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Cointegration between trends and their estimators in state space models and CVAR models

Author

Listed:
  • Søren Johansen

    (Department of Economics, University of Copenhagen)

  • Morten Nyboe Tabor

    (Department of Economics, University of Copenhagen)

Abstract

In a linear state space model Y(t)=BT(t)+e(t), we investigate if the unobserved trend, T(t), cointegrates with the predicted trend, E(t), and with the estimated predicted trend, in the sense that the spreads are stationary. We find that this result holds for the spread B(T(t)-E(t)) and the estimated spread. For the spread between the trend and the estimated trend, T(t)-E(t), however, cointegration depends on the identification of B. The same results are found, if the observations Y(t), from the state space model are analysed using a cointegrated vector autoregressive model, where the trend is defined as the common trend. Finally, we investigate cointegration between the spread beteween trends and their estimators based on the two models, and find the same results. We illustrate with two examples and confirm the results by a small simulation study.

Suggested Citation

  • Søren Johansen & Morten Nyboe Tabor, 2017. "Cointegration between trends and their estimators in state space models and CVAR models," Discussion Papers 17-02, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:1702
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    References listed on IDEAS

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    1. 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.
    2. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    3. 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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    Cited by:

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    4. Franchi, Massimo, 2018. "Testing for cointegration in I(1) state space systems via a finite order approximation," Economics Letters, Elsevier, vol. 165(C), pages 73-76.

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    More about this item

    Keywords

    Cointegration of trends; State space models; CVAR models;
    All these keywords.

    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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