Gibbs Samplers for VARMA and Its Extensions

Empirical work in macroeconometrics has mostly restricted to using VARs, even though there are strong theoretical reasons to consider general VARMAs. This is perhaps because estimation of VARMAs is perceived to be challenging. In this article, we develop a Gibbs sampler for the basic VARMA, and demonstrate how it can be extended to models with stochastic volatility and time-varying parameters. We illustrate the methodology through a macroeconomic forecasting exercise. We show that VARMAs produce better density forecasts than VARs, particularly for short forecast horizons.