Factor MIDAS for Nowcasting and Forecasting with Ragged‐Edge Data: A Model Comparison for German GDP*
| Published date | 01 August 2010 |
| Date | 01 August 2010 |
| Author | Massimiliano Marcellino,Christian Schumacher |
| DOI | http://doi.org/10.1111/j.1468-0084.2010.00591.x |
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©Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2010. Published by Blackwell Publishing Ltd,
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OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 72, 4 (2010) 0305-9049
doi: 10.1111/j.1468-0084.2010.00591.x
Factor MIDAS for Nowcasting and Forecasting
with Ragged-Edge Data: A Model Comparison for
German GDPÅ
Massimiliano Marcellino† and Christian Schumacher‡
†Economics Department, European University Institute, Villa San Paolo, Florence and
Bocconi University, Milan, Italy (e-mail: massimiliano.marcellino@eui.eu)
‡Deutsche Bundesbank, Economics Research Centre, Wilhelm-Epstein-Straße 14, 60431
Frankfurt/Main, Germany (e-mail: christian.schumacher@bundesbank.de)
Abstract
In this article, we merge two strands from the recent econometric literature. First,
factor models based on large sets of macroeconomic variables for forecasting, which
have generally proven useful for forecasting. However, there is some disagreement
in the literature as to the appropriate method. Second, forecast methods based on
mixed-frequency data sampling (MIDAS). This regression technique can take into
account unbalanced datasets that emerge from publication lags of high- and low-
frequency indicators, a problem practitioner have to cope with in real time. In this
article, we introduce Factor MIDAS, an approach for nowcasting and forecasting
low-frequency variables like gross domestic product (GDP) exploiting information
in a large set of higher-frequency indicators. We consider three alternative MIDAS
approaches (basic, smoothed and unrestricted) that provide harmonized projection
ÅThe authors are grateful for helpful comments and discussions to three anonymous referees, Riccardo
Cristadoro, Sandra Eickmeier, Petra Gerlach-Kristen, Malte Kn¨uppel,Gerhard R ¨unstler, Karsten Ruth, Klaus
Wohlrabe and participants at the Bank of England CCBS research forum ‘New Developments in Dynamic
Factor Modelling’ 2007, the Workshop ‘Forecasting Short-Term Developments and the Role of Econometric
Models’ at the Bank of Canada 2007, the Pfingsttagung of the DStatG 2008, the Annual Conference of
the Verein f¨ur Socialpolitik 2008, the Joint Research Workshop OeNB-SNB-Bbk 2008, the Workshop
‘Forecasting Macroeconomic Variables Using Dynamic Factor Models’ at the Banque de France 2008,
the CFE Workshop 2008 in Neuchatel and a seminar at the Bundesbank. The codes for this article were
written in Matlab. Some functions were taken from the Econometrics Toolbox written by James P. LeSage
from http://www.spatial-econometrics.com. Other codes were kindly provided by Mario Forni from
http://www.economia.unimore.it/forni mario/matlab.htm,Arthur Sinko from www.unc.edu/∼sinko/midas.zip
and Gerhard R¨unstler.
JEL Classification numbers: E37, C53.
Factor MIDAS 519
methods that allow for a comparison of the alternative factor estimation methods with
respect to nowcasting and forecasting. Common to all the factor estimation methods
employed here is that they can handle unbalanced datasets, as typically faced in
real-time forecast applications owing to publication lags. In particular, we focus on
variants of static and dynamic principal components as well as Kalman filter estimates
in state-space factor models. As an empirical illustration of the technique, we use a
large monthly dataset of the German economy to nowcast and forecast quarterly GDP
growth. Wefind that the factor estimation methods do not differ substantially, whereas
the most parsimonious MIDAS projection performs best overall. Finally, quarterly
models are in general outperformed by the Factor MIDAS models, which confirms
the usefulness of the mixed-frequency techniques that can exploit timely information
from business cycle indicators.
I. Introduction
The use of large sets of macroeconomic variables for forecasting has received
increased attention in the recent literature. In particular, different types of large factor
models have been widely discussed; see, for example, the comparisons and surveys by
Boivin and Ng (2005), Stock and Watson (2006), D’Agostino and Giannone (2006),
Eickmeier and Ziegler (2008) and Schumacher (2007). Another strand of the recent
literature has considered modelling and forecasting with mixed-frequency data, in
particular the mixed-data sampling (MIDAS) approach, as introduced by Ghysels,
Sinko and Valkanov (2007). This approach allows for forecasting a low-frequency
variable like quarterly gross domestic product (GDP) with a small number of high-
frequency indicators, and this has been introduced to the macroeconomic forecast
literature by Clements and Galv˜ao (2008, 2009); see also Ghysels and Wright (2009).
In this article, we bring together these two recent strands of the literature, and intro-
duce Factor MIDAS, an approach for nowcasting and forecasting low-frequency
variables exploiting information in a large set of higher-frequency indicators.
The basic MIDAS framework consists of a regression of a low-frequency variable
on a set of higher-frequency indicators, where distributed lag functions are employed
to specify the dynamic relationship. The Factor MIDAS approach exploits estimated
factors rather than single or small groups of economic indicators as regressors. There-
fore, it directly translates the well-known two-step approach of factor forecasting
as introduced by Stock and Watson (2002) and Bai and Ng (2006) for the single-
frequency case to the mixed-frequency case, where factors are sampled at higher
frequencies than the variable to be predicted. As in the standard MIDAS case, see
Clements and Galv˜ao (2008), Factor MIDAS is a tool for direct multi-step nowcasting
and forecasting; see Marcellino, Stock and Watson (2006). As a modification to
MIDAS, we follow Koenig, Dolmas and Piger (2003) and also evaluate a more
general regression approach, where the dynamic relationship between the low-
frequency variable and the high-frequency indicators – factors in our case – is
unrestricted, in contrast to the distributed lag functions as proposed by Ghysels et al.
©Blackwell Publishing Ltd and the Department of Economics, University of Oxford 2010
520 Bulletin
(2007). This approach is labelled as unrestricted Factor MIDAS. As a third alterna-
tive, we consider a special regression scheme proposed by Altissimo et al. (2006) that
considers only certain frequencies of correlation between variables sampled at high
and low frequencies. As the regression essentially eliminates high-frequency correla-
tions, we call it smoothed MIDAS. To motivate and compare these variants of Factor
MIDAS, we discuss time aggregation in a theoretical high-frequency factor model
with dynamic factors from Boivin and Ng (2005) and derive how mixed-data sampling
can approximate the forecasts from the theoretical model.
Alternative factor estimators can be used for nowcasting and forecasting in the
Factor MIDAS framework, and as an additional novelty of the article, we compare
three different factor estimation methods that have been developed in the recent
literature, but have not been compared with each other so far in a standardized frame-
work. The factor estimation methods we discuss have in common that they can account
for unbalanced datasets. In empirical real-time applications, multivariate datasets are
typically unbalanced because of non-synchronous publication dates and different
publication delays of the economic indicators. This leads to the so-called ragged
edge of the data, see Wallis (1986). We focus on three factor estimators that are all
suited for this case. First, the factor estimator by Altissimo et al. (2006), which builds
upon the one-sided non-parametric dynamic principal component analysis (DPCA)
factor estimator of Forni et al. (2005). To take into account the ragged edge of the
data, Altissimo et al. (2006) simply apply a realignment of each time series to obtain
a balanced dataset. Second, the expectation-maximization (EM) algorithm combined
with the factor estimator-based static principal component analysis (PCA), as intro-
duced by Stock and Watson (2002) and applied for forecasting and interpolation by
Bernanke and Boivin (2003),Angelini, Henry and Marcellino (2006) and Schumacher
and Breitung (2008). Third, the two-step parametric state-space factor estimator based
on the Kalman smoother of Doz, Giannone and Reichlin (2006), as applied in Gian-
none, Reichlin and Small (2008),Angelini et al. (2008), Matheson (2007) and Aastveit
and Trovik (2007). Which one of the estimation performs best, is a priori unclear.
There is a large literature on comparing factor estimation methods based on large and
balanced datasets, see Boivin and Ng (2005), Stock and Watson (2006), D’Agostino
and Giannone (2006), Schumacher (2007), Kapetanios and Marcellino (2009) and we
extend that literature by taking into account estimation methods suited for unbalanced
datasets.
Combining the three alternative MIDAS regressions with the three competing
factor estimators, we have a total of nine Factor MIDAS approaches. To illustrate
their implementation and assess their relative merits, we conduct a detailed empirical
analysis. In particular, as policy makers regularly request information on the current
state of the economy in terms of GDP, which is only available on a quarterly basis and
often with substantial delays, we consider Factor MIDAS nowcasting and short-term
forecasting of quarterly GDP growth with a large set of timely monthly economic
indicators. We focus on Germany, the largest economy in the euro area, where GDP
is released about 5–6 weeks after the end of the reference quarter.
©Blackwell Publishing Ltd and the Department of Economics, University of Oxford 2010
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