The main objective of this paper is to examine the adequacy of using the t approximation in handling the Bayesian inferential problems of autoregressive-moving average (ARMA) processes. Simulation studies, with a wide variety of ARMA models, are carried out to demonstrate the performance of the t approximation and to check its adequacy in estimating the parameters and forecasting the future observations of ARMA processes. The adequacy of using the t approximation is measured by computing the percentages of the highest posterior density (HPD) regions which contain the true coefficients and future observations. The simulation is carried out with different realization sizes, using a non-informative prior density, in order to study the behavior of the t approximation when adding more observations. The numerical results support the adequacy of using the t approximation in making Bayesian inferences about the parameters and future observations of ARMA processes.