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Seasonal Unit Root Tests under Structural Breaks

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  • Hassler, Uwe
  • Rodrigues, Paulo M. M.

Abstract

In this paper, several seasonal unit root tests are analysed in the context of structural breaks at known time and a new break corrected test is suggested. We show that the widely used HEGY test as well as an LM variant thereof are asymptotically robust to seasonal mean shifts of finite magnitude. In finite samples, however, experiments reveal that such tests suffer from severe size distortions and power reductions when breaks are present. Hence, a new break corrected LM test is proposed in order to overcome this problem. Importantly, the correction for seasonal mean shifts bears no consequence on the limiting distributions thereby maintaining the legitimacy of canonical critical values. Moreover, although this test assumes a breakpoint a priori, it is robust in terms of misspecification of the time of the break. This asymptotic property is well reproduced in finite samples. Based on a Monte Carlo study, our new test is compared with other procedures suggested in the literature and shown to hold superior finite sample properties.

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Bibliographic Info

Paper provided by Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL) in its series Darmstadt Discussion Papers in Economics with number 37696.

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Date of creation: Jan 2002
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Publication status: Published in Darmstadt Discussion Papers in Economics . 113 (2002-01)
Handle: RePEc:dar:ddpeco:37696

Note: for complete metadata visit http://tubiblio.ulb.tu-darmstadt.de/37696/
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Related research

Keywords: Structural Breaks; Unit Roots; Seasonal Unit Root Tests;

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References

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  1. Balcombe, Kelvin, 1999. " Seasonal Unit Root Tests with Structural Breaks in Deterministic Seasonality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(4), pages 569-82, November.
  2. 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.
  3. Perron, P., 1989. "Testing For A Unit Root In A Time Series With A Changing Mean," Papers 347, Princeton, Department of Economics - Econometric Research Program.
  4. da Silva Lopes, Artur C. B., 2001. "The robustness of tests for seasonal differencing to structural breaks," Economics Letters, Elsevier, vol. 71(2), pages 173-179, May.
  5. Hyllerberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988. "Seasonal Integration And Cointegration," Papers 0-88-2, Pennsylvania State - Department of Economics.
  6. Smith, J. & Otero, J., 1995. "Structural Breaks and Seasonal Integration," The Warwick Economics Research Paper Series (TWERPS) 435, University of Warwick, Department of Economics.
  7. Richard J. Smith & A. M. Robert Taylor & Tomas del Barrio Castro, 2007. "Regression-based seasonal unit root tests," Discussion Papers 07/05, University of Nottingham, Granger Centre for Time Series Econometrics.
  8. Canova, Fabio & Hansen, Bruce E, 1995. "Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 237-52, July.
  9. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  10. Park, Joon Y. & Sung, Jaewhan, 1994. "Testing for Unit Roots in Models with Structural Change," Econometric Theory, Cambridge University Press, vol. 10(05), pages 917-936, December.
  11. J. Breitung & P. H. Franses, 1996. "On Phillips-Perron Type Tests for Seasonal Unit Roots," SFB 373 Discussion Papers 1996,27, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  12. Philip Hans Franses & Timothy J. Vogelsang, 1998. "On Seasonal Cycles, Unit Roots, And Mean Shifts," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 231-240, May.
  13. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  14. Ghysels, Eric & Lee, Hahn S. & Noh, Jaesum, 1994. "Testing for unit roots in seasonal time series : Some theoretical extensions and a Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 62(2), pages 415-442, June.
  15. Franses, Ph.H.B.F. & Hoek, H. & Paap, R., 1995. "Bayesian Analysis of Seasonal Unit Roots and Seasonal Mean Shifts," Econometric Institute Research Papers EI 9527-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  16. Amsler, Christine & Lee, Junsoo, 1995. "An LM Test for a Unit Root in the Presence of a Structural Change," Econometric Theory, Cambridge University Press, vol. 11(02), pages 359-368, February.
  17. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-87, August.
  18. Philip Hans Franses & Bart Hobijn, 1997. "Critical values for unit root tests in seasonal time series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(1), pages 25-48.
  19. Denise Osborn & Paulo Rodrigues, 2002. "Asymptotic Distributions Of Seasonal Unit Root Tests: A Unifying Approach," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 221-241.
  20. Osborn, Denise R, et al, 1988. "Seasonality and the Order of Integration for Consumption," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 50(4), pages 361-77, November.
  21. Paulo M. M. Rodrigues, 2002. "On LM type tests for seasonal unit roots in quarterly data," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 176-195, June.
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Cited by:
  1. El Montasser, Ghassen & Boufateh, Talel & Issaoui, Fakhri, 2013. "The seasonal KPSS test when neglecting seasonal dummies: a Monte Carlo analysis," MPRA Paper 46226, University Library of Munich, Germany.
  2. B. da Silva Lopes, Artur C., 2005. "Finite sample effects of pure seasonal mean shifts on Dickey-Fuller tests," MPRA Paper 125, University Library of Munich, Germany, revised May 2006.
  3. Gabriel Pons, 2006. "Testing Monthly Seasonal Unit Roots With Monthly and Quarterly Information," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 191-209, 03.
  4. Artur C. B. da Silva Lopes & Antonio Montañés, 2004. "The Behavior of HEGY Tests for Quarterly Time Series with Seasonal Mean Shifts," Econometrics 0411010, EconWPA.
  5. Junsoo Lee & Mark C. Strazicich, 2004. "Minimum LM Unit Root Test with One Structural Break," Working Papers 04-17, Department of Economics, Appalachian State University.
  6. Luís Catela Nunes & Paulo M.M. Rodrigues, 2009. "On LM-Type Tests for Seasonal Unit Roots in the Presence of a Break in Trend," Working Papers w200920, Banco de Portugal, Economics and Research Department.

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