Testing the Number of Factors: An Empirical Assessment for a Forecasting Purpose*
| Author | Olivier Darné,Laurent Ferrara,Karim Barhoumi |
| Published date | 01 February 2013 |
| Date | 01 February 2013 |
| DOI | http://doi.org/10.1111/obes.12010 |
64
©Blackwell Publishing Ltd and the Department of Economics, University of Oxford 2012. Published by Blackwell Publishing Ltd,
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OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 75, 1 (2013) 0305-9049
doi: 10.1111/obes.12010
Testing the Number of Factors: An Empirical
Assessment for a Forecasting PurposeÅ
Karim Barhoumi†, Olivier Darn´
e‡ and Laurent Ferrara§
†International Monetary Fund, Middle East Center for Economics and Finance, Salmiya, Sym-
phony Mall, 22003, Kuwait (e-mail: KBarhoumi@imf.org)
‡LEMNA, University of Nantes and Banque de France, IEMN–IAE, Chemin de la Censive du
Tertre, BP 52231, 44322 Nantes, France (e-mail: olivier.darne@univ-nantes.fr)
§International Macroeconomics Division, Directorate General Economics and International
Relations, Banque de France, 31 rue Croix des Petits Champs, 75049 Paris, France (e-mail:
laurent.ferrara@banque-france.fr)
Abstract
GDP forecasts based on dynamic factor models, applied to a large data set, are now widely
used by practitioners involved in nowcasting and short-term macroeconomic forecasting.
One recurrent empirical question that arises when dealing with such models is the way to
determine the optimal number of factors. At the same time, statistical tests have recently
been put forward in the literature in order to optimally determine the number of significant
factors. In this article, we propose to reconcile both fields of interest by selecting the num-
ber of factors, through a testing procedure, to include in the forecasting equation. Through
an empirical exercise on French and German GDPs, we assess the impact of a battery of
recent statistical tests for the number of factors for a forecasting purpose. By implementing
a rolling experience, we also assess the stability of the results overtime.
I. Introduction
In recent years, the number of economic time series available to economists in charge
of monitoring and forecasting economic activity has dramatically increased. In this respect,
several econometric methods have been put forward in the literature in order to han-
dle simultaneously hundreds of variables – hard and soft, aggregated and disaggregated,
real and nominal variables. A particular scope is put on gross domestic product (GDP)
nowcasting and forecasting in a data-rich environment, which has considerably drawn
attention, mainly due to the pioneering work of Stock and Watson (2002) and Forni et al.
(2004, 2005) on dynamic factor models. Such models enable the reduce of information
ÅWe would like to thank DanteAmengual, Marco Capasso, Marc Hallin, Roman Liska and Uta Pigorsch for pro-
viding their codes, Christian Schumacher for sending the German database, Cl´ement Marsilli for excellent research
assistance, as well as the participants of the 29th International Symposium on Forecasting, San Diego, US, June 2010,
and the 6th Colloquium on Modern Tools for Business CycleAnalysis, Luxembourg, September 2010. In addition,
we would like to thank two anonymous referees for helpful remarks. The views expressed herein are those of the
authors and do not necessarily reflect those of the Banque de France and the International Monetary Fund.
JEL Classification numbers: C13, C52, C53, F47.
GDP forecasts based on dynamic factor models 65
contained in large databases into few common factors that can then be put into standard
econometric models such as regression equations (Stock and Watson, 2002),VAR models
(Bernanke, Boivin and Eliasz, 2005), probit models (Bell´ego and Ferrara, 2009) or mixed
data sampling (MIDAS) approaches (Marcellino and Schumacher, 2010). Dynamic factor
models are now widely used by governments and central banks, which need to have an
accurate and timely assessment of GDP growth rate for the current and the next quarters.
We refer for example to Boivin and Ng (2005), Giannone, Reichlin and Small (2008),
Barhoumi, Darn´e and Ferrara (2010) or D’Agostino and Giannone (2012) for applications
of such approaches.
The optimal number of factors that should be put into the standard econometric models
is of crucial importance in modelling. Relatively few authors have dealt with the model
selection problem related to the number of common factors when both the time (T) and
the cross-section (n) dimensions diverge. Generally, the number of factors to be included
in the models is selected through minimization of information criteria, as in Stock and
Watson (2002) or Boivin and Ng (2005). Naive approaches by searching for the optimal
number through a grid-search procedure can also be used (Marcellino and Schumacher,
2010). In the static factor framework, Bai and Ng (2002) (BN02 thereafter) pioneered the
literature by proposing a criterion that basically modifies the Akaike (AIC) and Bayesian
(BIC) information criteria in order to take into account both dimensions of the dataset as
arguments of the function penalizing overparametrization. Alessi, Barigozzi and Capasso
(2010) propose a refinement of the criterion by BN02 by multiplying the penalty function
by a constant which tunes the penalizing power of the function itself.1The BN02 criterion
has been recently adapted by Amengualand Watson (2007), Bai and Ng (2007) and Hallin
and Liska (2007) to the dynamic factor framework whereas Breitung and Pigorsch (2010)
suggested selection procedures based on a canonical correlation analysis for the number
of dynamic factors in a dynamic factor model (DFM).
In this article, we propose to reconcile both fields of interest by selecting the number
of factors to include in the forecasting equation by using a testing procedure. Through
an empirical exercise on French and German GDPs, we assess the impact of a battery of
recent statistical tests on h-step-ahead forecasts using various dynamic factor models. The
forecasting accuracy of alternative factor models, associated with a choice of the number
of factors, is assessed using the Giacomini and White (2006) test and then discussed. The
results, although limited to the two main euro area countries, seem of great interest for the
empirical use in forecasting of dynamic factor models. In a quasi-real-time experience, we
also assess the stability of the results overtime, which is quite important for forecasters in
search for stability in their models.
II. Factor models
In this section, we recall briefly the two basic factor models that we use in this study, namely
the static diffusion index of Stock and Watson (2002) and the dynamic factor model of
Forni et al. (2004, 2005).
1Alternative criteria based on the theory of random matrices have been developed by Kapetanios (2010) and
Onatski (2010) for the number of static factors. Onatski (2009) also proposed alternative tests in the context of the
generalized dynamic factor models (2010) for the number of static factors. Onatski (2009) also proposed alternative
tests in the context of the generalized dynamic factor models.
©Blackwell Publishing Ltd and the Department of Economics, University of Oxford 2012
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