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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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  • 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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    1. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    2. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, September.
    3. 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.
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    5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    6. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    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(3), pages 587-636, June.
    10. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    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. 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. Maggie E. C. Jones & Morten Ørregaard Nielsen & Michał Ksawery Popiel, 2014. "A fractionally cointegrated VAR analysis of economic voting and political support," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 47(4), pages 1078-1130, November.
    2. Bo Zhou, 2023. "Semiparametrically Optimal Cointegration Test," Papers 2305.08880, arXiv.org.
    3. 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.
    4. Skrobotov, Anton, 2018. "On bootstrap implementation of likelihood ratio test for a unit root," Economics Letters, Elsevier, vol. 171(C), pages 154-158.
    5. Gaowen Wang, 2017. "Modified Unit Root Tests with Nuisance Parameter Free Asymptotic Distributions," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 519-538, June.
    6. Samuel Brien & Michael Jansson & Morten Ørregaard Nielsen, 2022. "Nearly Efficient Likelihood Ratio Tests of a Unit Root in an Autoregressive Model of Arbitrary Order," Working Paper 1429, Economics Department, Queen's University.
    7. 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.
    8. 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.
    9. 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.
    10. Hernández, Juan R., 2016. "Unit Root Testing in ARMA Models: A Likelihood Ratio Approach," MPRA Paper 100857, University Library of Munich, Germany.
    11. 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.
    12. Petrenko, Victoria (Петренко, ВИктория) & Skrobotov, Anton (Скроботов, Антон) & Turuntseva, Maria (Турунцева, Мария), 2016. "Testing of Changes in Persistence and Their Effect on the Forecasting Quality [Тестирование Изменения Инерционности И Влияние На Качество Прогнозов]," Working Papers 542, Russian Presidential Academy of National Economy and Public Administration.
    13. Skrobotov, Anton, 2015. "Likelihood Ratio Test for Change in Persistence," Published Papers skr001, Russian Presidential Academy of National Economy and Public Administration.
    14. Walter Distaso & Rustam Ibragimov & Alexander Semenov & Anton Skrobotov, 2020. "COVID-19: Tail Risk and Predictive Regressions," Papers 2009.02486, arXiv.org, revised Oct 2021.
    15. Hernández Juan R., 2016. "Unit Root Testing in ARMA Models: A Likelihood Ratio Approach," Working Papers 2016-03, Banco de México.
    16. 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.

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    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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