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Using the HEGY Procedure When Not All Roots Are Present

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  • Tomas del Barrio Castro

Abstract

Empirical studies have shown little evidence to support the presence of all unit roots present in the Delta_4 filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo [Journal of Econometrics (1990) Vol. 44, pp. 215-238] (HEGY) procedure when the roots under the null are not all present. We exploit the vector of quarters representation and cointegration relationship between the quarters when factors (1 - L), (1 + L), (1 + L-super-2), (1 - L-super-2) and (1 + L + L-super-2 + L-super-3) are a source of nonstationarity in a process in order to obtain the distribution of tests of the HEGY procedure when the underlying processes have a root at the zero, Nyquist frequency, two complex conjugates of frequency pi/2 and two combinations of the previous cases. We show both theoretically and through a Monte Carlo analysis that the t-ratios t and t and the F-type tests used in the HEGY procedure have the same distribution as under the null of a seasonal random walk when the root(s) is (are) present, although this is not the case for the t-ratio tests associated with unit roots at frequency pi/2. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 28 (2007)
Issue (Month): 6 (November)
Pages: 910-922

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Handle: RePEc:bla:jtsera:v:28:y:2007:i:6:p:910-922

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  1. 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.
  2. 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.
  3. 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.
  4. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  5. 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.
  6. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882, October.
  7. Hyllerberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988. "Seasonal Integration And Cointegration," Papers 0-88-2, Pennsylvania State - Department of Economics.
  8. Hylleberg, Svend & Jorgensen, Clara & Sorensen, Nils Karl, 1993. "Seasonality in Macroeconomic Time Series," Empirical Economics, Springer, vol. 18(2), pages 321-35.
  9. 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.
  10. Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2004. "Asymptotic Distributions For Regression-Based Seasonal Unit Root Test Statistics In A Near-Integrated Model," Econometric Theory, Cambridge University Press, vol. 20(04), pages 645-670, August.
  11. Taylor, A.M. Robert, 2003. "On The Asymptotic Properties Of Some Seasonal Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(02), pages 311-321, April.
  12. Osborn, Denise R., 1993. "Seasonal cointegration," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 299-303.
  13. Denise Osborn & Paulo Rodrigues, 2002. "Asymptotic Distributions Of Seasonal Unit Root Tests: A Unifying Approach," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 221-241.
  14. Castro, Tomas del Barrio & Osborn, Denise R., 2008. "Testing For Seasonal Unit Roots In Periodic Integrated Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 24(04), pages 1093-1129, August.
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Cited by:
  1. Tomás Del Barrio Castro & Denise R. Osborn, 2011. "HEGY Tests in the Presence of Moving Averages," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 691-704, October.
  2. Ghassen El Montasser, 2011. "The overall seasonal integration tests under non-stationary alternatives," Journal of Economics and Econometrics, Economics and Econometrics Research Institute (EERI), Brussels, vol. 54(1), pages 24-39.
  3. Ghassen El Montasser, 2011. "The overall seasonal integration tests under non-stationary alternatives: A methodological note," EERI Research Paper Series EERI_RP_2011_06, Economics and Econometrics Research Institute (EERI), Brussels.

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