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The cointegrated vector autoregressive model with general deterministic terms

Author

Listed:
  • Søren Johansen

    (University of Copenhagen and CREATES)

  • Morten Ørregaard Nielsen

    (Queen?s University and CREATES)

Abstract

In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive unified treatment of deterministic terms in the additive model X(t)= Z(t) + Y(t), where Z(t) belongs to a large class of deterministic regressors and Y(t) is a zero-mean CVAR. We suggest an extended model that can be estimated by reduced rank regression and give a condition for when the additive and extended models are asymptotically equivalent, as well as an algorithm for deriving the additive model parameters from the extended model parameters. We derive asymptotic properties of the maximum likelihood estimators and discuss tests for rank and tests on the deterministic terms. In particular, we give conditions under which the estimators are asymptotically (mixed) Gaussian, such that associated tests are khi squared distributed.

Suggested Citation

  • Søren Johansen & Morten Ørregaard Nielsen, 2016. "The cointegrated vector autoregressive model with general deterministic terms," CREATES Research Papers 2016-22, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2016-22
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    References listed on IDEAS

    as
    1. Søren Johansen & Morten Ørregaard Nielsen, 2012. "Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model," Econometrica, Econometric Society, vol. 80(6), pages 2667-2732, November.
    2. Belke, Ansgar & Beckmann, Joscha, 2015. "Monetary policy and stock prices – Cross-country evidence from cointegrated VAR models," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 254-265.
    3. Felix Pretis, 2015. "Econometric Models of Climate Systems: The Equivalence of Two-Component Energy Balance Models and Cointegrated VARs," Economics Series Working Papers 750, University of Oxford, Department of Economics.
    4. Søren Johansen & Rocco Mosconi & Bent Nielsen, 2000. "Cointegration analysis in the presence of structural breaks in the deterministic trend," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 216-249.
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    Cited by:

    1. Rocco Mosconi & Paolo Paruolo, 2022. "A Conversation with Søren Johansen," Econometrics, MDPI, vol. 10(2), pages 1-16, April.
    2. Dietmar Bauer & Lukas Matuschek & Patrick de Matos Ribeiro & Martin Wagner, 2020. "A Parameterization of Models for Unit Root Processes: Structure Theory and Hypothesis Testing," Econometrics, MDPI, vol. 8(4), pages 1-54, November.
    3. Emilia Gosińska & Aleksander Welfe, 2022. "The Cointegrated VAR Model with Deterministic Structural Breaks," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 14(3), pages 335-350, September.
    4. Dimitriou, Dimitrios & Kenourgios, Dimitris & Simos, Theodore, 2020. "Are there any other safe haven assets? Evidence for “exotic” and alternative assets," International Review of Economics & Finance, Elsevier, vol. 69(C), pages 614-628.

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    More about this item

    Keywords

    Additive formulation; cointegration; deterministic terms; extended model; likelihood inference; VAR model;
    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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