A BAYESIAN ANALYSIS OF THE UNIT ROOT HYPOTHESIS

Abstract

We propose a posterior odds analysis in order to compare a random walk model with a first-order stationary autoregressive model. We will study in detail the effect of the presence of a constant term representing an unknown mean of the series. Since the unconditional mean is not identifiable under the random walk hypothesis, one must be careful in specifying a reasonable prior for this model. The sampling properties of the posterior odds statistic are compared with such classical test statistics as proposed by Fuller [1976], and by Bhargava [1986]. The results indicate that the posterior odds compare favorably with these classical tests. Empirical results on time series of real exchange rates indicate that a Bayesian analysis can lead to different conclusions concerning the random walk behaviour of real exchange rates.