This paper discusses model based inference in a vector autoregressive model for cofractional processes based on the Gaussian likelihood. The model allows the process to be 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. The parameters b and d satisfy d=b>1/2.
    We model the data X1,...,X_{T} given initial values X_{-n}, n=0,1,..., under the assumption that the errors are i.i.d. N_{p}(0,O). We consider the conditional likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to find the asymptotic distribution of the estimators and the likelihood ratio test for cointegrating rank.