The cointegrated vector autoregressive model with general deterministic terms

Søren Johansen; Morten Ørregaard Nielsen

doi:10.1016/j.jeconom.2017.10.003

The cointegrated vector autoregressive model with general deterministic terms

Søren Johansen, Morten Ørregaard Nielsen

3 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=γZ_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 χ²-distributed.

Original language	English
Journal	Journal of Econometrics
Volume	202
Issue number	2
Pages (from-to)	214-229
ISSN	0304-4076
DOIs	https://doi.org/10.1016/j.jeconom.2017.10.003
Publication status	Published - Feb 2018

Keywords

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

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10.1016/j.jeconom.2017.10.003

http://linkinghub.elsevier.com/retrieve/pii/S0304407617302117

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title = "The cointegrated vector autoregressive model with general deterministic terms",

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 Xt=γZt+Yt, where Zt belongs to a large class of deterministic regressors and Yt 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 χ2-distributed.",

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author = "S{\o}ren Johansen and Nielsen, {Morten {\O}rregaard}",

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doi = "10.1016/j.jeconom.2017.10.003",

language = "English",

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pages = "214--229",

journal = "Journal of Econometrics",

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T1 - The cointegrated vector autoregressive model with general deterministic terms

AU - Johansen, Søren

AU - Nielsen, Morten Ørregaard

PY - 2018/2

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N2 - 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 Xt=γZt+Yt, where Zt belongs to a large class of deterministic regressors and Yt 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 χ2-distributed.

AB - 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 Xt=γZt+Yt, where Zt belongs to a large class of deterministic regressors and Yt 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 χ2-distributed.

KW - Faculty of Social Sciences

KW - Additive formulation

KW - Cointegration

KW - Deterministic terms

KW - Extended model

KW - Likelihood inference

KW - VAR model

U2 - 10.1016/j.jeconom.2017.10.003

DO - 10.1016/j.jeconom.2017.10.003

M3 - Journal article

SN - 0304-4076

VL - 202

SP - 214

EP - 229

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 2

ER -

The cointegrated vector autoregressive model with general deterministic terms

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Keywords

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