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The cointegrated vector autoregressive model with general deterministic terms

Author

Listed:
  • Søren Johansen

    (Department of Economics, University of Copenhagen)

  • Morten Ørregaard Nielsen

    (Department of Economics, Queen's University, Ontario)

Abstract

In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive unified treatment of deterministic terms in the additive model X(t)=Z(t) + Y(t), where Z(t) belongs to a large class of deterministic regressors and Y(t) is a zero-mean CVAR. We suggest an extended model that can be estimated by reduced rank regression and give a condition for when the additive and extended models are asymptotically equivalent, as well as an algorithm for deriving the additive model parameters from the extended model parameters. We derive asymptotic properties of the maximum likelihood estimators and discuss tests for rank and tests on the deterministic terms. In particular, we give conditions under which the estimators are asymptotically (mixed) Gaussian, such that associated tests are khi squared distributed.

Suggested Citation

  • Søren Johansen & Morten Ørregaard Nielsen, 2016. "The cointegrated vector autoregressive model with general deterministic terms," Discussion Papers 16-07, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:1607
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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. Brian Chi-ang Lin & Siqi Zheng & Felix Pretis & Lea Schneider & Jason E. Smerdon & David F. Hendry, 2016. "Detecting Volcanic Eruptions In Temperature Reconstructions By Designed Break-Indicator Saturation," Journal of Economic Surveys, Wiley Blackwell, vol. 30(3), pages 403-429, July.
    3. Haldrup, Niels, 1996. "Mirror image distributions and the Dickey-Fuller regression with a maintained trend," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 301-312.
    4. Saikkonen, Pentti & L tkepohl, Helmut, 2000. "Testing For The Cointegrating Rank Of A Var Process With An Intercept," Econometric Theory, Cambridge University Press, vol. 16(03), pages 373-406, June.
    5. Søren Johansen & Rocco Mosconi & Bent Nielsen, 2000. "Cointegration analysis in the presence of structural breaks in the deterministic trend," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 216-249.
    6. Lutkepohl, Helmut & Saikkonen, Pentti, 2000. "Testing for the cointegrating rank of a VAR process with a time trend," Journal of Econometrics, Elsevier, vol. 95(1), pages 177-198, March.
    7. Lutkepohl, Helmut & Saikkonen, Pentti & Trenkler, Carsten, 2003. "Comparison of tests for the cointegrating rank of a VAR process with a structural shift," Journal of Econometrics, Elsevier, vol. 113(2), pages 201-229, April.
    8. Doornik, Jurgen A & Hendry, David F & Nielsen, Bent, 1998. " Inference in Cointegrating Models: UK M1 Revisited," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 533-572, December.
    9. Giuseppe Cavaliere & Anders Rahbek & Taylor A.M.Robert, 2011. "Bootstrap determination of the co-integration rank in VAR models," Quaderni di Dipartimento 9, Department of Statistics, University of Bologna.
    10. Heino Bohn Nielsen, 2004. "Cointegration analysis in the presence of outliers," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 249-271, June.
    11. Nielsen, Bent & Rahbek, Anders, 2000. " Similarity Issues in Cointegration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(1), pages 5-22, February.
    12. Johansen, Soren, 2006. "Statistical analysis of hypotheses on the cointegrating relations in the I(2) model," Journal of Econometrics, Elsevier, vol. 132(1), pages 81-115, May.
    13. David F. Hendry & Katarina Juselius, 2001. "Explaining Cointegration Analysis: Part II," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 75-120.
    14. Soren Johansen, 2002. "A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model," Econometrica, Econometric Society, vol. 70(5), pages 1929-1961, September.
    15. Saikkonen, Pentti & Lutkepohl, Helmut, 2000. "Testing for the Cointegrating Rank of a VAR Process with Structural Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 451-464, October.
    16. Søren Johansen & Rocco Mosconi & Bent Nielsen, 2000. "Cointegration analysis in the presence of structural breaks in the deterministic trend," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 216-249.
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    More about this item

    Keywords

    Additive formulation; cointegration; deterministic terms; extended model; likelihood inference; VAR model;

    JEL classification:

    • 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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