In this paper, we propose a Bayesian estimation and prediction procedure for noncausal autoregressive (AR) models. Specifically, we derive the joint posterior density of the past and future errors and the parameters, which gives posterior predictive densities as a byproduct. We show that the...

In this paper, we propose a new noncausal vector autoregressive (VAR) model for non-Gaussian time series. The assumption of non-Gaussianity is needed for reasons of identifiability. Assuming that the error distribution belongs to a fairly general class of elliptical distributions, we develop an...

We use noncausal autoregressions to examine the persistence properties of quarterly U.S. consumer price inflation from 1970:1-2012:2. These nonlinear models capture the autocorrelation structure of the inflation series as accurately as their conventional causal counterparts, but they allow for...