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Likelihood based testing for no fractional cointegration

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  • Katarzyna Lasak

    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

We consider two likelihood ratio tests, so-called maximum eigenvalue and trace tests, for the null of no cointegration when fractional cointegration is allowed under the alternative, which is a first step to generalize the so-called Johansen's procedure to the fractional cointegration case. The standard cointegration analysis only considers the assumption that deviations from equilibrium can be integrated of order zero, which is very restrictive in many cases and may imply an important loss of power in the fractional case. We consider the alternative hypotheses with equilibrium deviations that can be mean reverting with order of integration possibly greater than zero. Moreover, the degree of fractional cointegration is not assumed to be known, and the asymptotic null distribution of both tests is found when considering an interval of possible values. The power of the proposed tests under fractional alternatives and size accuracy provided by the asymptotic distribution in finite samples are investigated.

Suggested Citation

  • Katarzyna Lasak, 2008. "Likelihood based testing for no fractional cointegration," CREATES Research Papers 2008-52, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2008-52
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    Citations

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    Cited by:

    1. Federico Carlini & Paolo Santucci de Magistris, 2019. "Resuscitating the co-fractional model of Granger (1986)," CREATES Research Papers 2019-02, Department of Economics and Business Economics, Aarhus University.
    2. Søren Johansen, 2010. "An Extension of Cointegration to Fractional Autoregressive Processes," Discussion Papers 10-28, University of Copenhagen. Department of Economics.
    3. Tobias Hartl & Roland Weigand, 2018. "Multivariate Fractional Components Analysis," Papers 1812.09149, arXiv.org, revised Jan 2019.
    4. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    5. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "A comparison of semiparametric tests for fractional cointegration," Statistical Papers, Springer, vol. 62(4), pages 1997-2030, August.
    6. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.
    7. Federico Carlini & Paolo Santucci de Magistris, 2019. "On the Identification of Fractionally Cointegrated VAR Models With the Condition," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 134-146, January.
    8. Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers 2014-19, Department of Economics and Business Economics, Aarhus University.
    9. Bosupeng, Mpho, 2015. "Payoffs of Education Expenditure In Botswana: Long Run Economic Growth Implications," MPRA Paper 77915, University Library of Munich, Germany, revised 2015.
    10. Katarzyna Łasak & Johannes Lont, 2020. "Observation Driven Long Run Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 551-575, February.
    11. Hui, Eddie C.M. & Chen, Jia & Chan, Ka Kwan Kevin, 2016. "Are international securitized property markets converging or diverging?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 1-10.
    12. Federico Carlini & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," Tinbergen Institute Discussion Papers 14-052/III, Tinbergen Institute.
    13. Demetrescu, Matei & Kusin, Vladimir & Salish, Nazarii, 2022. "Testing for no cointegration in vector autoregressions with estimated degree of fractional integration," Economic Modelling, Elsevier, vol. 108(C).
    14. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
    15. Federico Carlini & Paolo Santucci de Magistris, 2019. "Resuscitating the co-fractional model of Granger (1986)," Discussion Papers 19/01, University of Nottingham, Granger Centre for Time Series Econometrics.

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    Keywords

    Error correction model; Gaussian VAR model; Maximum likelihood estimation; Fractional cointegration; Likelihood ratio tests; fractional Brownian motion;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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