PRIORS FOR THE AR(1) MODEL - PARAMETERIZATION ISSUES AND TIME-SERIES CONSIDERATIONS

Two issues have come up in the specification of a prior in the Bayesia n analysis of time series with possible unit roots. The first issue de als with the singularity that is due to the local identification probl em of the unconditional mean of an AR(1) process in the limit of a ran dom walk. This singularity problem is related to the difference betwee n a structural parameterization and the linear reduced form in a stand ard regression model with fixed regressors. The second is related to t he time series nature of the regressor in an AR(1) model. In this pape r we will concentrate on the parameterization issue. First, it is show n that the posterior of the autoregressive parameter can be very sensi tive to the degree of prior dependence between the unconditional mean and the autocorrelation parameter. Second, the time series nature of t he problem suggests a particular form of this dependence.