray, Atanu & Kejriwal, Mohitosh & Wohar, Mark E., 2011. "Breaking Trends and the Prebisch-Singer Hypothesis: A Further Investigation," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 120387, European Association of Agricultural Economists.
  8. Manuel Gomez & Daniel Ventosa-Santaularia, 2008. "Testing for a Deterministic Trend when there is Evidence of Unit-Root," Department of Economics and Finance Working Papers EM200801, Universidad de Guanajuato, Department of Economics and Finance, revised Jun 2010.
  9. Paulo M.M. Rodrigues & A. M. Robert Taylor, 2009. "The Flexible Fourier Form and Local GLS De-trended Unit Root Tests," Working Papers w200919, Banco de Portugal, Economics and Research Department.

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