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

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  • Søren Johansen

    (University of Copenhagen and CREATES)

  • Morten Nyboe Tabor

    (University of Copenhagen)

Abstract

In a linear state space model, y_{t+1}=BT_{t}+eps_{t+1}, we investigate if the unobserved trend, T_{t}, cointegrates with the extracted trend E_{t}T_{t}, and with the estimated trend E^_{t}T_{t}, in the sense that the spreads T_{t}-E_{t}T_{t} and E_{t}T_{t}-E^_{t}T_{t} are stationary. We find that this result holds for BT_{t}-BE_{t}T_{t} and BE_{t}T_{t}-B^E^_{t}T_{t}. For the trends T_{t} and E^_{t}T_{t}, however, this type cointegration depends on the identification of B and T_{t}. 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 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," CREATES Research Papers 2017-11, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2017-11
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    References listed on IDEAS

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

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    4. Kevin D. Hoover, 2020. "The Discovery of Long-Run Causal Order: A Preliminary Investigation," Econometrics, MDPI, vol. 8(3), pages 1-25, August.

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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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