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Numerical distribution functions of fractional unit root and cointegration tests

Author

Listed:
  • James G. MacKinnon

    (Queen's University)

  • Morten Ørregaard Nielsen

    (Queen?s University and CREATES)

Abstract

We calculate numerically the asymptotic distribution functions of likelihood ratio tests for fractional unit roots and cointegration rank. Because these distributions depend on a real-valued parameter, b, which must be estimated, simple tabulation is not feasible. Partly due to the presence of this parameter, the choice of model specification for the response surface regressions used to obtain the numerical distribution functions is more involved than is usually the case. We deal with model uncertainty by model averaging rather than by model selection. We make available a computer program which, given the dimension of the problem, q, and a value of b, provides either a set of critical values or the asymptotic P value for any value of the likelihood ratio statistic. The use of this program is illustrated by means of an empirical example involving opinion poll data.

Suggested Citation

  • James G. MacKinnon & Morten Ørregaard Nielsen, 2010. "Numerical distribution functions of fractional unit root and cointegration tests," CREATES Research Papers 2010-59, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2010-59
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    File URL: https://repec.econ.au.dk/repec/creates/rp/10/rp10_59.pdf
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    References listed on IDEAS

    as
    1. Box-Steffensmeier, Janet M. & Smith, Renée M., 1996. "The Dynamics of Aggregate Partisanship," American Political Science Review, Cambridge University Press, vol. 90(3), pages 567-580, September.
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    More about this item

    Keywords

    Cofractional process; fractional unit root; fractional cointegration; response surface regression; cointegration rank; numerical distribution function; model averaging.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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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