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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

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 125.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:125

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Keywords: Seasonal unit roots; bootstrap tests; higher-order serial correlation; periodic heteroscedasticity; data-based lag selection;

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References

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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.
  2. Donald W. K. Andrews & Moshe Buchinsky, 2000. "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, Econometric Society, vol. 68(1), pages 23-52, January.
  3. 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, vol. 14(2), pages 161-68, April.
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  5. Davidson, R. & Mackinnon, J.G., 1997. "Bootstrap Tests of Nonnested Linear Regression Models," ASSET - Instituto De Economia Publica 170, ASSET (Association of Southern European Economic Theorists).
  6. 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.
  7. Hylleberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988. "Seasonal, Integration And Cointegration," Papers 6-88-2, Pennsylvania State - Department of Economics.
  8. 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, vol. 8(2), pages 251-63, April.
  9. 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.
  10. Smith, R.J. & Taylor, A.M.R., 1999. "Regression-Based Seasonal Unit Root Tests," Discussion Papers 99-15, Department of Economics, University of Birmingham.
  11. J. Joseph Beaulieu & Jeffrey A. Miron, 1992. "Seasonal Unit Roots in Aggregate U.S. Data," NBER Technical Working Papers 0126, National Bureau of Economic Research, Inc.
  12. 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 374-79, July.
  13. Andrews, Donald W. K. & Buchinsky, Moshe, 2001. "Evaluation of a three-step method for choosing the number of bootstrap repetitions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 345-386, July.
  14. 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.
  15. Psaradakis, Zacharias, 2000. "Bootstrap tests for unit roots in seasonal autoregressive models," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 389-395, December.
  16. 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, vol. 62(2), pages 415-442, June.
  17. Peter C.B. Phillips, 2001. "Bootstrapping Spurious Regression," Cowles Foundation Discussion Papers 1330, Cowles Foundation for Research in Economics, Yale University.
  18. Atsushi Inoue & Lutz Kilian, 2000. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometric Society World Congress 2000 Contributed Papers 0401, Econometric Society.
  19. Taylor, A. M. Robert, 1997. "On the practical problems of computing seasonal unit root tests," International Journal of Forecasting, Elsevier, vol. 13(3), pages 307-318, September.
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  21. Russell Davidson & James MacKinnon, 2002. "Fast Double Bootstrap Tests Of Nonnested Linear Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 419-429.
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Citations

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Cited by:
  1. repec:dgr:uvatin:2006101 is not listed on IDEAS
  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. Deckers, Thomas & Hanck, Christoph, 2009. "Multiple Testing Techniques in Growth Econometrics," MPRA Paper 17843, University Library of Munich, Germany.
  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. Smith, R.J. & Taylor, A.M.R., 1999. "Regression-Based Seasonal Unit Root Tests," Discussion Papers 99-15, Department of Economics, University of Birmingham.
  6. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
  7. 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.
  8. 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.
  9. 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.
  10. Francesco Bravo, 2010. "Nonparametric likelihood inference for general autoregressive models," Statistical Methods and Applications, Springer, vol. 19(1), pages 79-106, March.
  11. Lacroix, R., 2008. "Analyse conjoncturelle de données brutes et estimation de cycles Partie 1 : estimation et tests," Working papers 209, Banque de France.

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