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The cointegrated vector autoregressive model with general deterministic terms

Listed author(s):
  • Søren Johansen

    (Department of Economics, University of Copenhagen)

  • Morten Ørregaard Nielsen

    (Department of Economics, Queen's University, Ontario)

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.

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File URL: http://www.econ.ku.dk/english/research/publications/wp/dp_2016/1607.pdf
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Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 16-07.

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Length: 29 pages
Date of creation: 27 Jul 2016
Handle: RePEc:kud:kuiedp:1607
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  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. 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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