GLS-based unit root tests with multiple structural breaks both under the null and the alternative hypotheses
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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- 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,"
07/04, University of Nottingham, Granger Centre for Time Series Econometrics.
- 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.
- 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.
- 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.
- Tom Doan, . "PERRONRODRIGUEZ: RATS procedure to perform Perron-Rodriguez unit root test allowing for break at unknown date," Statistical Software Components RTS00156, Boston College Department of Economics.
- Tom Doan, . "GLSDETREND: RATS procedure to perform local to unity GLS detrending," Statistical Software Components RTS00077, Boston College Department of Economics.
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- BAI, Jushan & PERRON, Pierre, 1998.
"Computation and Analysis of Multiple Structural-Change Models,"
Cahiers de recherche
9807, Universite de Montreal, Departement de sciences economiques.
- 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.
- 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.
- Vogelsang, T.I. & Perron, P., 1991. "Nonstationary and Level Shifts With An Application To Purchasing Power Parity," Papers 359, Princeton, Department of Economics - Econometric Research Program.
- Perron, Pierre & Qu, Zhongjun, 2007.
"A simple modification to improve the finite sample properties of Ng and Perron's unit root tests,"
Elsevier, vol. 94(1), pages 12-19, January.
- Pierre Perron & Zhongjun Qu, 2006. "A Simple Modification to Improve the Finite Sample Properties of Ng and Perron’s Unit Root Tests," Boston University - Department of Economics - Working Papers Series WP2006-010, Boston University - Department of Economics.
- Pierre Perron & Tomoyoshi Yabu, 2007.
"Testing for Shifts in Trend with an Integrated or Stationary Noise Component,"
Boston University - Department of Economics - Working Papers Series
WP2007-025, Boston University - Department of Economics.
- 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.
- Pierre Perron & Tomoyoshi Yabu, 2005. "Testing for Shifts in Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2005-026, Boston University - Department of Economics.
- Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
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