Root cancellation in Auto Regressive Moving Average (ARMA) models leads tolocal non-identification of parameters. When we use diffuse or normal priorson the parameters of the ARMA model, posteriors in Bayesian analyzes show ana posteriori favor for this local non-identification. We show that the priorand posterior of the parameters of an ARMA model are the (unique)conditional density of a prior and posterior of the parameters of anencompassing AR model. We can therefore specify priors and posteriors on theparameters of the encompassing AR model and use the prior and posterior thatit implies on the parameters of the ARMA model, and vice versa. Theposteriors of the ARMA parameters that result from standard priors on theparameters of an encompassing AR model do not lead to an a posteriori favorof root cancellation. We develop simulators to generate parameters fromthese priors and posteriors. As a byproduct, Bayes factors can be computedto compare (non-nested) parsimonious ARMA models. The procedures are appliedto the (extended) Nelson-Plosser data. For approximately 50% of the seriesan ARMA model is favored above an AR model.