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Improved Likelihood Ratio Tests for Cointegration Rank in the VAR Model

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  • H. Peter Boswijk

    (University of Amsterdam)

  • Michael Jansson

    (UC Berkeley, and CREATES)

  • Morten �. Nielsen

    (Queen's University, and CREATES)

Abstract

We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but of course the asymptotic results apply more generally. The power gains relative to existing tests are due to two factors. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott, Rothenberg, and Stock (1996). Secondly, our tests incorporate a 'sign' restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 12-097/III.

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Date of creation: 21 Sep 2012
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Handle: RePEc:dgr:uvatin:20120097

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Web page: http://www.tinbergen.nl

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Keywords: Cointegration rank; efficiency; likelihood ratio test; vector autoregression;

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References

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  1. Michael Jansson & Morten Ørregaard Nielsen, 2009. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," CREATES Research Papers 2009-37, School of Economics and Management, University of Aarhus.
  2. Xiao, Zhijie & Phillips, Peter C.B., 1999. "Efficient Detrending In Cointegrating Regression," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 15(04), pages 519-548, August.
  3. Hubrich, Kirstin & Lütkepohl, Helmut & Saikkonen, Pentti, 1998. "A review of systemscointegration tests," SFB 373 Discussion Papers 1998,101, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  4. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, Elsevier, vol. 81(1), pages 93-126, November.
  5. H. Lütkepohl & P. Saikkonen, 1997. "Testing for the Cointegrating Rank of a VAR Process with a Time Trend," SFB 373 Discussion Papers 1997,79, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. Helmut Lütkepohl & Pentti Saikkonen & Carsten Trenkler, 2001. "Maximum eigenvalue versus trace tests for the cointegrating rank of a VAR process," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 4(2), pages 8.
  7. Hansen, Peter Reinhard & Johansen, Soren, 1998. "Workbook on Cointegration," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198776079, October.
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Cited by:
  1. Marc Hallin & Ramon van den Akker & Bas Werker, 2012. "Rank-Based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Working Papers ECARES, ULB -- Universite Libre de Bruxelles ECARES 2012-042, ULB -- Universite Libre de Bruxelles.

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