The Cointegrated Vector Autoregressive Model with General Deterministic Terms

28 Pages Posted: 27 Jul 2016

See all articles by Soren Johansen

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Morten Ørregaard Nielsen

Aarhus University - Department of Economics and Business Economics

Date Written: July 24, 2016

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.

Keywords: Additive formulation, cointegration, deterministic terms, extended model, likelihood inference, VAR model

JEL Classification: C32

Suggested Citation

Johansen, Soren and Nielsen, Morten Orregaard, The Cointegrated Vector Autoregressive Model with General Deterministic Terms (July 24, 2016). Available at SSRN: https://ssrn.com/abstract=2814482 or http://dx.doi.org/10.2139/ssrn.2814482

Soren Johansen (Contact Author)

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

Morten Orregaard Nielsen

Aarhus University - Department of Economics and Business Economics ( email )

Denmark

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