Translating Priors about Observables in Autoregressions and the Role of Initial Conditions in Small Samples

Abstract

We discuss estimation of autoregressive models with a prior about initial growth rates of the modeled series. This prior allows to specify prior beliefs about the behavior of time series in a natural way and it serves to replace arbitrary assumptions on initial conditions. To implement this prior we develop a technique for translating priors about observables into priors about coecients. The posterior mean is attractive even from the frequentist point of view: it is often less biased than the OLS estimate and has better frequentist risk than bias corrected estimates. We apply our prior to some empirical studies from the literature and that it makes a big diference for the estimated persistence of output responses to monetary policy shocks in a vector autoregression for the United States.