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Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots

Listed author(s):
  • Michael Jansson

    ()

    (UC Berkeley and CREATES)

  • Morten Ørregaard Nielsen

    ()

    (Queen's University and CREATES)

In an important generalization of zero frequency autoregressive unit root tests, Hylleberg, Engle, Granger, and Yoo (1990) developed regression-based tests for unit roots at the seasonal frequencies in quarterly time series. We develop likelihood ratio tests for seasonal unit roots and show that these tests are "nearly efficient" in the sense of Elliott, Rothenberg, and Stock (1996), i.e. that their asymptotic local power functions are indistinguishable from the Gaussian power envelope. Nearly efficient testing procedures for seasonal unit roots have been developed, including point optimal tests based on the Neyman-Pearson Lemma as well as regression-based tests, e.g. Rodrigues and Taylor (2007). However, both require the choice of a GLS detrending parameter, which our likelihood ratio tests do not.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1224.pdf
File Function: First version 2009
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Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1224.

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Length: 22 pages
Date of creation: Nov 2009
Handle: RePEc:qed:wpaper:1224
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  1. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(03), pages 587-636, June.
  2. Joseph Beaulieu, J. & Miron, Jeffrey A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 305-328.
  3. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
  4. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, 07.
  5. 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.
  6. 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.
  7. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
  8. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-783, August.
  9. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, December.
  10. Gregoir, Stephane, 2006. "Efficient tests for the presence of a pair of complex conjugate unit roots in real time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 45-100, January.
  11. Michael Jansson, 2007. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," CREATES Research Papers 2007-12, Department of Economics and Business Economics, Aarhus University.
  12. Rothenberg, Thomas J. & Stock, James H., 1997. "Inference in a nearly integrated autoregressive model with nonnormal innovations," Journal of Econometrics, Elsevier, vol. 80(2), pages 269-286, October.
  13. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
  14. Michael Jansson & Morten Ørregaard Nielsen, 2009. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," Working Papers 1213, Queen's University, Department of Economics.
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