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Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots

Author

Listed:
  • Michael Jansson

    () (UC Berkeley and CREATES)

  • Morten Ørregaard Nielsen

    () (Queen's University and CREATES)

Abstract

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.

Suggested Citation

  • Michael Jansson & Morten Ørregaard Nielsen, 2009. "Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots," Working Papers 1224, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:1224
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    File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1224.pdf
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    References listed on IDEAS

    as
    1. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    2. 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.
    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. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, September.
    5. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    6. Michael Jansson & Morten Ørregaard Nielsen, 2012. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 80(5), pages 2321-2332, September.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    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. 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.
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    Keywords

    Likelihood Ratio Test; Seasonal Unit Root Hypothesis;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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