In this paper, we propose a Bayesian estimation and forecasting procedure for noncausal autoregressive (AR) models. Specifically, we derive the joint posterior density of the past and future errors and the parameters, yielding predictive densities as a by-product. We show that the posterior model probabilities provide a convenient model selection criterion in discriminating between alternative causal and noncausal specifications. As an empirical application, we consider US inflation. The posterior probability of noncausality is found to be high-over 98%. Furthermore, the purely noncausal specifications yield more accurate inflation forecasts than alternative causal and noncausal AR models.
