This thesis explores several aspects of Bayesian model selection in time series forecasting of macroeconomic variables. The contribution is provided in three essays. In the first essay (Chapter 2) I forecast quarterly US inflation based on the generalized Phillips curve using econometric methods which incorporate dynamic model averaging. These methods not only allow for coefficients to change over time, but also for the entire forecasting model to change over time. I find that dynamic model averaging leads to substantial forecasting improvements over simple benchmark regressions and more sophisticated approaches such as those using time varying coefficient models. I also provide evidence on which sets of predictors are relevant for forecasting in each period. In the second essay (Chapter 3) I address the issue of improving the forecasting performance of vector autoregressions (VARs) when the set of available predictors is inconveniently large to handle with methods and diagnostics used in traditional small-scale models. First, I summarize available information from a large dataset into a considerably smaller set of variables through factors estimated using standard principal components. However, even in the case of reducing the dimension of the data the true number of factors may still be large. For that reason I introduce in my analysis simple and efficient Bayesian model selction methods. I conduct model estimation and selection of predictors automatically through a stochastic search variable selection (SSVS) algorithm which requires minimal input by the user. I apply these methods to forecast 8 main U.S. macroeconomic variables using 124 potential predictors. I find improved out of sample fit in high dimensional specifications that would otherwise suffer from the proliferation of parameters. Finally, in the third essay (Chapter 4) I develop methods for automatic selection of variables in forecasting Bayesian vector autoregressions (VARs) using the Gibbs sampler. In particular, I extend the algorithms of Chapter 3 and provide computationally efficient algorithms for stochastic variable selection in generic (linear and nonlinear) VARs. The performance of the proposed variable selection method is assessed in a small Monte Carlo experiment, and in forecasting four short macroeconmic series for the UK using time-varying parameters vector autoregressions (TVP-VARs). I find that restricted models consistently improve upon their unrestricted counterparts in forecasting, showing the merits of variable selection in selecting parsimonious models.