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Numerical Distribution Functions Of Fractional Unit Root And Cointegration Tests

Author

Listed:
  • James G. MacKinnon

    (Queen's University)

  • Morten Ø. 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 real valued parameters, d and b, which must be estimated, simple tabulation isnot feasible. Partly due to the presence of these parameters, 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 modelaveraging rather than by model selection. We make available a computer program which, given the dimension of the problem, q, and values of d and b, provides either a set of critical values or the asymptotic P value for any value of the likelihood ratio statistic.

Suggested Citation

  • James G. MacKinnon & Morten Ø. Nielsen, 2010. "Numerical Distribution Functions Of Fractional Unit Root And Cointegration Tests," Working Paper 1240, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1240
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    References listed on IDEAS

    as
    1. Søren Johansen & Morten Ørregaard Nielsen, 2012. "Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model," Econometrica, Econometric Society, vol. 80(6), pages 2667-2732, November.
    2. MacKinnon, James G & Haug, Alfred A & Michelis, Leo, 1999. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 563-577, Sept.-Oct.
    3. 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.
    4. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    5. Johansen, SÃÿren & ßrregaard Nielsen, Morten, 2010. "Likelihood inference for a fractionally cointegrated vector autoregressive model," Queen's Economics Department Working Papers 273737, Queen's University - Department of Economics.
    6. Johansen, Søren & Nielsen, Morten Ørregaard, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Journal of Econometrics, Elsevier, vol. 158(1), pages 51-66, September.
    7. MacKinnon, James G., 1995. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Queen's Economics Department Working Papers 273322, Queen's University - Department of Economics.
    8. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(3), pages 651-676, June.
    9. 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.
    10. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-618, Nov.-Dec..
    11. Johansen, Soren & Orregaard Nielsen, Morten, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Queen's Economics Department Working Papers 273648, Queen's University - Department of Economics.
    12. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    13. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
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    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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