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

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+