Vector autoregressions model, jointly, the dynamics of a collection of series. These models have become a popular and widely researched tool in macroeconomic forecasting. In this thesis, we propose several new ideas for these models in the context of macroeconomic forecasting using Bayesian MCMC techniques. In Chapter 2, we attempt to create a realistic data model which addresses structural mean changes, stochastic volatility, and inference concerning the unknown lag for an autoregressive process. We improve upon the estimation of multivariate stochastic volatility in Chapter 3 and propose a flexible and efficient sampling procedure. In Chapter 4, we explore various shrinkage and sparsitiy prior schemes aiming at improving forecast performance.