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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, by simulations, numerical 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.

Suggested Citation

  • James G. MacKinnon & Morten Ørregaard Nielsen, 2012. "Numerical distribution functions of fractional unit root and cointegration tests," Working Papers 1240, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:1240
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    File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1240.pdf
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    Citations

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    Cited by:

    1. Daniela Osterrieder, 2013. "Interest Rates with Long Memory: A Generalized Affine Term-Structure Model," CREATES Research Papers 2013-17, Department of Economics and Business Economics, Aarhus University.
    2. Gagnon, Marie-Hélène & Power, Gabriel J. & Toupin, Dominique, 2016. "International stock market cointegration under the risk-neutral measure," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 243-255.
    3. Dolatabadi, Sepideh & Nielsen, Morten Ørregaard & Xu, Ke, 2016. "A fractionally cointegrated VAR model with deterministic trends and application to commodity futures markets," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 623-639.
    4. Sepideh Dolatabadi & Morten Ørregaard Nielsen & Ke Xu, 2015. "A Fractionally Cointegrated VAR Analysis of Price Discovery in Commodity Futures Markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(4), pages 339-356, April.
    5. Baruník, Jozef & Dvořáková, Sylvie, 2015. "An empirical model of fractionally cointegrated daily high and low stock market prices," Economic Modelling, Elsevier, vol. 45(C), pages 193-206.
    6. Orregaard Nielsen, Morten & Shibaev, Sergei S., 2015. "Forecasting daily political opinion polls using the fractionally cointegrated VAR model," Queen's Economics Department Working Papers 274666, Queen's University - Department of Economics.
    7. Vadim Kufenko & Niels Geiger, 2016. "Business cycles in the economy and in economics: an econometric analysis," Scientometrics, Springer;Akadémiai Kiadó, vol. 107(1), pages 43-69, April.
    8. repec:kap:compec:v:50:y:2017:i:1:d:10.1007_s10614-016-9586-z is not listed on IDEAS
    9. Clements, A.E. & Hurn, A.S. & Volkov, V.V., 2016. "Common trends in global volatility," Journal of International Money and Finance, Elsevier, vol. 67(C), pages 194-214.
    10. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.

    More about this item

    Keywords

    fractional unit root; fractional cointegration; likelihood ratio test; model averaging; numerical CDF; response surface regression;

    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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