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An invariance property of the common trends under linear transformations of the data

Author

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  • Søren Johansen

    (Department of Economics, University of Copenhagen and CREATES, University of Aarhus)

  • Katarina Juselius

    (Department of Economics, University of Copenhagen, University of Aarhus)

Abstract

It is well known that if X(t) is a nonstationary process and Y(t) is a linear function of X(t), then cointegration of Y(t) implies cointegration of X(t). We want to find an analogous result for common trends if X(t) is generated by a finite order VAR. We first show that Y(t) has an infinite order VAR representation in terms of its prediction errors, which are a linear process in the prediction error for X(t). We then apply this result to show that the limit of the common trends for Y(t) are linear functions of the common trends for X(t). We illustrate the findings with a small analysis of the term structure of interest rates.

Suggested Citation

  • Søren Johansen & Katarina Juselius, 2010. "An invariance property of the common trends under linear transformations of the data," CREATES Research Papers 2010-72, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2010-72
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    References listed on IDEAS

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    1. Giese, Julia V., 2008. "Level, Slope, Curvature: Characterising the Yield Curve in a Cointegrated VAR Model," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 2, pages 1-20.
    2. Søren Johansen, 2009. "Representation of Cointegrated Autoregressive Processes with Application to Fractional Processes," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 121-145.
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    Cited by:

    1. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(3), pages 447-481, June.
    2. Katarina Juselius, 2021. "Searching for a Theory That Fits the Data: A Personal Research Odyssey," Econometrics, MDPI, vol. 9(1), pages 1-27, February.

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    More about this item

    Keywords

    Cointegration vectors; common trends; prediction errors.;
    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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