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Likelihood Ratio Tests for Seasonal Unit Roots

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  • Richard J. Smith
  • A. M. Robert Taylor

Abstract

This paper proposes regression‐based likelihood ratio or F tests for the seasonal unit root hypothesis which fully incorporate the implicit restrictions on the parameters associated with the deterministics. These statistics are similar both exactly and asymptotically with respect to initial values and seasonal drift parameters. The limiting representations of the statistics are presented for a general seasonal aspect. These limiting representations allow those for other scenarios concerning the deterministics to be simply obtained and provide an explanation for the similarity between critical values in apparently quite different cases of interest. We re‐examine the seasonal unit root properties of the logarithm of monthly seasonally unadjusted real industrial production in Canada.

Suggested Citation

  • Richard J. Smith & A. M. Robert Taylor, 1999. "Likelihood Ratio Tests for Seasonal Unit Roots," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(4), pages 453-476, July.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:4:p:453-476
    DOI: 10.1111/1467-9892.00149
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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. Gustavsson, Patrik & Nordström, Jonas, 1999. "The Impact of Seasonal Unit Roots and Vector ARMA Modeling on Forecasting Monthly Tourism Flows," Working Paper Series 150, Trade Union Institute for Economic Research, revised 01 Jul 2000.
    3. Taylor, A. M. Robert, 2005. "Variance ratio tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 124(1), pages 33-54, January.
    4. 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.
    5. Olivier Darné & Claude Diebolt, 2002. "A Note on Seasonal Unit Root Tests," Quality & Quantity: International Journal of Methodology, Springer, vol. 36(3), pages 305-310, August.
    6. Luis Gil-Alana, 2010. "A seasonal fractional multivariate model. A testing procedure and impulse responses for the analysis of GDP and unemployment dynamics," Empirical Economics, Springer, vol. 38(2), pages 471-501, April.
    7. Tomás Barrio Castro & Andrii Bodnar & Andreu Sansó, 2017. "Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending," Computational Statistics, Springer, vol. 32(4), pages 1533-1568, December.
    8. Tom�s del Barrio Castro & Denise R. Osborn & A.M. Robert Taylor, 2016. "The Performance of Lag Selection and Detrending Methods for HEGY Seasonal Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 35(1), pages 122-168, January.
    9. 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.
    10. 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, March.
    11. Gabriel Pons Rotger, 2004. "Seasonal Unit Root Testing Based on the Temporal Aggregation of Seasonal Cycles," Economics Working Papers 2004-1, Department of Economics and Business Economics, Aarhus University.
    12. Taiyeong Lee & David A. Dickey, 2004. "Limiting distributions of unconditional maximum likelihood unit root test statistics in seasonal time–series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 551-561, July.
    13. Rotger, Gabriel Pons, "undated". "Testing for Seasonal Unit Roots with Temporally Aggregated Time Series," Economics Working Papers 2003-16, Department of Economics and Business Economics, Aarhus University.
    14. Kunst, Robert M., 2009. "A Nonparametric Test for Seasonal Unit Roots," Economics Series 233, Institute for Advanced Studies.
    15. del Barrio Castro Tomás & Osborn Denise R, 2011. "Nonparametric Tests for Periodic Integration," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-35, February.
    16. Burridge, Peter & Taylor, A. M. Robert, 2001. "On regression-based tests for seasonal unit roots in the presence of periodic heteroscedasticity," Journal of Econometrics, Elsevier, vol. 104(1), pages 91-117, August.
    17. Burridge, Peter & Robert Taylor, A. M., 2004. "Bootstrapping the HEGY seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 123(1), pages 67-87, November.
    18. Zou, Nan & Politis, Dimitris N., 2021. "Bootstrap seasonal unit root test under periodic variation," Econometrics and Statistics, Elsevier, vol. 19(C), pages 1-21.
    19. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.
    20. Pereira, Diogo Santos & Marques, António Cardoso, 2022. "An analysis of the interactions between daily electricity demand levels in France," Utilities Policy, Elsevier, vol. 76(C).

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