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Bootstrapping the HEGY Seasonal Unit Root Tests

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  • Robert Taylor
  • Peter Burridge

Abstract

This paper proposes bootstrap versions of the seasonal unit root tests of, inter alia, Hylleberg, Engle, Granger and Yoo (1990,Journal of Econometrics 55, 305-328)[HEGY]. We report a simulation study of the properties of both the conventional and bootstrapped seasonal unit root tests when applied to series having higher-order serial correlation and/or periodic heteroscedasticity, both of which are known to severely distort the significance level of the conventional tests. Our results demonstrate that the bootstrap provides good approximations to the statistics' null distributions. Moreover, the bootstrap corrects the adverse effects of data-dependent lag selection seen in the conventional augmented HEGY tests. The bootstrapped tests have comparable power to (infeasible) exactly significance-level-corrected lag-augmented HEGY tests, and their use is recommended

Suggested Citation

  • Robert Taylor & Peter Burridge, 2004. "Bootstrapping the HEGY Seasonal Unit Root Tests," Econometric Society 2004 North American Summer Meetings 125, Econometric Society.
    • Handle: RePEc:ecm:nasm04:125
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    1. Ghysels, E. & Hall, A. & Lee, H.S., 1995. "On Periodic Structures and Testing for Seasonal Unit Roots," Cahiers de recherche 9518, Universite de Montreal, Departement de sciences economiques.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    5. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2009. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 683-713, October.
    6. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, September.
    7. Kemal Çag̃lar Gög̃ebakan & Burak Alparslan Eroglu, 2022. "Non-parametric seasonal unit root tests under periodic non-stationary volatility," Computational Statistics, Springer, vol. 37(5), pages 2581-2636, November.
    8. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.
    9. 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(2), pages 527-560, April.
    10. 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.
    11. Deckers, Thomas & Hanck, Christoph, 2009. "Multiple Testing Techniques in Growth Econometrics," MPRA Paper 17843, University Library of Munich, Germany.
    12. Francesco Bravo, 2010. "Nonparametric likelihood inference for general autoregressive models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(1), pages 79-106, March.
    13. Fabio Busetti & Silvestro di Sanzo, 2011. "Bootstrap LR tests of stationarity, common trends and cointegration," Temi di discussione (Economic working papers) 799, Bank of Italy, Economic Research and International Relations Area.
    14. Lacroix, R., 2008. "Analyse conjoncturelle de données brutes et estimation de cycles Partie 1 : estimation et tests," Working papers 209, Banque de France.
    15. Zou, Nan & Politis, Dimitris N., 2021. "Bootstrap seasonal unit root test under periodic variation," Econometrics and Statistics, Elsevier, vol. 19(C), pages 1-21.

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    More about this item

    Keywords

    Seasonal unit roots; bootstrap tests; higher-order serial correlation; periodic heteroscedasticity; data-based lag selection;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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