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The Integration Order of Vector Autoregressive Processes

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  • Massimo Franchi

    (Department of Economics, University of Copenhagen)

Abstract

We show that the order of integration of a vector autoregressive process is equal to the difference between the multiplicity of the unit root in the characteristic equation and the multiplicity of the unit root in the adjoint matrix polynomial. The equivalence with the standard I(1) and I(2) conditions (Johansen, 1996) is proved and polynomial cointegration discussed in the general setup.

Suggested Citation

  • Massimo Franchi, "undated". "The Integration Order of Vector Autoregressive Processes," Discussion Papers 06-05, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:0605
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/2006/0605.pdf/
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    References listed on IDEAS

    as
    1. la Cour, Lisbeth, 1998. "A Parametric Characterization Of Integrated Vector Autoregressive (Var) Processes," Econometric Theory, Cambridge University Press, vol. 14(2), pages 187-199, April.
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    Cited by:

    1. Beare, Brendan K. & Seo, Won-Ki, 2020. "Representation Of I(1) And I(2) Autoregressive Hilbertian Processes," Econometric Theory, Cambridge University Press, vol. 36(5), pages 773-802, October.
    2. Arbués, Ignacio & Ledo, Ramiro & Matilla-García, Mariano, 2016. "Automatic identification of general vector error correction models," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 10, pages 1-41.
    3. 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.
    4. Massimo Franchi, 2017. "On the structure of state space systems with unit roots," DSS Empirical Economics and Econometrics Working Papers Series 2017/4, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.

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    2. Beare, Brendan K. & Seo, Won-Ki, 2020. "Representation Of I(1) And I(2) Autoregressive Hilbertian Processes," Econometric Theory, Cambridge University Press, vol. 36(5), pages 773-802, October.
    3. Massimo Franchi, 2006. "A General Representation Theorem for Integrated Vector Autoregressive Processes," Discussion Papers 06-16, University of Copenhagen. Department of Economics.
    4. Massimo Franchi, 2017. "On the structure of state space systems with unit roots," DSS Empirical Economics and Econometrics Working Papers Series 2017/4, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
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    More about this item

    Keywords

    unit roots; order of integration; polynomial cointegration;
    All these keywords.

    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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