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THE LIKELIHOOD RATIO TEST FOR COINTEGRATION RANKS IN THE I(2) MODEL

Published online by Cambridge University Press:  25 April 2007

Heino Bohn Nielsen  and
Anders Rahbek
Heino Bohn Nielsen
Affiliation:
University of Copenhagen
Anders Rahbek
Affiliation:
University of Copenhagen
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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.Discussions with Søren Johansen, Hans Christian Kongsted, and Bent Nielsen are gratefully acknowledged. We also thank the editor and three anonymous referees for very constructive comments that have led to a much improved version of the paper. This research was supported by Danish Social Sciences Research Council grant 2114-04-0001.

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 4 , August 2007 , pp. 615 - 637
Copyright
© 2007 Cambridge University Press

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