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.