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On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation

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  • Burridge, Peter
  • Taylor, A M Robert

Abstract

We analyze the behavior of widely used regression-based tests for seasonal unit roots when the shocks are serially correlated. We show, in the quarterly case, that the common assumption that serial correlation may be accommodated by augmenting the test regression with appropriate lagged seasonal differences is only partially correct. The limiting null distributions of t statistics for unit roots at the zero and Nyquist frequencies are corrected by the lag augmentation, but those of t statistics at the harmonic seasonal frequency are not. Fortunately, the joint F-type tests at the harmonic frequency, which are in widespread use, do remain pivotal and should therefore supplant the individual t statistics in applied work. That the latter are indeed badly behaved in finite samples, while the F-type tests are correctly sized, is demonstrated by a Monte Carlo experiment.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 19 (2001)
Issue (Month): 3 (July)
Pages: 374-79

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Handle: RePEc:bes:jnlbes:v:19:y:2001:i:3:p:374-79

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Cited by:
  1. Luis C. Nunes & Paulo M. M. Rodrigues, 2011. "On LM‐type tests for seasonal unit roots in the presence of a break in trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 108-134, 03.
  2. 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.
  3. 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.
  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. 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. Castro, Tomás del Barrio & Osborn, Denise R. & Taylor, A.M. Robert, 2012. "On Augmented Hegy Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 28(05), pages 1121-1143, October.
  7. Artur C. B. da Silva Lopes & Antonio Montañés, 2004. "The Behavior of HEGY Tests for Quarterly Time Series with Seasonal Mean Shifts," Econometrics 0411010, EconWPA.
  8. Tomas del Barrio Castro, 2007. "Using the HEGY Procedure When Not All Roots Are Present," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(6), pages 910-922, November.
  9. Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2007. "Efficient tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 141(2), pages 548-573, December.
  10. Niels Haldrup & Antonio Montanés & Andreu Sanso, . "Measurement Errors and Outliers in Seasonal Unit Root Testing," Economics Working Papers 2000-8, School of Economics and Management, University of Aarhus.
  11. Robert Taylor, 2005. "On the limiting behaviour of augmented seasonal unit root tests," Economics Bulletin, AccessEcon, vol. 3(3), pages 1-10.
  12. Rotger, Gabriel Pons, . "Testing for Seasonal Unit Roots with Temporally Aggregated Time Series," Economics Working Papers 2003-16, School of Economics and Management, University of Aarhus.
  13. Burridge, Peter & Robert Taylor, A. M., 2004. "Bootstrapping the HEGY seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 123(1), pages 67-87, November.

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