Based on the concept of causality, a physically reasonable form of the parameter matrix of the random part of multivariate time‐series models is proposed. This general form can be simplified into the full‐matrix form used by Matalas and the lower triangular form assumed by Young. Application conditions for these two simplified forms are identified. Furthermore, a technique of decomposing the Gramian matrix to obtain the solution for the parameter matrix of the general form is presented. This technique is simple and permits a direct solution for the parameter matrix. This technique can also be used to obtain the direct solution for a parameter matrix of full‐matrix form.