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On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation

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  • Burridge, Peter
  • Taylor, A M Robert

Abstract

We analyze the behavior of widely used regression-based tests for seasonal unit roots when the shocks are serially correlated. We show, in the quarterly case, that the common assumption that serial correlation may be accommodated by augmenting the test regression with appropriate lagged seasonal differences is only partially correct. The limiting null distributions of t statistics for unit roots at the zero and Nyquist frequencies are corrected by the lag augmentation, but those of t statistics at the harmonic seasonal frequency are not. Fortunately, the joint F-type tests at the harmonic frequency, which are in widespread use, do remain pivotal and should therefore supplant the individual t statistics in applied work. That the latter are indeed badly behaved in finite samples, while the F-type tests are correctly sized, is demonstrated by a Monte Carlo experiment.

Suggested Citation

  • Burridge, Peter & Taylor, A M Robert, 2001. "On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 374-379, July.
  • Handle: RePEc:bes:jnlbes:v:19:y:2001:i:3:p:374-79
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    Cited by:

    1. Luis C. Nunes & Paulo M. M. Rodrigues, 2011. "On LM‐type tests for seasonal unit roots in the presence of a break in trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 108-134, March.
    2. 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(02), pages 447-476, April.
    3. 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.
    4. Harvey, David I. & van Dijk, Dick, 2006. "Sample size, lag order and critical values of seasonal unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2734-2751, June.
    5. Hanck, Christoph & Demetrescu, Matei & Kruse, Robinson, 2015. "Fixed-b Asymptotics for t-Statistics in the Presence of Time-Varying Volatility," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112916, Verein für Socialpolitik / German Economic Association.
    6. Burridge, P. & Gjorstrup, F. & Robert Taylor, A. M., 2004. "Robust Inference on Seasonal Unit Roots via a Bootstrap Applied to OECD Macroeconomic Series," Working Papers 04/08, Department of Economics, City University London.
    7. Artur C. B. da Silva Lopes & Antonio Montanes, 2005. "The Behavior Of Hegy Tests For Quarterly Time Series With Seasonal Mean Shifts," Econometric Reviews, Taylor & Francis Journals, vol. 24(1), pages 83-108.
    8. Chambers, Marcus J. & Ercolani, Joanne S. & Taylor, A.M. Robert, 2014. "Testing for seasonal unit roots by frequency domain regression," Journal of Econometrics, Elsevier, vol. 178(P2), pages 243-258.
    9. 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.
    10. Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2007. "Efficient tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 141(2), pages 548-573, December.
    11. 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.
    12. Skrobotov Anton & Cavaliere Giuseppe & Taylor Robert, 2016. "Wild Bootstrap Seasonal Unit Root Tests for Time Series with Periodic Non-Stationary Volatility," Working Papers wpaper-2016-269, Gaidar Institute for Economic Policy, revised 2016.
    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. 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.
    15. 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(05), pages 1121-1143, October.
    16. Tomás del Barrio Castro & Paulo M.M. Rodrigues & A. M. Robert Taylor, 2018. "Temporal Aggregation of Seasonally Near-Integrated Processes," DEA Working Papers 86, Universitat de les Illes Balears, Departament d'Economía Aplicada.
    17. Smith, Richard J. & Taylor, A.M. Robert & del Barrio Castro, Tomas, 2009. "Regression-Based Seasonal Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 25(02), pages 527-560, April.
    18. Politis, Dimitris, 2016. "HEGY test under seasonal heterogeneity," University of California at San Diego, Economics Working Paper Series qt2q4054kf, Department of Economics, UC San Diego.
    19. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, March.
    20. Matei Demetrescu & Christoph Hanck & Robinson Kruse, 2016. "Fixed-b Inference in the Presence of Time-Varying Volatility," CREATES Research Papers 2016-01, Department of Economics and Business Economics, Aarhus University.
    21. Mario G.R. Pagliacci & Constantin Anghelache & Alexandru Manole & Madalina Gabriela Anghel, 2016. "The Econometric Model for the Economic and Financial Analysis of Romanian International Trade," Romanian Statistical Review, Romanian Statistical Review, vol. 64(3), pages 53-66, September.
    22. Robert Taylor, 2005. "On the limiting behaviour of augmented seasonal unit root tests," Economics Bulletin, AccessEcon, vol. 3(3), pages 1-10.
    23. Łukasz Lenart, 2017. "Examination of Seasonal Volatility in HICP for Baltic Region Countries: Non-Parametric Test versus Forecasting Experiment," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 9(1), pages 29-67, March.
    24. 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.
    25. Łukasz Lenart & Mateusz Pipień, 2015. "Empirical Properties of the Credit and Equity Cycle within Almost Periodically Correlated Stochastic Processes - the Case of Poland, UK and USA," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 7(3), pages 169-186, September.

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