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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. Catherine Doz & Pierre Malgrange, 1992. "Modèles VAR et prévisions à court terme," Économie et Prévision, Programme National Persée, vol. 106(5), pages 109-122.
    4. 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.
    5. 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.
    6. 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.
    7. Comte, F., 1998. "Discrete and continuous time cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 207-226, November.
    8. 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.
    9. 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.
    10. Paruolo, Paolo & Rahbek, Anders, 1999. "Weak exogeneity in I(2) VAR systems," Journal of Econometrics, Elsevier, vol. 93(2), pages 281-308, December.
    11. 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.

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