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

Listed author(s):
  • 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)

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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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
Handle: RePEc:bos:wpaper:wp2008-019
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  1. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
  2. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-783, August.
  3. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
  4. 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.
  5. 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.
  6. Harris, David & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Testing For A Unit Root In The Presence Of A Possible Break In Trend," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1545-1588, December.
  7. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
  8. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
  9. 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 301-320, July.
  10. 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.
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