  We discuss Bayesian model uncertainty analysis and forecasting in sequential
dynamic modeling of multivariate time series. The perspective is that of a
decision-maker with a specific forecasting objective that guides thinking about
relevant models. Based on formal Bayesian decision-theoretic reasoning, we
develop a time-adaptive approach to exploring, weighting, combining and
selecting models that differ in terms of predictive variables included. The
adaptivity allows for changes in the sets of favored models over time, and is
guided by the specific forecasting goals. A synthetic example illustrates how
decision-guided variable selection differs from traditional Bayesian model
uncertainty analysis and standard model averaging. An applied study in one
motivating application of long-term macroeconomic forecasting highlights the
utility of the new approach in terms of improving predictions as well as its
ability to identify and interpret different sets of relevant models over time
with respect to specific, defined forecasting goals.
