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Normalization in cointegrated time series systems

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  • Robert J. Rossana

Abstract

A method for normalizing cointegrating vectors is proposed for cointegrated time series systems containing multiple cointegrating vectors, a method requiring that an identity matrix appear in the normalized cointegrating matrix with unit coefficients attached to the endogenous or choice variables. The preferred method causes the normalized cointegrating matrix and the adjustment matrix to be consistent with the implications of static and dynamic economic theory. Alternative normalizations generate cointegrating and adjustment matrices that do not match up well with economic theory and do not reveal the testable restrictions implied by static economic theory. On propose une méthode pour normaliser les vecteurs co‐intégrants pour des systèmes de séries chronologiques co‐intégrées contenant de multiples vecteurs co‐intégrants. Cette méthode requiert qu'une matrice identitaire apparaisse dans la matrice co‐intégrante normalisée avec des coefficients unitaires attachés aux variables endogènes et de choix. La méthode préférée assure que la matrice co‐intégrante normalisée et la matrice d'ajustement soient consistantes avec les implications de la théorie économique statique et dynamique. Des normalisations de rechange engendrent des matrices qui s'arriment mal à la théorie économique et ne révèlent pas les restrictions vérifiables impliquées par la théorie statique.

Suggested Citation

  • Robert J. Rossana, 2009. "Normalization in cointegrated time series systems," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 42(4), pages 1547-1560, November.
  • Handle: RePEc:wly:canjec:v:42:y:2009:i:4:p:1547-1560
    DOI: 10.1111/j.1540-5982.2009.01557.x
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    References listed on IDEAS

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    1. Rossana, Robert J., 1998. "On the adjustment matrix in error correction models," Journal of Monetary Economics, Elsevier, vol. 42(2), pages 427-444, July.
    2. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    3. Rossana, Robert J, 1995. "Technology Shocks and Cointegration in Quadratic Models of the Firm," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(1), pages 5-17, February.
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