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Multivariate Time Series: A Polynomial Error Correction Representation Theorem

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  • Gregoir, Stéphane
  • Laroque, Guy

Abstract

We consider a class of multivariate processes which, when differenced enough, yield covariance stationary processes whose determinants of the Wold representation have I as their only root on the unit circle. A representation theorem is proved for this class of processes that generalizes the Granger representation theorem.

Suggested Citation

  • Gregoir, Stéphane & Laroque, Guy, 1993. "Multivariate Time Series: A Polynomial Error Correction Representation Theorem," Econometric Theory, Cambridge University Press, vol. 9(3), pages 329-342, June.
    • Handle: RePEc:cup:etheor:v:9:y:1993:i:03:p:329-342_00
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    Citations

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    Cited by:

    1. Paruolo, Paolo, 1996. "On the determination of integration indices in I(2) systems," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 313-356.
    2. Antoine d'Autume, 1992. "Coïntégration et modèles dynamiques," Économie et Prévision, Programme National Persée, vol. 106(5), pages 71-83.
    3. Fragiskos Archontakis, 1998. "An alternative proof of Granger’s Representation Theorem forI(1) systems through Jordan matrices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(2), pages 111-127, August.
    4. Anindya Banerjee & Lynne Cockerell & Bill Russell, 2001. "An I(2) analysis of inflation and the markup," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 221-240.
    5. Murasawa Yasutomo, 2022. "Bayesian multivariate Beveridge–Nelson decomposition of I(1) and I(2) series with cointegration," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 26(3), pages 387-415, June.
    6. Banerjee, A. & Russell, B., 1999. "The Relationship Between the Markup and Inflation in the G7 Plus One Economies," Economics Series Working Papers 99205, University of Oxford, Department of Economics.
    7. Breitung, Jörg, 1998. "On model based seasonal adjustment procedures," SFB 373 Discussion Papers 1998,12, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Paruolo, Paolo & Rahbek, Anders, 1999. "Weak exogeneity in I(2) VAR systems," Journal of Econometrics, Elsevier, vol. 93(2), pages 281-308, December.
    9. Catherine Doz & Pierre Malgrange, 1992. "Modèles VAR et prévisions à court terme," Économie et Prévision, Programme National Persée, vol. 106(5), pages 109-122.
    10. Paolo Paruolo, 1994. "The role of the drift in I(2) systems," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 3(1), pages 93-123, February.
    11. Comte, F., 1998. "Discrete and continuous time cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 207-226, November.

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