A mixed-frequency Bayesian vector autoregression with a steady-state prior

We consider a Bayesian vector autoregressive (VAR) model allowing for an explicit prior specification for the included variables' "steady states" (unconditional means) for data measured at different frequencies. We propose a Gibbs sampler to sample from the posterior distribution derived from a normal prior for the steady state and a normal-inverse-Wishart prior for the dynamics and error covariance. Moreover, we suggest a numerical algorithm for computing the marginal data density that is useful for finding appropriate values for the necessary hyperparameters. We evaluate the proposed model by applying it to a real-time data set where we forecast Swedish GDP growth. The results indicate that the inclusion of high-frequency data improves the accuracy of low-frequency forecasts, in particular for shorter time horizons. The proposed model thus facilitates a simple and helpful way of incorporating information about the long run through the steady-state prior as well as about the near future through its ability to cope with mixed frequencies of the data.