Improved likelihood ratio tests for cointegration rank in the VAR model

H. Peter Boswijk; Michael Jansson; Morten Ørregaard Nielsen

doi:10.1016/j.jeconom.2014.08.007

Improved likelihood ratio tests for cointegration rank in the VAR model

H. Peter Boswijk, Michael Jansson, Morten Ørregaard Nielsen

Department of Economics and Business Economics - CREATES

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

10 Citations (Scopus)

Abstract

We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but as usual the asymptotic results do not require normally distributed innovations. Our tests differ from existing tests in two respects. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott et al. (1996). Second, our tests incorporate a “sign” restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests.

Original language	English
Journal	Journal of Econometrics
Volume	184
Issue	1
Pages (from-to)	97-110
Number of pages	14
ISSN	0304-4076
DOIs	https://doi.org/10.1016/j.jeconom.2014.08.007
Publication status	Published - 2015

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10.1016/j.jeconom.2014.08.007

http://www.sciencedirect.com/science/article/pii/S0304407614001869

Cite this

@article{406ec12fd9d8447b886e83fd163e31e7,

title = "Improved likelihood ratio tests for cointegration rank in the VAR model",

abstract = "We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but as usual the asymptotic results do not require normally distributed innovations. Our tests differ from existing tests in two respects. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott et al. (1996). Second, our tests incorporate a “sign” restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests.",

keywords = "Cointegration rank, Efficiency, Likelihood ratio test, Vector autoregression",

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year = "2015",

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language = "English",

volume = "184",

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journal = "Journal of Econometrics",

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T1 - Improved likelihood ratio tests for cointegration rank in the VAR model

AU - Boswijk, H. Peter

AU - Jansson, Michael

AU - Nielsen, Morten Ørregaard

PY - 2015

Y1 - 2015

N2 - We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but as usual the asymptotic results do not require normally distributed innovations. Our tests differ from existing tests in two respects. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott et al. (1996). Second, our tests incorporate a “sign” restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests.

AB - We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but as usual the asymptotic results do not require normally distributed innovations. Our tests differ from existing tests in two respects. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott et al. (1996). Second, our tests incorporate a “sign” restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests.

KW - Cointegration rank

KW - Efficiency

KW - Likelihood ratio test

KW - Vector autoregression

U2 - 10.1016/j.jeconom.2014.08.007

DO - 10.1016/j.jeconom.2014.08.007

M3 - Journal article

SN - 0304-4076

VL - 184

SP - 97

EP - 110

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 1

ER -