In this article, a new Bayesian approach is used to identify the autoregressive moving average models. Employing approximation error is the foundation of the suggested Bayesian methodology. We take into consideration presence of an approximation error when  substituting lagged errors of the original autoregressive moving average model with suitably lagged residuals from along autoregression . The direct Bayesian identification approach is utilized for solving the Bayesian identification issue of autoregressive moving average processes  employing both informative and non-informative priors. The theoretical derivations of the direct Bayesian identification approach are carried out utilizing the aforementioned priors. We compare the effectiveness of the Broemeling and Shaarawy approach with proposed Bayesian approach for determining the orders of autoregressive moving average models by utilizing an actual data set and numerous simulated experiments. The outcomes  of simulations and actual data demonstrate  that the suggested approach is superior to the Broemeling and Shaarawy approach for determining the orders of autoregressive moving average processes.