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