Mixed frequency models: Bayesian approaches to estimation and prediction

We describe Bayesian models for economic and financial time series that use regressors sampled at higher frequencies than the outcome of interest. The models are developed within the framework of dynamic linear models, which provides a high level of flexibility and allows direct interpretation of the results. The problem of the collinearity of intraperiod observations is solved using model selection and model averaging approaches. Bayesian approaches to model selection automatically adjust for multiple comparisons, while predictions based on model averaging allow us to account for both model and parameter uncertainty when predicting future observations. A novel aspect of the models presented here is the introduction of new formulations for the prior distribution on the model space that allow us to favor sparse models where the significant coefficients cluster on adjacent lags of the high frequency predictor. We illustrate our approach by predicting the gross national product of the United States using the term structure of interest rates.