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Seasonal Unit Root Tests Under Structural Breaks

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Author Info
Uwe Hassler
Paulo M. M. Rodrigues

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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 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. Copyright 2004 Blackwell Publishing Ltd.

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Article provided by Blackwell Publishing in its journal Journal of Time Series Analysis.

Volume (Year): 25 (2004)
Issue (Month): 1 (01)
Pages: 33-53
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Handle: RePEc:bla:jtsera:v:25:y:2004:i:1:p:33-53

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
  3. 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. [Downloadable!]
  4. 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.
  5. 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. [Downloadable!] (restricted)
  6. J. Breitung & P. H. Franses, . "On Phillips-Perron Type Tests for Seasonal Unit Roots," Sonderforschungsbereich 373 1996-27, Humboldt Universitaet Berlin.
  7. 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. [Downloadable!] (restricted)
  8. Smith, R.J. & Taylor, A.M.R., 1999. "Regression-Based Seasonal Unit Root Tests," Discussion Papers 99-15, Department of Economics, University of Birmingham.
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  9. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238. [Downloadable!] (restricted)
    Other versions:
  10. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
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  11. repec:cup:etheor:v:10:y:1994:i:5:p:917-36 is not listed on IDEAS
  12. 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. [Downloadable!] (restricted)
  13. Uwe Hassler & Paulo M. M. Rodrigues, 2004. "Seasonal Unit Root Tests Under Structural Breaks," Journal of Time Series Analysis, Blackwell Publishing, vol. 25(1), pages 33-53, 01. [Downloadable!] (restricted)
    Other versions:
  14. 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.
    Other versions:
  15. Franses, Philip Hans & Hoek, Henk & Paap, Richard, 1997. "Bayesian analysis of seasonal unit roots and seasonal mean shifts," Journal of Econometrics, Elsevier, vol. 78(2), pages 359-380, June. [Downloadable!] (restricted)
    Other versions:
  16. 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.
    Other versions:
  17. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-62, April.
    Other versions:
  18. 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. [Downloadable!] (restricted)
  19. 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.
  20. repec:cup:etheor:v:11:y:1995:i:2:p:359-68 is not listed on IDEAS
  21. Schmidt, Peter & Lee, Junsoo, 1991. "A modification of the Schmidt-Phillips unit root test," Economics Letters, Elsevier, vol. 36(3), pages 285-289, July. [Downloadable!] (restricted)
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  22. Denise Osborn & Paulo Rodrigues, 2002. "Asymptotic Distributions Of Seasonal Unit Root Tests: A Unifying Approach," Econometric Reviews, Taylor and Francis Journals, vol. 21(2), pages 221-241. [Downloadable!] (restricted)
  23. 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.
  24. Smith, Jeremy & Otero, Jesus, 1997. "Structural breaks and seasonal integration," Economics Letters, Elsevier, vol. 56(1), pages 13-19, September. [Downloadable!] (restricted)
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  25. Ghysels, E., 1990. "On the Economic and Econometrics of Seasonality," Cahiers de recherche 9028, Universite de Montreal, Departement de sciences economiques.
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  26. PHILIP HANS FRANSES & BART HOBIJN,, 1997. "Critical values for unit root tests in seasonal time series," Journal of Applied Statistics, Taylor and Francis Journals, vol. 24(1), pages 25-48, February. [Downloadable!] (restricted)
  27. 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. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Gabriel Pons, 2006. "Testing Monthly Seasonal Unit Roots With Monthly and Quarterly Information," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(2), pages 191-209, 03. [Downloadable!] (restricted)
  2. Uwe Hassler & Paulo M. M. Rodrigues, 2002. "Seasonal Unit Root Tests under Structural Breaks," Darmstadt Discussion Papers in Economics 113, Institut für Volkswirtschaftslehre (Department of Economics), Technische Universität Darmstadt (Darmstadt University of Technology). [Downloadable!]
    Other versions:
  3. 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. [Downloadable!]
  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. [Downloadable!]
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