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On Augmented HEGY Tests for Seasonal Unit Roots

  • Tomás del Barrio Castro
  • Denise R. Osborn
  • A.M. Robert Taylor

In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey ( 1984 , Biometrika 71, 599–607) and Chang and Park ( 2002 , Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo ( 1990 , Journal of Econometrics 44, 215–238), inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park ( 2002 ), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t -statistics for unit roots at the zero and Nyquist frequencies and joint F -type statistics are pivotal, whereas those of the t -statistics at the harmonic seasonal frequencies depend on nuisance parameters that derive from the lag parameters characterizing the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park ( 2002 ); in particular, an o (T 1/2 ) rate is shown to be sufficient.

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Paper provided by Economics, The University of Manchester in its series The School of Economics Discussion Paper Series with number 1121.

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Date of creation: 2011
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Handle: RePEc:man:sespap:1121
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  1. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 461-70, October.
  2. Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  4. 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.
  5. Paulo M.M. Rodrigues & A.M. Robert Taylor, . "Efficient Tests of the Seasonal Unit Root Hypothesis," Discussion Papers 06/12, University of Nottingham, School of Economics.
  6. 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.
  7. Richard Smith & Robert Taylor, . "Additional Critical Values and Asymptotic Representations for Seasonal Unit Root Tests," Discussion Papers 95/43, Department of Economics, University of York.
  8. 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.
  9. 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.
  10. 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.
  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. 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.
  13. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
  14. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
  15. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, March.
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