A Canonical Correlation Approach for Selecting the Number of Dynamic Factors
| Date | 01 February 2013 |
| DOI | http://doi.org/10.1111/obes.12003 |
| Author | Jörg Breitung,Uta Pigorsch |
| Published date | 01 February 2013 |
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OXFORD BULLETIN OF ECONOMICS AND 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.
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