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Seasonal Unit Root Tests under Structural Breaks

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

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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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
Date of revision:
Publication status: Published in Darmstadt Discussion Papers in Economics . 113 (2002-01)
Handle: RePEc:dar:ddpeco:37696
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  1. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
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  3. 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.
  4. 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.
  5. Breitung, J rg & Franses, Philip Hans, 1998. "On Phillips Perron-Type Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 14(02), pages 200-221, April.
  6. 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.
  7. Smith, J. & Otero, J., 1995. "Structural Breaks and Seasonal Integration," The Warwick Economics Research Paper Series (TWERPS) 435, University of Warwick, Department of Economics.
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  11. 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.
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  14. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
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  20. 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.
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