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Asymptotic Distributions Of Seasonal Unit Root Tests: A Unifying Approach

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  • Denise Osborn
  • Paulo Rodrigues

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.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:emetrv:v:21:y:2002:i:2:p:221-241
    DOI: 10.1081/ETC-120014350
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    References listed on IDEAS

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    17. Paulo Rodrigues & Denise Osborn, 1999. "Performance of seasonal unit root tests for monthly data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 985-1004.
    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.
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    Cited by:

    1. del Barrio Castro, Tomás & Rodrigues, Paulo M.M. & Robert Taylor, A.M., 2018. "Semi-Parametric Seasonal Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 34(2), pages 447-476, April.
    2. Rodrigues, Paulo M. M. & Taylor, A. M. Robert, 2004. "Alternative estimators and unit root tests for seasonal autoregressive processes," Journal of Econometrics, Elsevier, vol. 120(1), pages 35-73, May.
    3. Swanson, Norman R. & Urbach, Richard, 2015. "Prediction and simulation using simple models characterized by nonstationarity and seasonality," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 312-323.
    4. Haldrup, Niels & Montanes, Antonio & Sanso, Andreu, 2005. "Measurement errors and outliers in seasonal unit root testing," Journal of Econometrics, Elsevier, vol. 127(1), pages 103-128, July.
    5. Castro, Tomás del Barrio & Osborn, Denise R. & Taylor, A.M. Robert, 2012. "On Augmented Hegy Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1121-1143, October.
    6. Eric Ghysels & Denise R. Osborn & Paulo M. M. Rodrigues, 1999. "Seasonal Nonstationarity and Near-Nonstationarity," CIRANO Working Papers 99s-05, CIRANO.
    7. Zou, Nan & Politis, Dimitris N., 2021. "Bootstrap seasonal unit root test under periodic variation," Econometrics and Statistics, Elsevier, vol. 19(C), pages 1-21.
    8. del Barrio Castro, Tomas, 2006. "On the performance of the DHF tests against nonstationary alternatives," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 291-297, February.
    9. 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.
    10. Tomas del Barrio Castro, 2007. "Using the HEGY Procedure When Not All Roots Are Present," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(6), pages 910-922, November.
    11. 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.
    12. Rodrigues, Paulo M. M., 2000. "A note on the application of the DF test to seasonal data," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 171-175, April.

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    More about this item

    Keywords

    Seasonal unit roots; Asymptotic distributions; Unit root tests; Brownian motions; JEL Classification ; C12; C22;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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