The cointegrated vector autoregressive model with general deterministic terms
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The cointegrated vector autoregressive model with general deterministic terms. / Johansen, Søren; Nielsen, Morten Ørregaard.
In: Journal of Econometrics, Vol. 202, No. 2, 02.2018, p. 214-229.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The cointegrated vector autoregressive model with general deterministic terms
AU - Johansen, Søren
AU - Nielsen, Morten Ørregaard
PY - 2018/2
Y1 - 2018/2
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 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.
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 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.
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
VL - 202
SP - 214
EP - 229
JO - Journal of Econometrics
JF - Journal of Econometrics
SN - 0304-4076
IS - 2
ER -
ID: 222753068