Comments on "Parameter estimation in multivariate stochastic difference equations

In the above paper Kashyap and Nasburg introduced canonical forms II and III to represent multivariate systems. The limited informarion estimate to obtain the parameters of the system was presented, in which the system is decomposed by using either of the proposed canonical forms into subsystems. As a result the estimation problem was considerably simplified. In this correspondence, it is observed that the canonical form I which has the smallest number of parameters can be decomposed into subsystems just as well, and that the class of models in canonical form I, which is the usual representation, is wider than canonical forms II or III. The question therefore is: what is the real merit of implementing those new canonical forms II and III?