We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model with a restricted constant term, ¿, based on the Gaussian likelihood conditional on initial values. The model nests the I(d) VAR model. We give conditions on the parameters such that the process X_{t} is fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß'X_{t} is fractional of order d-b, and no other fractionality order is possible. We define the statistical model by 01/2, we prove that the limit distribution of (ß',¿')' is mixed Gaussian and for the remaining parameters it is Gaussian. The limit distribution of the likelihood ratio test for cointegration rank is a functional of fractional Brownian motion of type II extended by u^{-(d0-b0)}. If b0<1/2 all limit distributions are Gaussian or chi-squared.
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