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Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis

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  • Michael Jansson
  • Morten Ørregaard Nielsen

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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Suggested Citation

  • 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.
  • Handle: RePEc:ecm:emetrp:v:80:y:2012:i:5:p:2321-2332
    DOI: ECTA10306
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    References listed on IDEAS

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    1. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-469, December.
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    4. 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.
    5. 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.
    6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    7. 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.
    8. 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.
    9. 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.
    10. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    11. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    12. 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.
    13. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
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    Citations

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    Cited by:

    1. Jansson Michael & Nielsen Morten Ørregaard, 2011. "Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-21, February.
    2. Maggie E. C. Jones & Morten Ørregaard Nielsen & Micha Ksawery Popiel, 2014. "A fractionally cointegrated VAR analysis of economic voting and political support," Canadian Journal of Economics, Canadian Economics Association, vol. 47(4), pages 1078-1130, November.
    3. Skrobotov Anton, 2018. "On Bootstrap Implementation of Likelihood Ratio Test for a Unit Root," Working Papers wpaper-2018-302, Gaidar Institute for Economic Policy, revised 2018.
    4. Popiel Michal Ksawery, 2017. "Interest rate pass-through: a nonlinear vector error-correction approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(5), pages 1-20, December.
    5. Boswijk, H. Peter & Jansson, Michael & Nielsen, Morten Ørregaard, 2015. "Improved likelihood ratio tests for cointegration rank in the VAR model," Journal of Econometrics, Elsevier, vol. 184(1), pages 97-110.
    6. Hernández Juan R., 2016. "Unit Root Testing in ARMA Models: A Likelihood Ratio Approach," Working Papers 2016-03, Banco de México.
    7. Bent Jesper Christensen & Robinson Kruse & Philipp Sibbertsen, 2013. "A unified framework for testing in the linear regression model under unknown order of fractional integration," CREATES Research Papers 2013-35, Department of Economics and Business Economics, Aarhus University.
    8. Mehdi Hosseinkouchack & Uwe Hassler, 2016. "Powerful Unit Root Tests Free of Nuisance Parameters," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 533-554, July.
    9. Skrobotov, Anton, 2015. "Likelihood Ratio Test for Change in Persistence," Published Papers skr001, Russian Presidential Academy of National Economy and Public Administration.
    10. James Morley & Irina B. Panovska & Tara M. Sinclair, 2014. "Testing Stationarity for Unobserved Components Models," Discussion Papers 2012-41B, School of Economics, The University of New South Wales.

    More about this item

    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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