Bayesian model selection approaches to MIDAS re- gression

We describe Bayesian models for economic and financial time series that use regressors sampled at finer frequencies than the outcome of interest. The models are developed within the framework of dynamic linear models, which provide a great level of flexibility and direct interpretation of results. The problem of collinearity of intraperiod observations is solved using model selection and model averaging approaches which, within a Bayesian framework, automatically adjust for multiple comparisons and allows us to accurately account for all uncertainty when predicting future observations. We also introduce novel formulations for the prior distribution on model space that allow us to include additional information in a flexible manner. We illustrate our approach by predicting the gross domestic product of United Stated using the term structure of interest rates.