The cointegrated vector autoregressive model with general deterministic terms

Søren Johansen, Morten Ørregaard Nielsen

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5 Citations (Scopus)

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 X 2 -distributed.
Original languageEnglish
JournalJournal of Econometrics
Volume202
Issue number2
Pages (from-to)214-229
ISSN0304-4076
DOIs
Publication statusPublished - Feb 2018

Keywords

  • Faculty of Social Sciences
  • Additive formulation
  • Cointegration
  • Deterministic terms
  • Extended model
  • Likelihood inference
  • VAR model

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