The likelihood ratio test for cointegration ranks in the I(2) model

Heino Bohn Nielsen; Anders Christian Rahbek

doi:10.1017/S0266466607070272

The likelihood ratio test for cointegration ranks in the I(2) model

Heino Bohn Nielsen, Anders Christian Rahbek

21 Citations (Scopus)

Abstract

This paper presents the likelihood ratio (LR) test for the number of cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the cointegration ranks is identical to the asymptotic distribution of the much applied test statistic based on the two-step estimation procedure in Johansen (1995, Econometric Theory 11, 25-59), Paruolo (1996, Journal of Econometrics 72, 313-356), and Rahbek, Kongsted, and Jørgensen (1999, Journal of Econometrics 90, 265-289). By construction the LR test statistic is smaller than the non-LR test statistic from the two-step procedure, and application of the LR test may change rank selection in empirical work. Based on a study of existing empirical applications and related Monte Carlo simulations we conclude that the LR test has much better size properties when compared to the two-step-based test. Overall, we propose use of the LR test for rank determination in I(2) analysis

Original language	English
Journal	Econometric Theory
Volume	23
Issue number	4
Pages (from-to)	615-637
ISSN	0266-4666
DOIs	https://doi.org/10.1017/S0266466607070272
Publication status	Published - 2007

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title = "The likelihood ratio test for cointegration ranks in the I(2) model",

abstract = "This paper presents the likelihood ratio (LR) test for the number of cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the cointegration ranks is identical to the asymptotic distribution of the much applied test statistic based on the two-step estimation procedure in Johansen (1995, Econometric Theory 11, 25-59), Paruolo (1996, Journal of Econometrics 72, 313-356), and Rahbek, Kongsted, and J{\o}rgensen (1999, Journal of Econometrics 90, 265-289). By construction the LR test statistic is smaller than the non-LR test statistic from the two-step procedure, and application of the LR test may change rank selection in empirical work. Based on a study of existing empirical applications and related Monte Carlo simulations we conclude that the LR test has much better size properties when compared to the two-step-based test. Overall, we propose use of the LR test for rank determination in I(2) analysis",

author = "Nielsen, {Heino Bohn} and Rahbek, {Anders Christian}",

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T1 - The likelihood ratio test for cointegration ranks in the I(2) model

AU - Nielsen, Heino Bohn

AU - Rahbek, Anders Christian

N1 - JEL Classification: C32

PY - 2007

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N2 - This paper presents the likelihood ratio (LR) test for the number of cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the cointegration ranks is identical to the asymptotic distribution of the much applied test statistic based on the two-step estimation procedure in Johansen (1995, Econometric Theory 11, 25-59), Paruolo (1996, Journal of Econometrics 72, 313-356), and Rahbek, Kongsted, and Jørgensen (1999, Journal of Econometrics 90, 265-289). By construction the LR test statistic is smaller than the non-LR test statistic from the two-step procedure, and application of the LR test may change rank selection in empirical work. Based on a study of existing empirical applications and related Monte Carlo simulations we conclude that the LR test has much better size properties when compared to the two-step-based test. Overall, we propose use of the LR test for rank determination in I(2) analysis

AB - This paper presents the likelihood ratio (LR) test for the number of cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the cointegration ranks is identical to the asymptotic distribution of the much applied test statistic based on the two-step estimation procedure in Johansen (1995, Econometric Theory 11, 25-59), Paruolo (1996, Journal of Econometrics 72, 313-356), and Rahbek, Kongsted, and Jørgensen (1999, Journal of Econometrics 90, 265-289). By construction the LR test statistic is smaller than the non-LR test statistic from the two-step procedure, and application of the LR test may change rank selection in empirical work. Based on a study of existing empirical applications and related Monte Carlo simulations we conclude that the LR test has much better size properties when compared to the two-step-based test. Overall, we propose use of the LR test for rank determination in I(2) analysis

U2 - 10.1017/S0266466607070272

DO - 10.1017/S0266466607070272

M3 - Journal article

SN - 0266-4666

VL - 23

SP - 615

EP - 637

JO - Econometric Theory

JF - Econometric Theory

IS - 4

ER -

The likelihood ratio test for cointegration ranks in the I(2) model

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