Bayesian long-run prediction in time series models

This paper considers Bayesian long-run prediction in time series models. We allow time series to exhibit stationary or nonstationary behavior and show how differences between prior structures which have little effect on posterior inferences can have a large effect in a prediction exercise. In particular, the Jeffreys prior given in Phillips (1991) is seen to prevent the existence of one-period-ahead predictive moments. In a more general context, a Bayesian counterpart is provided to Sampson (1991) who takes parameter uncertainty into account in a classical framework. An empirical example illustrates our results.