We consider Bayesian statistical inference for univariate time series models where one of the autoregressive roots is close to or equals unity. Classical sampling theory for this type of models is hampered by the vast differences between asymptotic approximations in the stationary case and under the unit root hypothesis. Because of this dichotomy one has to decide early on in an empirical study whether a given time series is stationary or not. The present paper shows that a Bayesian approach allows for a smooth continuous transition between stationary and integrated time series models. Empirical results are presented for time series of annual real per capita GNP for 16 OECD countries.