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Bootstrapping the HEGY seasonal unit root tests

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  • Burridge, Peter
  • Robert Taylor, A. M.

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

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 123 (2004)
Issue (Month): 1 (November)
Pages: 67-87

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Handle: RePEc:eee:econom:v:123:y:2004:i:1:p:67-87

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Joseph Beaulieu, J. & Miron, Jeffrey A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, Elsevier, vol. 55(1-2), pages 305-328.
  2. 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, American Statistical Association, vol. 19(3), pages 374-79, July.
  3. Davidson, R. & Mackinnon, J.G., 1997. "Bootstrap Tests of Nonnested Linear Regression Models," ASSET - Instituto De Economia Publica, ASSET (Association of Southern European Economic Theorists) 170, ASSET (Association of Southern European Economic Theorists).
  4. 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, Elsevier, vol. 62(2), pages 415-442, June.
  5. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, Elsevier, vol. 95(2), pages 375-389, April.
  6. Rayner, Robert K, 1990. "Bootstrapping p Values and Power in the First-Order Autoregression: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 8(2), pages 251-63, April.
  7. Peter C.B. Phillips, 2001. "Bootstrapping Spurious Regression," Cowles Foundation Discussion Papers 1330, Cowles Foundation for Research in Economics, Yale University.
  8. Richard J. Smith & A. M. Robert Taylor & Tomas del Barrio Castro, 2007. "Regression-based seasonal unit root tests," Discussion Papers 07/05, University of Nottingham, Granger Centre for Time Series Econometrics.
  9. Ghysels, E. & Hall, A. & Lee, H.S., 1995. "On Periodic Structures and Testing for Seasonal Unit Roots," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9518, Universite de Montreal, Departement de sciences economiques.
  10. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(02), pages 469-490, April.
  11. Russell Davidson & James MacKinnon, 2002. "Fast Double Bootstrap Tests Of Nonnested Linear Regression Models," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 21(4), pages 419-429.
  12. Smith, R.J. & Taylor, R., 1995. "Additional Critical Values and Asymptotic Representations for Seasonal Unit Roots Tests," Cambridge Working Papers in Economics 9529, Faculty of Economics, University of Cambridge.
  13. Psaradakis, Zacharias, 2000. "Bootstrap tests for unit roots in seasonal autoregressive models," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 389-395, December.
  14. Hyllerberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988. "Seasonal Integration And Cointegration," Papers, Pennsylvania State - Department of Economics 0-88-2, Pennsylvania State - Department of Economics.
  15. Nankervis, John C & Savin, N E, 1996. "The Level and Power of the Bootstrap t Test in the AR(1) Model with Trend," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 14(2), pages 161-68, April.
  16. Andrews, Donald W. K. & Buchinsky, Moshe, 2001. "Evaluation of a three-step method for choosing the number of bootstrap repetitions," Journal of Econometrics, Elsevier, Elsevier, vol. 103(1-2), pages 345-386, July.
  17. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 19(1), pages 55-68.
  18. Burridge, P. & Taylor, A.M.R., 1999. "On Regression-Based Tests for Seasonal Unit Roots in the Presence of Periodic Heteroscedasticity," Discussion Papers, Department of Economics, University of Birmingham 99-10, Department of Economics, University of Birmingham.
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Cited by:
  1. 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.
  2. Smith, R.J. & Taylor, A.M.R., 1999. "Regression-Based Seasonal Unit Root Tests," Discussion Papers, Department of Economics, University of Birmingham 99-15, Department of Economics, University of Birmingham.
  3. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
  4. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2006. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Tinbergen Institute Discussion Papers 06-101/4, Tinbergen Institute.
  5. 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.
  6. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2006. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Tinbergen Institute Discussion Papers 06-101/4, Tinbergen Institute.
  7. Deckers, Thomas & Hanck, Christoph, 2009. "Multiple Testing Techniques in Growth Econometrics," MPRA Paper 17843, University Library of Munich, Germany.
  8. Francesco Bravo, 2010. "Nonparametric likelihood inference for general autoregressive models," Statistical Methods and Applications, Springer, vol. 19(1), pages 79-106, March.
  9. Fabio Busetti & Silvestro di Sanzo, 2011. "Bootstrap LR tests of stationarity, common trends and cointegration," Temi di discussione (Economic working papers), Bank of Italy, Economic Research and International Relations Area 799, Bank of Italy, Economic Research and International Relations Area.
  10. Rodrigues, Paulo M. M. & Taylor, A. M. Robert, 2004. "Alternative estimators and unit root tests for seasonal autoregressive processes," Journal of Econometrics, Elsevier, Elsevier, vol. 120(1), pages 35-73, May.
  11. Lacroix, R., 2008. "Analyse conjoncturelle de données brutes et estimation de cycles Partie 1 : estimation et tests," Working papers, Banque de France 209, Banque de France.

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