23  Blackwell Publishing Ltd and the Department of Economics, University of Oxford 2012. Published by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 75, 1 (2013) 0305-9049 doi: 10.1111/obes.12003 A Canonical Correlation Approach for Selecting the Number of Dynamic Factors J¨ org Breitung† and Uta Pigorsch‡ †Institute of Macroeconomics and Econometrics, University of Bonn, Adenauerallee 24-42, 53113 Bonn, Germany (e-mail: breitung@uni-bonn.de). ‡Department of Economics, University of Mannheim, L7, 3-5,68131 Mannheim, Germany (e-mail: uta.pigorsch@vwl.uni-mannheim.de) Abstract In this article, we propose a selection procedure that allows us to consistently estimate the number of dynamic factors in a dynamic factor model. The procedure is based on a canon- ical correlation analysis of the static factors which has the advantage of being invariant to a rescaling of the factors. Monte Carlo simulations suggest that the proposed selection rule outperforms existing ones, in particular, if the contribution of the common factors to the overall variance is moderate or low. The new selection procedure is applied to the US macroeconomic data panel used in Stock and Watson [NBER working paper 11467 (2005)]. I. Introduction In many economic and financial applications it is interesting to represent a large num- ber of time series by a small number of latent factors. In macroeconomics, for example, (dynamic) factor models have been applied in the analysis of the business cycle (see e.g. Forni and Reichlin, 1998; Gianonne, Reichlin and Sala, 2006) and in the identification of common macroeconomic or policy shocks (see e.g. Favero, Marcellino and Neglia, 2005; Stock and Waston 2005; Forni et al., 2009). Recently, they have also been widely used in forecasting macroeconomic variables and it has been found that forecasts based on a few number of so-called diffusion indices, i.e. common factors extracted from a large num- ber of candidate predictor variables, obtain smaller forecast errors relative to alternative techniques such as (vector) autoregressions (see e.g. Stock and Waston, 1999, 2002a,b; Angelini, Henry and Mestre, 2001; Brisson, Campbell and Galbraith, 2003; Artis, Banerjee and Marcellino, 2005; Marcellino, Stock and Waston, 2003; den Reijer, 2005; Bruneau et al., 2007; Schumacher, 2007; Eickmeier and Ziegler, 2008) or error correction models, see Banerjee, Marcellino and Masten (2010). Many of these applications typically assume a dynamic factor model. In particular, consider the following dynamic factor model: JEL Classification numbers: C33, C52.