Noninformative Priors and Bayesian Testing for the AR(1) Model

Various approaches to the development of a noninformative prior for the AR(1) model are considered and compared. Particular attention is given to the <italic>reference prior</italic> approach, which seems to work well for the stationary case but encounters difficulties in the explosive case. A symmetrized (proper) version of the stationary reference prior is ultimately recommended for the problem. Bayesian testing of the unit root, stationary, and explosive hypotheses is considered also. Bounds on the Bayes factors are developed and shown to yield answers that appear to conflict with classical tests.