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Asymptotic Distributions Of Seasonal Unit Root Tests: A Unifying Approach

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Author Info
Denise Osborn
Paulo Rodrigues

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Abstract

This paper adopts a unified approach to the derivation of the asymptotic distributions of various seasonal unit root tests. The procedures considered are those of Dickey et al. [DHF], Kunst, Hylleberg et al. [HEGY], Osborn et al. [OCSB], Ghysels et al. [GHL] and Franses. This unified approach shows that the asymptotic distributions of all these test statistics are functions of the same vector of Brownian motions. The Kunst test and the overall HEGY F-test are, indeed, equivalent both asymptotically and in finite samples, while the Franses and GHL tests are shown to have equivalent parameterizations. The OCSB and DHF test regressions are viewed as restricted forms of the Kunst-HEGY regressions, and these restrictions may have non-trivial asymptotic implications.

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File URL: http://www.informaworld.com/openurl?genre=article&doi=10.1081/ETC-120014350&magic=repec&7C&7C8674ECAB8BB840C6AD35DC6213A474B5
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Publisher Info
Article provided by Taylor and Francis Journals in its journal Econometric Reviews.

Volume (Year): 21 (2002)
Issue (Month): 2 ()
Pages: 221-241
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Handle: RePEc:taf:emetrv:v:21:y:2002:i:2:p:221-241

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Related research
Keywords: Seasonal unit roots; Asymptotic distributions; Unit root tests; Brownian motions; JEL+Classification> JEL Classification; C12; C22;

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. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Blackwell Publishing, vol. 53(4), pages 473-95, August. [Downloadable!] (restricted)
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  2. 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.
  3. Hylleberg, Svend, 1995. "Tests for seasonal unit roots general to specific or specific to general?," Journal of Econometrics, Elsevier, vol. 69(1), pages 5-25, September. [Downloadable!] (restricted)
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  4. Ghysels, E. & Hall, A. & Lee, H.S., 1995. "On Periodic Structures and Testing for Seasonal Unit Roots," Cahiers de recherche 9518, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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  5. 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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  6. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December. [Downloadable!] (restricted)
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  7. 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)
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  8. 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)
  9. Dickey, David A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 329-331. [Downloadable!] (restricted)
  10. Paulo M. M. Rodrigues, Denise R. Osborn, 1999. "Performance of seasonal unit root tests for monthly data," Journal of Applied Statistics, Taylor and Francis Journals, vol. 26(8), pages 985-1004, December. [Downloadable!] (restricted)
  11. Smith, Richard J. & Taylor, A. M. Robert, 1998. "Additional critical values and asymptotic representations for seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 85(2), pages 269-288, August. [Downloadable!] (restricted)
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  12. 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)
  13. Joseph Beaulieu, J. & Miron, Jeffrey A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 305-328. [Downloadable!] (restricted)
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  14. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)
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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. Sandra G. Feltham & David E.A. Giles, 1999. "Testing for Unit Roots in Semi-Annual Data," Econometrics Working Papers 9912, Department of Economics, University of Victoria. [Downloadable!]
  2. Eric Ghysels & Denise R. Osborn & Paulo M. M. Rodrigues, 1999. "Seasonal Nonstationarity and Near-Nonstationarity," CIRANO Working Papers 99s-05, CIRANO. [Downloadable!]
  3. Tomas del Barrio Castro, 2007. "Using the HEGY Procedure When Not All Roots Are Present," Working Papers in Economics 170, Universitat de Barcelona. Espai de Recerca en Economia. [Downloadable!]
    Other versions:
  4. 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!]
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  5. Niels Haldrup & Antonio Montanés & Andreu Sanso, . "Measurement Errors and Outliers in Seasonal Unit Root Testing," Economics Working Papers 2000-8, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
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