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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 & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," Tinbergen Institute Discussion Papers 14-052/III, Tinbergen Institute.
    2. Søren Johansen, 2010. "An Extension of Cointegration to Fractional Autoregressive Processes," Discussion Papers 10-28, University of Copenhagen. Department of Economics.
    3. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    4. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.
    5. 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.
    6. Bosupeng, Mpho, 2015. "Payoffs of Education Expenditure In Botswana: Long Run Economic Growth Implications," MPRA Paper 77915, University Library of Munich, Germany, revised 2015.
    7. Paolo Santucci de Magistris & Federico Carlini, 2014. "On the identification of fractionally cointegrated VAR models with the F(d) condition," CREATES Research Papers 2014-43, Department of Economics and Business Economics, Aarhus University.
    8. 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.

    More about this item

    Keywords

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

    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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