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Improved Likelihood Ratio Tests for Cointegration Rank in the VAR Model

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Author Info

  • H. Peter Boswijk

    ()
    (University of Amsterdam)

  • Michael Jansson

    ()
    (UC Berkeley and CREATES)

  • Morten Ørregaard 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 School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-39.

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Length: 21
Date of creation: 09 2012
Date of revision:
Handle: RePEc:aah:create:2012-39

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Web page: http://www.econ.au.dk/afn/

Related research

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

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  1. Lütkepohl, Helmut & Saikkonen, Pentti & Trenkler, Carsten, 2000. "Maximum eigenvalue versus trace tests for the cointegrating rank of a VAR process," SFB 373 Discussion Papers 2000,83, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. 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.
  3. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
  4. 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.
  5. 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.
  6. Hansen, Peter Reinhard & Johansen, Soren, 1998. "Workbook on Cointegration," OUP Catalogue, Oxford University Press, number 9780198776079.
  7. Xiao, Zhijie & Phillips, Peter C.B., 1999. "Efficient Detrending In Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 15(04), pages 519-548, August.
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Cited by:
  1. Hallin, M. & Akker, R. van den & Werker, B.J.M., 2012. "Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Discussion Paper 2012-089, Tilburg University, Center for Economic Research.

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