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Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis

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  • Michael Jansson

    ()
    (UC Berkeley and CREATES)

  • Morten Ørregaard Nielsen

    ()
    (Queen's University and CREATES)

Abstract

Seemingly absent from the arsenal of currently available "nearly efficient" testing procedures for the unit root hypothesis, i.e. tests whose local asymptotic power functions are indistinguishable from the Gaussian power envelope, is a test admitting a (quasi-)likelihood ratio interpretation. We show that the likelihood ratio unit root test derived in a Gaussian AR(1) model with standard normal innovations is nearly efficient in that model. Moreover, these desirable properties carry over to more complicated models allowing for serially correlated and/or non-Gaussian innovations.

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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 2009-37.

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Length: 16
Date of creation: 31 Aug 2009
Date of revision:
Handle: RePEc:aah:create:2009-37

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

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Keywords: Likelihood Ratio Test; Unit Root Hypothesis;

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References

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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, Cambridge University Press, vol. 25(03), pages 587-636, June.
  2. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 12(5), pages 423-69, December.
  3. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, Econometric Society, vol. 69(6), pages 1519-1554, November.
  4. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  5. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0130, National Bureau of Economic Research, Inc.
  6. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, Econometric Society, vol. 71(4), pages 1269-1286, 07.
  7. Michael Jansson, 2007. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," CREATES Research Papers, School of Economics and Management, University of Aarhus 2007-12, School of Economics and Management, University of Aarhus.
  8. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 12(2-3), pages 231-254.
  9. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 49(4), pages 1057-72, June.
  10. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1551-80, November.
  11. repec:cup:cbooks:9780521496032 is not listed on IDEAS
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Cited by:
  1. Maggie E.C. Jones & Morten Ørregaard Nielsen & Michal Ksawery Popiel, 2014. "A fractionally cointegrated VAR analysis of economic voting and political support," Working Papers, Queen's University, Department of Economics 1326, Queen's University, Department of Economics.
  2. Joakim Westerlund, . "On the Asymptotic Distribution of the DF–GLS Test Statistic," Financial Econometics Series, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance 2014_03, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  3. Christensen, Bent Jesper & Kruse, Robinson & Sibbertsen, Philipp, 2013. "A unified framework for testing in the linear regression model under unknown order of fractional integration," Hannover Economic Papers (HEP), Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät dp-519, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  4. H. Peter Boswijk & Michael Jansson & Morten �. Nielsen, 2012. "Improved Likelihood Ratio Tests for Cointegration Rank in the VAR Model," Tinbergen Institute Discussion Papers, Tinbergen Institute 12-097/III, Tinbergen Institute.

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