This paper develops an approximate Bayesian technique to assign a univariate time series realization to one of several autoregressive moving average sources, with unknown coefficients, that share common known orders and unknown precision. By employing an approximate conditional likelihood function, the proposed technique is based on the marginal posterior mass function of a classification vector. A time series realization is assigned to the r-th autoregressive moving average source whenever the posterior mass function of the classification vector has the largest value at the r-th mass point. A comprehensive simulation study is carried out to demonstrate the performance of the proposed technique and to test its adequacy in handling the classification problems. The simulation is carried out for a wide variety of ARMA sources. The selected sources are chosen in such a way to include different orders and parameters.