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The Integration Order Of Vector Autoregressive Processes

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  • Franchi, Massimo

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, Likelihood-Based Inference in Cointegrated Vector Auto-Regressive Models) is proved.I am very grateful to Søren Johansen for his precious insights and his continuous help throughout the development of the paper. I also thank Paolo Paruolo (the coeditor) and the referees for valuable feedback. This paper was written while the author was a Post Doc at the Department of Economics, University of Copenhagen, and the hospitality of this institution is gratefully acknowledged.

Suggested Citation

  • Franchi, Massimo, 2007. "The Integration Order Of Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 23(3), pages 546-553, June.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:03:p:546-553_07
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    Cited by:

    1. 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, vol. 10, pages 1-41.
    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. 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.

    More about this item

    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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