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Cointegration and Adjustment in the CVAR(∞) Representation of Some Partially Observed CVAR(1) Models

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  • Søren Johansen

    (Department of Economics, University of Copenhagen, ∅ster Farimagsgade 5, building 26, DK-1353 Copenhagen K, Denmark)

Abstract

A multivariate CVAR(1) model for some observed variables and some unobserved variables is analysed using its infinite order CVAR representation of the observations. Cointegration and adjustment coefficients in the infinite order CVAR are found as functions of the parameters in the CVAR(1) model. Conditions for weak exogeneity for the cointegrating vectors in the approximating finite order CVAR are derived. The results are illustrated by two simple examples of relevance for modelling causal graphs.

Suggested Citation

  • Søren Johansen, 2019. "Cointegration and Adjustment in the CVAR(∞) Representation of Some Partially Observed CVAR(1) Models," Econometrics, MDPI, vol. 7(1), pages 1-10, January.
    • Handle: RePEc:gam:jecnmx:v:7:y:2019:i:1:p:2-:d:196454
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    References listed on IDEAS

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    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    2. Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, vol. 8(1), pages 1-27, March.
    3. Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(5), pages 814-844, December.
    4. Johansen, Søren & Juselius, Katarina, 2014. "An asymptotic invariance property of the common trends under linear transformations of the data," Journal of Econometrics, Elsevier, vol. 178(P2), pages 310-315.
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    3. Rocco Mosconi & Paolo Paruolo, 2022. "A Conversation with Søren Johansen," Econometrics, MDPI, vol. 10(2), pages 1-16, April.

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