This paper considers Bayesian long-run prediction in time series models. We allow time series to exhibit stationary or non-stationary 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. A Bayesian counterpart is provided to Sampson (1991) who takes parameter uncertainty into account in a classical framework. An empirical example illustrates our results
