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Representation of Cointegrated Autoregressive Processes with Application to Fractional Processes

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  • Søren Johansen

Abstract

We analyze vector autoregressive processes using the matrix valued characteristic polynomial. The purpose of this article is to give a survey of the mathematical results on inversion of a matrix polynomial in case there are unstable roots, to study integrated and cointegrated processes. The new results are in the I(2) representation, which contains explicit formulas for the first two terms and a useful property of the third. We define a new error correction model for fractional processes and derive a representation of the solution.

Suggested Citation

  • Søren Johansen, 2009. "Representation of Cointegrated Autoregressive Processes with Application to Fractional Processes," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 121-145.
  • Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:121-145
    DOI: 10.1080/07474930802387977
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    Citations

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    Cited by:

    1. de Truchis, Gilles, 2013. "Approximate Whittle analysis of fractional cointegration and the stock market synchronization issue," Economic Modelling, Elsevier, vol. 34(C), pages 98-105.
    2. Massimo Franchi & Paolo Paruolo, 2015. "Minimality of State Space Solutions of DSGE Models and Existence Conditions for Their VAR Representation," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 613-626, December.
    3. Massimo Franchi & Paolo Paruolo, 2012. "On ABCs (and Ds) of VAR representations of DSGE models," DSS Empirical Economics and Econometrics Working Papers Series 2012/4, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    4. Johansen, Søren & Juselius, Katarina, 2014. "An asymptotic invariance property of the common trends under linear transformations of the data," Journal of Econometrics, Elsevier, vol. 178(P2), pages 310-315.
    5. Franchi, Massimo & Paruolo, Paolo, 2011. "A characterization of vector autoregressive processes with common cyclical features," Journal of Econometrics, Elsevier, vol. 163(1), pages 105-117, July.
    6. Daniela Osterrieder & Daniel Ventosa-Santaulària & J. Eduardo Vera-Valdés, 2015. "Unbalanced Regressions and the Predictive Equation," CREATES Research Papers 2015-09, Department of Economics and Business Economics, Aarhus University.
    7. repec:bla:jtsera:v:38:y:2017:i:6:p:1010-1027 is not listed on IDEAS
    8. Federico Carlini & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," CREATES Research Papers 2014-15, Department of Economics and Business Economics, Aarhus University.
    9. Chen, Xiaoyu & Chiang, Thomas C., 2016. "Stock returns and economic forces—An empirical investigation of Chinese markets," Global Finance Journal, Elsevier, vol. 30(C), pages 45-65.
    10. Tim Bollerslev & Daniela Osterrieder & Natalia Sizova & George Tauchen, 2011. "Risk and Return: Long-Run Relationships, Fractional Cointegration, and Return Predictability," CREATES Research Papers 2011-51, Department of Economics and Business Economics, Aarhus University.
    11. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    12. Massimo Franchi & Paolo Paruolo, 2017. "A general inversion theorem for cointegration," DSS Empirical Economics and Econometrics Working Papers Series 2017/3, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    13. Cathy Yi-Hsuan Chen & Thomas C. Chiang & Wolfgang Karl Härdle, 2016. "Downside risk and stock returns: An empirical analysis of the long-run and short-run dynamics from the G-7 Countries," SFB 649 Discussion Papers SFB649DP2016-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. repec:gam:jecnmx:v:5:y:2017:i:3:p:28-:d:103006 is not listed on IDEAS

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