Eco 2009/31 Department of Economics Forecasting Large Datasets with Bayesian Reduced Rank Multivariate Models

The paper addresses the issue of forecasting a large set of variables using multivariate models. In particular, we propose three alternative reduced rank forecasting models and compare their predictive performance for US time series with the most promising existing alternatives, namely, factor models, large scale Bayesian VARs, and multivariate boosting. Speci…cally, we focus on classical reduced rank regression, a two-step procedure that applies, in turn, shrinkage and reduced rank restrictions, and the reduced rank Bayesian VAR of Geweke (1996). We …nd that using shrinkage and rank reduction in combination rather than separately improves substantially the accuracy of forecasts, both when the whole set of variables is to be forecast, and for key variables such as industrial production growth, in‡ation, and the federal funds rate. The robustness of this …nding is con…rmed by a Monte Carlo experiment based on bootstrapped data. We also provide a consistency result for the reduced rank regression valid when the dimension of the system tends to in…nity, which opens the ground to use large scale reduced rank models for empirical analysis. Keywords: Bayesian VARs, factor models, forecasting, reduced rank. J.E.L. Classi…cation: C11, C13, C33, C53. This paper has bene…ted from several comments and constructive criticisms from Herman van Dijk and two anonymous referees. We also thank seminar participants at Queen Mary University of London, Bank of France, and at the "Large Datasets and Dynamic Factor Models Workshop", October 2007, London.