The main objective of this paper is to develop a Bayesian technique that can be used to assign a multivariate time series realization to one of several. multivariate autoregressive sources, with unknown coefficients, that share a common known order and unknown precision matrix. The foundation of the proposed assignment technique is to derive the marginal posterior mass function of a classification vector using the exact conditional likelihood function. A multivariate time series realization is assigned to that multivariate autoregressive process with the largest posterior probability.