Testing for unit roots in a Bayesian framework

Classical tests for unit roots have been criticized for their unusual asymptotic theory leading to disconnected confidence intervals and their lack of power in small samples. Such critiques were initiated by Sims (1988), who promoted a Bayesian approach to the question. Various papers then appeared, which took up this idea. The Bayesian approach is however not exempt from criticism, as shown by Phillips (1991), who emphasizes the role of the prior as a bias toward stationarity. In this paper, I emphasize the role of the model and of the initial conditions. I show that with a structural model and an adequate treatment of the first observation, a Bayesian unit root test based on the computation of Pr(p ⩾ 1y) can produce results which are more or less in accordance with classical results. The extended Nelson-Plosser data set serves as an illustration.