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On The Asymptotic Properties Of Some Seasonal Unit Root Tests

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  • Taylor, A.M. Robert

Abstract

This paper analyzes the large sample behavior of the seasonal unit root tests of Dickey, Hasza, and Fuller (1984, Journal of the American Statistical Association 79, 355 367) when applied to a series that admits a unit root at the zero but not seasonal spectral frequencies. We show that in such cases the Dickey et al. statistics have nondegenerate limiting distributions. Consequently, there is a nonzero probability that, taken in isolation, they will lead the applied researcher to accept the seasonal unit root null hypothesis and hence, incorrectly, take seasonal differences of the series, even asymptotically. The same conclusion holds if the process displays unit root behavior at any of the zero and or seasonal frequencies. Our results therefore prove a conjecture made on the basis of Monte Carlo simulation evidence, in Ghysels, Lee, and Noh (1994, Journal of Econometrics 62, 415 442) that the tests of Dickey et al., unlike those of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215 238), are unable to separate between unit roots at the zero and seasonal frequencies.I thank Peter Burridge, Bruce Hansen, and three anonymous referees for helpful comments on earlier drafts of this paper.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 19 (2003)
Issue (Month): 02 (April)
Pages: 311-321

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Handle: RePEc:cup:etheor:v:19:y:2003:i:02:p:311-321_19

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Cited by:
  1. 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.
  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. repec:ebl:ecbull:v:3:y:2005:i:3:p:1-10 is not listed on IDEAS
  4. Robert Taylor, 2005. "On the limiting behaviour of augmented seasonal unit root tests," Economics Bulletin, AccessEcon, vol. 3(3), pages 1-10.
  5. del Barrio Castro, Tomas, 2006. "On the performance of the DHF tests against nonstationary alternatives," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 291-297, February.

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