Our general subject is model determination methods and their use in the prediction of economic time series. The methods suggested are Bayesian in spirit but they can be justified by classical as well as Bayesian arguments. The main part of the paper is concerned with model determination, forecast evaluation, and the construction of evolving sequences of models that can adapt in dimension and form (including the way in which any nonstationarity in the data is modelled) as new characteristics in the data become evident. The paper continues some recent work on Bayesian asymptotics by the author and Werner Ploberger (1995), develops embedding techniques for vector martingales that justify the role of a class of exponential densities in model selection and forecast evaluation, and implements the modelling ideas in a multivariate regression framework that includes Bayesian vector autoregressions (BVAR's) and reduced rank regressions (RRR's). It is shown how the theory in the paper can be used: (i) to construct optimized BVAR's with data-determined hyperparameters; (ii) to compare models such as BVAR's, optimized BVAR's, and RRR's; (iii) to perform joint order selection of cointegrating rank, lag length, and trend degree in a VAR; and (iv) to discard data that may be irrelevant and thereby reset the initial conditions of a model.