Forecasting in Dynamic Factor Models Using Bayesian Model Averaging

This paper considers the problem of forecasting in dynamic factor models using Bayesian model averaging. Theoretical justi…cations for averaging across models, as opposed to selecting a single model, are given. Practical methods for implementing Bayesian model averaging with factor models are described. These methods involve algorithms which simulate from the space de…ned by all possible models. We discuss how these simulation algorithms can also be used to select the model with the highest marginal likelihood (or highest value of an information criterion) in an e¢ cient manner. We apply these methods to the problem of forecasting GDP and in‡ation using quarterly U.S. data on 162 time series. For both GDP and in‡ation, we …nd that the models which contain factors do out-forecast an AR(p), but only by a relatively small amount and only at short horizons. We attribute these …ndings to the presence of structural instability and the fact that lags of dependent variable seem to contain most of the information relevant for forecasting. Relative to the small forecasting gains provided by including factors, the gains provided by using Bayesian model averaging over forecasting methods based on a single model are appreciable. Acknowledgements: We would like to thank seminar participants at the University of Pennsylvania and at the ESEM2003 conference and, in particular, Frank Diebold, Rafaella Giacomini, Sune Karlsson, John Maheu and Frank Schorfheide. The views expressed here are those of the authors and do not necessarily re‡ect the views of the Federal Reserve Bank of New York or the Federal Reserve System.