Fractional bayes factors for the analysis of autoregressive models with possible unit roots

In this paper we consider the problem of identifying an autoregressive model for an observed time series and detecting a possible unit root in its characteristic polynomial. This is a big issue concerned with distinguishing stationary time series from time series for which differencing is required to induce stationarity. We adopt the Bayes approach and assume that the prior information about the parameters of the model is weak. For the comparison of the models in this setting we introduce a modified version of the fractional Bayes factor.