ON THE SHAPE OF THE LIKELIHOOD POSTERIOR IN COINTEGRATION MODELS

A vector autoregressive (VAR) model is specified with equation system parameters, which directly reflect the possible cointegrating nature o f the analyzed time series. By using a flat/diffuse prior, we show tha t the marginal posteriors of the parameters of interest (multipliers o f the cointegrating vectors) may be nonintegrable and favor difference stationary models in an undesired way. To choose between stationary, cointegrated, and difference stationary models in a meaningful way, th e Jeffreys prior principle is used. We investigate the sensitivity of the posterior results with respect to the construction of the Jeffreys prior. In this context, we also analyze the effect of fixed and stoch astic initial values. The theoretical results are illustrated by using a VAR model for short- and long-term interest rates in the United Sta tes.