Posterior Analysis of Possibly Integrated Time Series with an Application to Real GNP

Abstract

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.KeywordsUnit RootPosterior DensityGross National ProductStochastic TrendPosterior OddsThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.