AGRIC. ECON. CZECH, 59, 2013 (9): 389–395 389
The global financial crisis caused economic cycles
in most European countries to become more strongly
synchronized without increasing of the real conver-
gence process. While there is a wide range of literature
focused on the economic cycle synchronization within
the Euro area, the developments since the crisis have
not yet been researched in detail. The point is to filter
the country-specific economic activity in order to
eliminate this global symmetric shock from the time
series. We apply the singular value decomposition
to estimate the long-term trend in time series and
the wavelet co-spectrum to identify the changes of
co-movements at different frequencies over time.
From the theoretical point of view, a currency union
is expected to increase trade and financial integration
because of the decrease in transaction costs and the
elimination of the exchange rate risk. Frankel and Rose
(1998) argued that the business cycles synchroniza-
tion would be higher because of the demand shocks
or the intra-industry trade. As well, they pioneered
the idea of the hypothesis of the endogeneity of the
Optimum Currency Area (OCA) criteria sig nificant
relation between the historically greater integration
and the more highly synchronized cycles.
The endogeneity of the OCA criteria was discussed
by many authors in several branches, which are not
isolated between themselves. Artis and Zhang (1997,
1999) identified the positive impact of the fixed ex-
change rate on the business cycles synchronization,
contributed by growing trade links between the EU
countries. The endogeneity of symmetric shocks
and trade was followed by Fontagné (1999), Fidrmuc
(2004), Artis et al. (2008) and many others. Blanchard
and Wolfers (2000) focused on the endogeneity of
labour market institutions, Kalemli-Ozcan et al.
(2003) provide the empirical evidence that the risk
sharing within the Euro area enhances specialization
The hypothesis assumes that the EU accessing
countries would be expected to meet the OCA criteria
better ex post than ex ante, which is an important
topic in discussion about the benefits and costs of
adopting a common currency. Joining a currency
area is related with the loss of autonomous monetary
policy and the exchange rate control. The traditional
version of the OCA theory argues that joining costs
are minimized and the benefits maximized with a
high degree of cyclical and structural synchroniza-
tion (Corden 1972).
However, the recent financial crisis confirmed the
Lucas Critique. Lucas (1976) assumed that the struc-
ture of all econometric models is not applicable for
The endogeneity of optimum currency area criteria
in the context of financial crisis: Evidence from
the time-frequency domain analysis
Svatopluk KAPOUNEK1, JitkaPOMĚNKOVÁ2
1Department of Finance, Faculty of Business Economics, Mendel University in Brno,
Brno, Czech Republic
2Department of Radio Electronics, Faculty of Electrical Engineering and Communication,
Brno University of Technology, Brno, Czech republic
Abstract: We provide the wavelet analysis of the economic cycle synchronization during the recent ﬁ nancial crisis. How-
ever, the global ﬁ nancial crisis caused economic cycles in most European countries to become more strongly synchronized
without increasing of the real convergence process. Our contribution is an application of the singular value decomposition
to identify and remove the long-term trend including outliers appearing in the year 2007–2010. We found that the histori-
cally greater integration provides more highly synchronized cycles in the core Euro area member countries.
Key words: Euro area, singular value decomposition, synchronization, wavelet analysis
Supported by the Czech Science Foundation (Grant No. P402/11/0570) and by Jean Monnet Multilateral Research Group
(Grant No. 530069-LLP-1-2012-1-CZ-AJM-RE).
390 AGRIC. ECON. CZECH, 59, 2013 (9): 389–395
policy decisions. He argued with the optimal decision
rules of economic agents which vary systematically
without any changes in the structure of series relevant
to the change in policy. Therefore, any experiments
based on the historical data cannot provide the prob-
ability of the future asymmetric shocks within the
Still, despite the critics, the empirical evidence of
the endogeneity of the OCA criteria is important to
assess the integration and homogeneity effects after
the Euro adoption, especially the economic cycle
synchronization. The most common methods in this
field are the unconditional correlation between the
two countries in different time periods, the identifi-
cation of delays of various phases of business cycles,
the volatility of cyclical fluctuations in economic
activity, the stability and similarity of sudden and
unexpected fluctuations in economic activity or the
shock responses at the regional level within the Euro
area (Darvas and Szapáry 2008) or the index of cyclical
conformity, called the Concordance Index (Harding
and Pagan 2006).
Growing literature in this area induced creation
of new methodological approaches. The traditional
analyses of the co-movements in time domain were
supplemented by the frequency domain (Croux et al.
2001; Messina et al. 2009; Fidrmuc and Korhonen 2010)
and developed into the time-frequency approaches
(Rua 2010; Aguiar-Conraria and Soares 2011).
We follow the time-frequency domain approach and
focus on the business cycles co-movements before and
during the global financial crisis of 2008. The crisis
period and its consequences are recently discussed in
many working papers. However, the authors provide
markedly different results depending on the applied
approaches. Dées and Zorell (2011) applied the sys-
tem of equations to identify production structures
and concluded that the financial integration tends
to raise the business cycle co-movement between
the EU countries. Antonakakis (2012) applied the
dynamic conditional correlation and identified an
unprecedented synchronization of business cycles
between the G7. On the contrary, Gaechter et al.
(2012) identified the divergent development of the
business cycles in the Euro area after the year 2008
and Filis et al. (2011) concluded that the recent fi-
nancial crisis has halted and reversed the process
of convergence of the business cycle synchroniza-
tion in Europe. Similarly to Fidrmuc and Korhonen
(2006), we consider that the results of analysis are
significantly influenced by the choice of the method
for the business cycle estimation.
Blumenstein et al. (2012) compared different ap-
proaches in the time-frequency domain (wavelet
analysis, multiple window method using Slepian
sequences, time-frequency varying autoregressive
process estimation and time-frequency Fourier
transform representation) to identify cyclical move-
ments in the Euro area industrial production index.
They found contrasting cyclical movements in the
years 2007–2010, especially two significant shocks
and effects in long-term cyclical movements. This
shock caused that other cyclical movements in the
time series were suppressed. Therefore, we sup-
pose that the commonly used filtering techniques
overestimate cyclical movements in the time series
during the financial crisis and co-movements as
well. Subsequently, the results of the analysis in the
time-frequency domain may be significantly biased.
The generally used methodological background in
the time-frequency domain provides only the iden-
tification of the significant symmetric shock in the
years 2007–2010. The problem is in the trend elimi-
nation. The standard filtering techniques identify
financial crisis as the business cycle. To contribute
to the recent methodology, we have to answer the
key question, whether the financial crisis changed
the business cycle frequency or not.
Now, let us focus on the shape of the time economic
activity during the financial crisis. We follow the US
experiences now. The economy was affected by the
subprime mortgage crisis and lost household wealth,
which led to a drop in consumer spending and in-
vestment activities. Before this demand shock, the
US experienced a rapid increase in the total loans.
Increased aggregate demand was followed by the
increase of prices at the asset market. Thus, the ex-
pansion stage with the peak in the year 2007 was
replaced by economic recession with the trough in
the year 2009 and the subsequent recovery. Note, that
the described development is a textbook example
of business cycle with driving force in the financial
market deregulation, credit money creation and fi-
However, the drop in economic activity after the
year 2008 is more than a cyclical discrepancy from the
potential output. Halmai and Vasary (2012) showed
that the European recession has an impact on the
growth through three different channels: capital
accumulation, labour input and the total factor pro-
ductivity. Applying the production function approach,
they concluded that the potential growth rate both
in the Euro area and the US falls in 2009–2010 (it is
lower by 1.5% in the US and by 0.8% in the Euro area).
The problem is that filtering techniques provide
nothing less than a well defined statistics which meas-
ures nothing that would have a direct connection to
the economic theory. Therefore, the results of the
AGRIC. ECON. CZECH, 59, 2013 (9): 389–395 391
economic cycle synchronization during the financial
crisis are rather the outliers than the evidence of the
Prior to the application of time-frequency analysis
methods the input data of the industry production
index is transformed by the natural logarithm and
the long-term trend is removed. Instead of using the
common filtering techniques (e.g. Hodrick-Prescott,
Kalman, Baxter-King or Christiano–Fitzgerald filter),
we apply the singular value decomposition to remove
the long-term trend (Carvalho et al. 2012). Our meth-
odological contribution is in the decomposition into
components which allow not only the elimination of
the trend but also the outliers caused by the financial
crisis in the years 2007–2010.
The main objective of this paper is to identify
changes of the co-movements in the time-frequency
domain to verify the hypothesis of the endogeneity
of the OCA. We focus on the crisis period during the
years 2007–2010 when a significant symmetric shock
affected economic activity across the whole Euro area.
The proposed methodological approach will be ap-
plied on the economic activity in the core Euro area
countries (Germany, France, Belgium, Austria and the
Netherlands), where the hypothesis of the endogeneity
of the OCA criteria is generally assumed. Obviously,
the acceptance of the hypothesis of endogeneity in
these countries is a significant contribution for the
policy makers to implement unconditionally the real
and nominal convergence criterions at the time of
joining the Euro area.
MATERIAL AND METHODS
In order to demonstrate the performance of the
investigated methods, we used the monthly data of
the industrial production index in the period 1958/
M2-2012/M4 (volume index year 2005 = 100). The
datasets were provided by the OECD open database
of short-term economic indicators. The additive
decomposition is applied in the following form:
yt = gt + ct + et, t = 1, ... , n (1)
where gt denotes the long-term trend, ct is the cyclical
component and et is the irregular component. For the
identification of long-term trend we use the singular
value decomposition (SVD) (Carvalho et al. 2012).
The first step of the SVD is to make the trajec-
tory matrix from the input time series y=(y1, y2,
…, yN)’ of the length N without any missing values.
The trajectory matrix T with K × L dimension and
takes the form:
The parameter L such that 2 < L < N/2 to embedded
into the initial time series y is defined by the user.
Consequently we apply the trajectory matrix T SVD to
obtain the trajectory matrices Ti, i = 1, …, L. From an
eigenanalysis of TT’ we collect the eigenvalues λ1≥ …
≥ λr, where r = rank(TT’) and the corresponding left
and right singular vectors, respectively denoted as
Ui and Vi. We can write:
In the following analytical step, we use the wavelet
transform (Mertins 1999). The continuous wavelet
transform of the time series yt with respect to the
mother wavelet Ψa,τ(t) is defined as
a > 0, τ ∈ R (3)
where the mother wavelet takes the form
is the time position, a is the parameter of dilatation
(scale), which is related to the Fourier frequency
and the numerator of the fraction
conservation of energy.
To be the invertible transform, the basis (mother
wavelets) functions must be mutually orthogonal,
have zero mean value and limited to finite time in-
terval. That is
\ Z< dtet ti
Where Ψ(ω) is the Fourier transform of Ψ(t). There
is an inverse wavelet transformation defined as
To satisfy the assumptions for the time-frequency
analysis, the waves must be compact in time as well as
in the frequency representation. There are a number
of wavelets used, such as the Daubeschie, Morlet, Haar
or Gaussian wavelet (Gençay et al. 2002).
All results are processed in the MATLAB software.
392 AGRIC. ECON. CZECH, 59, 2013 (9): 389–395
The used time series comprise a very long time
period including several significant and temporary
economic recessions called crises. The singular value
decomposition provides the band-pass filtered output
(Figure 1). Figure 1 presents the input time series
and the estimated trend including the slow-moving
component (trend) and the cyclical movements with
a frequency noticeably larger than 32 quarters (move-
ments regarded outside from the range of business
cycle). In the similar manner as in Carvalho et al.
(2012), we discard these two components for the
subsequent wavelet analysis. Noticeably, the singu-
lar value decomposition provides an instrument to
eliminate long waves from the time series caused by
the most significant global crisis. We can distinguish
the drop in economic activity after the first oil crisis
in the year 1973, the EMS currency crisis in the years
1992–1993 and the last financial crisis in the years
Figures 2– 4 provide the co-spectrum of movements
in economic activity of the selected core Euro area
countries. The figure presents the dynamic of business
cycles during the last 50 years. A few countries show
co-movements at shorter waves than the assumed
business cycle frequencies (range between 6 and
32 quarters or 32 and 96 months). Specifically, we
can find the most significant co-movements among
France, the Netherlands and Belgium. These countries
were synchronized in business cycles during the oil
crisis. On the contrary, we can find a lower degree
of business cycles synchronization in Germany and
Austria. In the all selected countries, we can find
significant co-movements before and during the
recent financial crisis, especially after the year 2004
with the centre in 2009.
Evidently, global macroeconomic shocks play an
important role in the business cycle synchroniza-
tion. However, we did not identify a symmetric shock
because the symmetric declines in economic activity
during the crises periods were eliminated from the
input time series. The identified co-movements con-
centrated on the residual fluctuation only. Of course,
the identified synchronization of cyclical movements
is related to the macroeconomic shocks, but only as
an indirect consequence sources reallocation be-
tween the economic sectors, the impact of changes
in macroeconomic policies or the mutual integration
of the Western European countries.
It is generally agreed that Germany, France, Austria
and the Benelux countries have a similar shape of the
business cycle since the 70s, but it was not yet clear
whether the European integration process contrib-
uted to the synchronization, especially after the Euro
adoption. The results of the analysis provide clear
evidence that the synchronization of cyclical move-
ments in economic activity between the selected core
Figure 1. Singular value decomposition of the Industrial Production Index
Source: OECD database
AGRIC. ECON. CZECH, 59, 2013 (9): 389–395 393
Figure 2. Economic cycle co-movements between Germany, France, Netherlands and Austria
Figure 3. Economic cycle co-movements between Belgium, Germany, France, Netherlands and Austria
Figure 4. Economic cycle co-movements between France, Austria and Netherlands
Belgium/Germany – wavelet cospectrum Belgium/France – wavelet cospectrum
Germany/France – wavelet cospectrum Germany/Netherlands – wavelet cospectrum
Germany/Austria – wavelet cospectrum France/Netherlands – wavelet cospectrum
Belgium/Netherlands – wavelet cospectrum Belgium/Austria – wavelet cospectrum
France/Austria – wavelet cospectrum Netherlands/Austria – wavelet cospectrum
394 AGRIC. ECON. CZECH, 59, 2013 (9): 389–395
Euro area member countries significantly increased
after the year 2002. The frequency of co-movements
was identified shorter than 6 years in all selected
DISCUSSION AND CONCLUSIONS
Modelling fluctuations in economic activity through
de-trending economic time series is common in the
measurement of the business cycle synchronization
among the Euro area member countries. There are
many technical approaches applied in this area, includ-
ing the analysis in frequency and the time-frequency
domains. However, the common filtering techniques
spuriously identify cyclical movements in economic
activity during the deeper and longer lasting economic
recessions. Therefore, we suppose that the results of
the synchronization analysis are overestimated dur-
ing the financial crisis. The results of co-movements
in the time-frequency domain subsequently identify
symmetric shocks that cannot be considered as the
business cycle synchronization.
Our contribution is to provide an alternative meth-
odological approach to eliminate the slow-moving
component including the drop in economic activity
caused by financial crisis. The subsequent wavelet
analysis identified a significant increase in the business
cycle synchronization in the core Euro area member
countries after the year 2002. We cannot conclude
that financial crisis contributed or reversed the pro-
cess of convergence because there is an insufficient
number of observations. However, we can confirm
the hypothesis of the endogeneity of the OCA criteria
during the last decade.
The conclusion provides important policy impli-
cations. The recent discussions deal with the asym-
metries within the whole Euro area or the EU. The
focus is mostly on the periphery countries (Greece,
Ireland, Portugal, and Spain) and the new EU member
countries. Kočenda (2001) or Kutan and Yigit (2005)
discovered that the real convergence of the new EU
member countries is rather idiosyncratic although
there is an empirical evidence showing that it will
take several decades for the convergence to be fully
completed (Kočenda et al. 2006). The point is that
many of the current Euro area members adopted the
Euro as soon as they fulfilled the Maastricht criteria
which means that just the nominal convergence has
We focused on the core Euro area countries and
confirmed that the business cycle synchronization
is historically greater – the endogeneity of the OCA
criteria was accepted. However, we assume that this
aims only at the countries where both the nominal
and real convergence to the OCA criteria is achieved.
Therefore, the assumptions of the OCA theory, es-
pecially the real convergence criteria, should not be
undervalued during the accession process.
We thank Evžen Kočenda and Jarko Fidrmuc for
useful comments and suggestions. We have also ben-
efited from discussions at the International Conference
Mathematical Methods in Economics (Karviná,
September 2012) and the 12th EACES International
Conference (Paisley, September 2012).
The results introduced in the paper are supported
by the Czech Science Foundation via the grant No.
P402/11/0570 with the title “Time-frequency approach
for the Czech Republic business cycle dating’ and by
the Jean Monnet Multilateral Research Group Grant
No. 530069-LLP-1-2012-1-CZ-AJM-RE with the title
“CEE Banking sector stability after the reform of the
European financial supervision”.
It was performed in the laboratories support-
ed by the SIX project; the registration number
CZ.1.05/2.1.00/03.0072, the operational program
Research and Development for Innovation.
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Received: 24th January 2013
Accepted: 11th February 2013
Svatopluk Kapounek, Mendel University in Brno, Zemedelska 1, 613 00 Brno, Czech Republic
Jitka Poměnková, Brno University of Technology, Purkynova 464/118, 61200, Brno, Czech Republic
e-mail: firstname.lastname@example.org, email@example.com