M*-BVAR: Bayesian Vector Autoregression with Macroeconomic Stars

This study presents a model that enables automatic trend detection in Bayesian vector autoregressions (BVARs). The proposed model features cyclical components that follow a stationary VAR and trend components that evolve as a random walk. We employ a spike-and-slab prior on the variance of shocks in the trend component, allowing for the automatic identification of stochastic trends and, if present, their estimation within the same Gibbs sampling procedure. A marginal likelihood comparison provides evidence in favor of the proposed model over standard BVARs. Furthermore, out-of-sample forecasting exercises demonstrate that our model significantly enhances predictive accuracy, particularly for highly persistent variables and longer-horizon forecasts. These results remain robust across models of different sizes, including small, medium, and large.