The cointegrated vector autoregressive model with general deterministic terms

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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 = gamma 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. (C) 2017 Elsevier B.V. All rights reserved.

Original languageEnglish
JournalJournal of Econometrics
Pages (from-to)214-229
Number of pages16
Publication statusPublished - 2018

    Research areas

  • Additive formulation, Cointegration, Deterministic terms, Extended model, Likelihood inference, VAR model, RANK, HYPOTHESES, TREND

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