Characterising the financial cycle : a multivariate and time-varying approach. No 1846 / September 2015.
Date: 2015-11-04
Institutions: European Central Bank
Subjects: econometrics, economic cycle, financial market, financial regulation, macroeconomics

Yves S. Schüler, Paul P. Hiebert and 
Tuomas A. Peltonen  

Working Paper Series 

Characterising the financial cycle: 
a multivariate and time-varying 
approach 

No 1846 / September 2015 

Note: This Working Paper should not be reported as representing the views of the European Central Bank (ECB). 
The views expressed are those of the authors and do not necessarily reflect those of the ECB 

 
 
 
 
 
 
Abstract

We introduce a methodology to characterise ﬁnancial cycles combining a novel multivariate spec-
tral approach to identifying common cycle frequencies across a set of indicators, and a time vary-
ing aggregation emphasising systemic developments. The methodology is applied to 13 European
Union countries as well a synthetic euro area aggregate, based on a quarterly dataset spanning
1970-2013. Results suggest that credit and asset prices share cyclical similarities, which, cap-
tured by a synthetic ﬁnancial cycle, outperform the credit-to-GDP gap in predicting systemic
banking crises on a horizon of up to three years. Financial cycles tend to be long, particularly
in upswing phases and with important dispersion across country cases. Concordance of ﬁnancial
and business cycles is observed only 2/3 of the time. While a similar degree of concordance for
ﬁnancial cycles is apparent across countries, heterogeneity is high – whereby a cluster of countries
tends to exhibit a high synchronisation in their ﬁnancial cycle phases.

Keywords: Financial cycle · Spectral analysis · Power cohesion · Macroprudential policy

JEL-Codes: E30 · E40 · C54

ECB Working Paper 1846, September 20151NON-TECHNICAL SUMMARY

The recent global ﬁnancial crisis provided a vivid illustration of the real effects of the materialisation

of systemic risk that was related to a build-up of various macro-ﬁnancial imbalances and vulnerabili-

ties that can be related to excesses in the ﬁnancial cycle.

Beyond enhancing ﬁnancial system resilience, attenuating ﬁnancial cycles is one of the two

fundamental goals of macroprudential policy. Despite the prominence of this goal in macroprudential

policy, there is no generally agreed deﬁnition of the ﬁnancial cycle. Moreover, existing analyses on

characterising ﬁnancial cycles remain scarce, and are in many ways not yet suitable for policy use.

Limitations include the geographic coverage of the analysis (in that it tends to focus on a limited

number of countries) and a lack of consensus on the mechanics of measurement, such as the choice of

indicators and the method used to construct them. Ideally, a unique synthetic measure of the ﬁnancial

cycle would summarise the (co-)movements over time of a range of ﬁnancial sector variables,

covering quantities and prices. In practice, however, over-reliance on a single composite measure

is not advisable as each constituent variable contains relevant information for macroprudential

policy-making.

Measuring ﬁnancial cycles has become critical for macroprudential policymaking in the EU

countries in the context of new macroprudential tools included in the European Union legislation, as

well as due to the launch of the Single Supervisory Mechanism (SSM) with new macroprudential

role for the European Central Bank (ECB). Thus, there is an urgent need to obtain a robust view on

capturing ﬁnancial cycles – balancing cross-country consistency with individual country relevance.

However, as ﬁnancial cycles are not directly observable, they must be inferred. Against this back-

drop, we present a methodology aimed at furthering the basis for country-speciﬁc macroprudential

policymaking.

More speciﬁcally, we suggest a methodological framework for capturing ﬁnancial or, in general,

economic cycles across a set of indicators, consisting of two main building blocks. First, a novel

multivariate spectral measure of power cohesion is introduced. This method allows for discovery

of common cycle frequencies across a set of indicators, on the basis of correlations of estimated

(cross-)spectral densities. Second, a time-varying aggregation method is presented which allows for

a unique composite cycle constructed from constituent indicators capturing economic ﬂuctuations of

a systemic nature.

The above method is applied to characterise and extract country ﬁnancial cycles for 13 European

ECB Working Paper 1846, September 20152Union (EU) countries and a euro area aggregate for a quarterly dataset spanning 1970-2013. As

indicators we employ series typically used in the growing body of literature to capture the ﬁnancial

cycle, which are total credit and measures for different asset markets (residential property prices

and equity prices). We complete this set, i.e., the portfolio choice faced by economic agents, by

including benchmark bond yields as a proxy for bond market pricing. To contrast the characteristics

of ﬁnancial and business cycles, we characterise business cycles applying the same methodology on

a set of business cycle indicators, which are economic output, unemployment rate, consumer price

inﬂation, and benchmark bond yields.

Our main empirical ﬁndings are threefold. First, credit and asset prices are marked by cyclical

similarities. That is, credit, residential property prices, equity prices and – to a lesser extent – bond

yields, exhibit common cycle frequencies, which, captured by a synthetic ﬁnancial cycle, outperform

the credit-to-GDP gap in predicting ﬁnancial crises at a horizon of one to three years ahead. Second,

ﬁnancial cycles tend to be long, particularly in upswing phases. On average ﬁnancial cycles last

7.2 years – though with important dispersion across countries. While ﬁnancial cycles exhibit

co-movement only 2/3 of the time across the countries analysed, the co-movement of some EU

country clusters is considerable – with the degree of co-movement among the six most synchronised

ﬁnancial cycles at 78% contrasting with 53% for the least synchronised one with the entire set

of cycles. Third, country level ﬁnancial cycles are not strongly aligned with their business cycle

counterparts (67% on average).

Overall, results suggest a need for careful implementation of macroprudential policy, taking into

account speciﬁcities in country level cycles, the possibility of cross-country co-movement of cycles,

and the need for mapping of macroeconomic and macroprudential policies to potentially diverging

economic and ﬁnancial developments.

ECB Working Paper 1846, September 20153“The following deﬁnition seems to capture what experts refer to as the business cycle: The business

cycle is the phenomenon of a number of important economic aggregates [. . .] being characterized by

high pairwise coherences [. . .]. This deﬁnition captures the notion of the business cycle as being a

condition symptomizing the common movements of a set of aggregates.”

(Sargent, 1987, p. 282)

1

INTRODUCTION

Attenuating ﬁnancial cycles is one of the main goals of macroprudential policy. Indeed, recent ex-

perience of euro area country stress, in a broader context of the global ﬁnancial crisis, has vividly

illustrated systemic risk inherent in the build-up and correction phases of ebullient ﬁnancial cycles.

At the same time, ﬁnancial cycles remain considerably less studied than their business cycle counter-

parts, despite a rapid ongoing expansion of research. While previous studies on ﬁnancial cycles have,

in many ways, been seminal in establishing the literature on the empirical measurement of ﬁnancial

cycles, still many open questions remain; especially with respect to country characteristics relevant

for applying macroprudential policies at the national level.

In this context, this paper addresses the following questions: i) Do credit and asset price indicators

embed cyclical similarities which can be exploited to construct a notional composite ﬁnancial cycle

that helps in the prediction of ﬁnancial crises? ii) What are the characteristics of ﬁnancial cycles,

and how do they differ across countries? iii) What is the relation of these ﬁnancial cycles to business

cycles?

To answer these questions, we propose a methodological framework for capturing ﬁnancial and

business cycles across a set of indicators, consisting of two main building blocks. First, a novel

multivariate spectral measure of power cohesion is introduced. This method allows for discovery of

common cycle frequencies across a set of indicators, on the basis of correlations of estimated (cross-

)spectral densities. Second, a time-varying aggregation method is presented which allows for a unique

composite cycle constructed from constituent indicators capturing ﬂuctuations of a systemic nature.

The above method is applied to characterise and extract country ﬁnancial cycles for 13 Euro-
pean Union (EU) countries and a euro area aggregate for a quarterly dataset spanning 1970-2013.1

Country-speciﬁc ﬁnancial cycle frequencies are captured by common contemporaneous cyclical

movements of total credit and representative asset prices from all major market segments (property,

equity, and bond), irrespective of phase differences, which in turn allow for extraction of country-

speciﬁc ﬁnancial cycles. To benchmark ﬁnancial cycle characteristics, we compare speciﬁcities to

1The countries are Austria (AT), Belgium (BE), Germany (DE), Denmark (DK), Spain (ES), Finland (FI), France (FR),

Ireland (IE), Italy (IT), the Netherlands (NL), Portugal (PT), Sweden (SE), and the United Kingdom (UK).

ECB Working Paper 1846, September 20154business cycles analogously derived from economic output, unemployment, consumer price inﬂation,

and benchmark bond yields.

Our main empirical ﬁndings are threefold. First, credit and asset prices are indeed marked by

cyclical similarities. That is, credit, residential property prices, equity prices and – to a lesser extent

– bond yields, exhibit common cycle frequencies, which, captured by a synthetic ﬁnancial cycle, out-

perform the credit-to-GDP gap in predicting systemic banking crises at a horizon of one to three years

ahead and also enhance the predictability of crises for longer horizons. Second, ﬁnancial cycles tend

to be long, particularly in upswing phases. On average ﬁnancial cycles last 7.2 years – though with

important dispersion across countries; shortest being around four (AT and PT) and longest around

17 years (ES). Further, while ﬁnancial cycles exhibit co-movement only 2/3 of the time, such co-

movement is quite considerable for many, but not all, of the countries analysed. Concordance among

the six most synchronised ﬁnancial cycles is 78% (BE, UK, SE, FI, ES, IE). Germany has the weak-

est link to cycles of other countries (53% on average). Third, country level ﬁnancial cycles are not

strongly aligned with their business cycle counterparts (67% on average), suggesting an important

role for macroprudential policy.

The ﬁnding that ﬁnancial cycles are generally longer than business cycles is consistent with the

existing literature on ﬁnancial cycles. Claessens et al. (2012), for a set of 43 countries and taking

a cross-country perspective, ﬁnd that ﬁnancial cycles as separately measured by credit, house, and

equity prices, are long and asymmetric. Focusing on measures of credit, Aikman et al. (2015) observe

that, in contrast to business cycles, credit cycles have an important medium term dimension. Likewise,

ﬁndings regarding the synchronisation of cycles and their relation to business cycles is in line with

Breitung and Eickmeier (2014), Claessens et al. (2012), and Hiebert et al. (2014).

Our ﬁndings differ from the existing literature, however, in highlighting country speciﬁcities in

cycle length as well as importance of individual contributing asset price series. While the aggregate

ﬁndings regarding cycle length are broadly in line with previous research, our study suggests a need

for caution in country attribution – given heterogeneity in features of underlying estimated country

cycles. Indeed, while we ﬁnd that ﬁnancial cycles tend to be long, there exist important ﬂuctuations at

shorter cycles given asymmetries and irregularities of indicator cycles – contrasting with the ﬁnding

by Drehmann et al. (2012) that ﬁnancial cycles derived on the basis of credit and house prices are

only characterised by ﬂuctuations in the range of 8 to 30 years and last on average 16 years. In this

way, there is the possibility of serious bias in extrapolating benchmark cycle estimates for a broader

group of countries. The same holds true in considering relevance of individual ﬁnancial series at the

country level, whereby equity and bond markets share important common cycle characteristics with
credit and residential property prices.2

2From a different perspective and with respect to equity, the cyclical importance of these markets, in addition to credit
and property prices, stems from their role in presaging systemic crises – as emphasised by Claessens et al. (2012) or Schüler

ECB Working Paper 1846, September 20155The empirical ﬁndings of our study contribute to this recent strand of literature in several other

ways. First, while previous research has suggested that cross-checking many indicators is important

for characterising ﬁnancial cycles, we provide a multivariate treatment. Second, we broaden asset

prices used to characterise the ﬁnancial cycle to encompass government bond markets (and not only

property and equity), which constitute a major asset class, and, thus, completes the portfolio choice

faced by economic agents. Third, we derive a composite indicator of ﬁnancial cycles, one which

allows for a time-varying importance of constituent indicators. In addition, given the preponderance

of year on year transformations in previous studies (e.g. Drehmann et al. (2012)), we examine the

implications of different transformations of ﬁnancial and business cycle indicators for their spectral

properties, which is vital to understand differences between cyclical ﬂuctuations in the real economy
versus the ﬁnancial sector.3

The paper is organised as follows. Section 2 discusses methodology and Section 3 presents the

application to European Union countries and the euro area aggregate. Section 4 concludes.

2 METHODOLOGY

Financial cycles are characterised by exploiting common movements of indicator series that pertain

to the ﬁnancial sector. The exposition of the methodology can be broken down into two main parts.

First, we detail the spectral approach for obtaining country-speciﬁc ﬁnancial cycle frequencies across

a set of variables, which we call power cohesion. Second, a time-varying aggregation method for this

set of variables to a unique composite ﬁnancial cycle measure is described.

2.1 Power cohesion - Discovering ﬁnancial cycle frequencies across a set of indicators

For identifying ﬁnancial cycle frequencies common to a set of variables, we propose a novel multi-

variate spectral measure that we call power cohesion (PCoh). It can be formulated as

PCohX (ω) =

1
(M − 1)M

(cid:88)

i(cid:54)=j

|fxixj (ω)|,

(1)

where 1 ≤ i ≤ M , 1 ≤ j ≤ M , X = (X (cid:48)

T )(cid:48) is a T ×M matrix and Xt = (x1,t, . . . , xM,t)
1, . . . , X (cid:48)
(1 × M ). Further, t = 1, . . . , T and M ≥ 2 reﬂect the time dimension and number of variables

respectively, and ω ∈ [−π, π] denotes the cycle frequency. Xt is assumed to contain stationary

stochastic processes with well-deﬁned normalised cross spectral densities, which can be written as

fxixj (ω) =

sxixj (ω)
σxiσxj

=

1
2π

∞
(cid:88)

k=−∞

Cov[xi,t, xj,t+k]
σxiσxj

e−ikω,

(2)

(2014), who show that recessions accompanied with equity market busts are more severe than without.

3See Appendix A.2.

ECB Working Paper 1846, September 20156where σxi and σxj are the standard deviations and sxixj (ω) is the cross-spectrum of xi,t and xj,t.

Cov[xi,t, xj,t+k] reﬂects the cross-covariance between xi,t and xj,t+k and i is the imaginary unit.

Phase shifts of cycles across variables should in principle not alter a notion of frequency common

to a set of variables. As such, they are discarded using PCoh by considering the absolute values of

the cross-spectra. Recall that the cross-spectrum may be written as sxixj (ω) = cxixj (ω) − iqxixj (ω),
where the real part is captured by the co-spectrum cxixj (ω) and the imaginary part by the quadrature
spectrum qxixj (ω). The real part describes the covariance in phase, whereas the imaginary part the
one out of phase.4 Using the modulus operation in Equation (1), we can see that

|fxixj (ω)| =

|sxixj (ω)|
σxiσxj

=

(cid:113)

c2
xixj

(ω) + q2

xixj

(ω)

σxiσxj

.

(3)

This implies that, using the PCoh methodology, both covariances (in phase and out of phase) are

preserved.

Further, we use the normalised cross-spectral densities to construct our measure of power cohe-

sion since the normalised measures are mapped into the same support which allows for a reasonable

averaging of densities. That is, the support of PCoh(ω) when integrating from −π to π lies within 0

and 1. Recall that the cross spectrum integrates to the unconditional covariance between xi,t and xj,t

(see e.g. Hamilton (1994, p. 271)),

From this it follows that

(cid:90) π

−π

sxixj (ω)dω = Cov[xi,t, xj,t].

− 1 ≤

(cid:90) π

−π

fxixj (ω)dω ≤ 1.

(4)

(5)

Further, taking the absolute value of the normalised cross-spectrum, i.e., |fxixj (ω)| and integrating

it from −π to π leads to the support

0 ≤

(cid:90) π

−π

|fxixj (ω)|dω ≤ 1.

(6)

The upper bound of 1 in Equation (6) holds as the covariance in phase and out of phase cannot

exceed the product of the standard deviations of both variables.

Since the normalised cross-spectra indicate the contribution of different cycle lengths or frequen-

cies to the overall co-variance, power cohesion depicts the importance of common ﬂuctuations across

cycle frequencies over a set of indicators. Of course, the importance given to each cross-spectrum,

reﬂected by the weight used for averaging may vary; in our setup these are assumed to be equal (see

Equation (1)) in order to be agnostic about the importance of speciﬁc indicators considered.

4Out of phase refers to cycles that are not contemporaneous. As a possible example consider two cosine waves that
are identical, just that one is shifted by π/2. The usual correlation coefﬁcient between the two series is zero, while the
underlying cycles are the same.

ECB Working Paper 1846, September 20157Contrasting power cohesion with squared coherency cohesion

To better understand our proposed measure, we contrast power cohesion to cohesion derived from

a comparable traditional measure of squared coherency. More speciﬁcally, we show that power co-

hesion should be preferred over the common spectral dependency measures if one is interested in

detecting cycle frequencies that contribute most strongly to overall (co-)variance.

Squared coherency differs in that it relates the cross-spectrum to the auto-spectra at each frequency

ω. Squared coherency is a textbook quantity, which has been used for researching on cyclical simi-

larities of business cycles across countries (see, e.g., A’Hearn and Woitek (2001)) and has important

parallels to other measures mentioned in the literature proposed for analysing cyclical similarities

across variables, as cohesion based on dynamic correlation (see Croux et al. (2001)). Dynamic cor-

relation similarly relates the co-spectrum to the autospectra at different frequencies and, thus, suffers
from a similar disadvantage.5 Let squared coherency cohesion be denoted by SCoh. It is deﬁned as

SCohX (ω) =

1
(M − 1)M

(cid:88)

i(cid:54)=j

|sxixj (ω)|2
sxixi(ω)sxjxj (ω)

.

(7)

SCoh(ω) of one, at frequency ω, indicates linear equivalence of processes and zero implies linear

unrelatedness. As can be seen, squared coherency cohesion relates each cross-spectrum, sxixj , to the
respective auto-spectra, sxixi(ω) and sxjxj (ω), at frequency ω. On the other hand, power cohesion
relates each cross-spectrum to the unconditional standard deviations, σxi and σxj . For power cohesion
this implies that frequencies, which do not contribute to the average covariance are mitigated. On

the contrary, in the case of squared coherency cohesion these frequencies may be emphasised. For

detecting important cyclical ﬂuctuations across a set of indicators this case has to be excluded and,

thus, we argue power cohesion should be preferred.

To further clarify this point, consider the following data generating process (DGP):

xi,t = ψi,t + εi,t,

which is characterised by a cyclical component

ψi,t = αi,t cos(λt).

(8)

(9)

αi,t denotes a random amplitude, which may follow a stationary autoregressive process of or-
der one, λ is the cycle frequency.6 The idiosyncratic component, εi,t, is white noise with possible
contemporaneous covariance.

5Dynamic correlation is deﬁned as cxixj (ω)/(sxixi (ω)sxj xj (ω)). With this measure, the authors analyse the cohesion

of business cycles in Europe and the US.

6A more realistic DGP would also include a phase shift of the cosine wave depending on i and t, however, as both PCoh
as well as SCoh measure by deﬁnition cyclical ﬂuctuations irrespective of phase shifts, we exclude this case for ease of
exposition.

ECB Working Paper 1846, September 20158A common cycle is present if αi,t = γiαt, where γi is assumed to be some nonzero constant.
t = (ε1,t, . . . , εM,t), and stacking equations

Then, writing ψt = αt cos(λt), γ(cid:48) = (γ1, . . . , γM ), ε(cid:48)
yields

Xt = γψt + εt.

(10)

Since ψt is uncorrelated with εt for all t and k, it follows that the spectrum of Xt is the sum of the

two spectra of ψt and εt, i.e.,

sX (ω) = γsψ(ω)γ(cid:48) + sε(ω).

For this DGP SCoh can be written as

SCohX (ω) =

1
(M − 1)M

=

1
(M − 1)M

(cid:88)

i(cid:54)=j

(cid:88)

i(cid:54)=j

|sxixj (ω)|2
sxixi(ω)sxjxj (ω)

(γiγjsψ(ω) + sεiεj (ω))2

(γ2

i sψ(ω) + sεiεi(ω))(γ2

j sψ(ω) + sεjεj (ω))

(11)

(12)

(13)

To illustrate the important difference between power cohesion and squared coherence cohesion,

two extreme cases are considered in the following: (1) The case of no white noise and (2) the case of

perfectly correlated white noise. In the ﬁrst case SCoh becomes:

SCohX (ω) =

1
(M − 1)M

(cid:88)

i(cid:54)=j

γ2
i γ2
i γ2
γ2

j s2
j s2

ψ(ω)
ψ(ω)

= 1

(14)

The last equality holds as, due to the random amplitude αt, sψ(ω) has nonzero power for all
frequencies. The result implies that SCoh cannot be used to detect the common cycle, as SCoh

indicates a one for all frequencies. In contrast, PCoh captures the common cycle, since it does not

relate the cross-spectra to the autospectra.

Adding white noise to ψi,t induces a trade-off between variances, i.e., if the white noise process
has greater variance contribution at each frequency then ψi,t, the common cycle, will not be apparent

using any of the two measures, PCoh or SCoh. In case it is smaller, the capturing of the cycle in case

of SCoh depends on the correlation between the noise components, εi,t and εj,t. This can be noted by
considering case (2). It implies that sεiεj (ω) = sεiεi(ω) = sε(ω) and yields

SCohX (ω) =

1
(M − 1)M

(cid:88)

i(cid:54)=j

(γiγjsψ(ω) + sε(ω))2

(γ2

i sψ(ω) + sε(ω))(γ2

j sψ(ω) + sε(ω))

lim
sψ(ω(cid:54)=λ)→0

SCohX (ω (cid:54)= λ) = 1

(15)

(16)

Thus, even in situations in which the white noise spectrum has a relatively small contribution to the

overall variance of the process, but is highly correlated, SCoh potentially does not capture a common

ECB Working Paper 1846, September 20159cycle. This result implies that if another common cycle with lower variance contribution is present, it

receives the same importance as the cycle with greater variance contribution. Contrarily, PCoh reports

cycles relative to their variance contribution. Note that this type of misleading conclusion can also

arise if spectra are close to zero, which may follow as a consequence of overdifferencing or seasonal

adjustment.

The use of power cohesion

Power cohesion serves the purpose of identifying most important ﬁnancial cycle frequencies. In this

paper we follow three different ways for locating these frequencies:

First, we identify the peak to locate the cycle lengths of maximum co-movement of indicators

capturing ﬁnancial cycles, building on A’Hearn and Woitek (2001) who identify peaks of single spec-

tra in the context of business cycles. This identiﬁcation of a peak is not necessarily consistent with

average cycle length in the presence of strong asymmetries and irregularities in variables capturing

ﬁnancial cycles.

Second, a window of cycle frequencies around the above peak to capture a certain percentage of

most important co-movements is speciﬁed. We use this range to ﬁlter the composite ﬁnancial cycle

and its underlying indicators. Since the major characteristics of ﬁnancial cycles are less established

than the ones of business cycles, we argue that the choice of percentage range around an estimated

peak is preferable to an exogenously ﬁxed frequency window for band-pass ﬁltering such as that

assumed in existing studies (e.g., Drehmann et al. (2012)).

Third, we identify a highest density region in the spirit of Hyndman (1996), that is especially ap-

propriate for summarising multimodal distributions. We report this highest density region in Section

3.2 and use it to compare characteristics of ﬁnancial and business cycles. We do not use it for ﬁlter-

ing the composite cycle, as highest density regions cannot always be summarised by one continuous

range. That is, highest density regions do not necessarily overlap.

Empirical issues

We estimate the (cross-)spectral densities through cross-correlations. Further, a Parzen window with

a bandwidth of

T · 5 is used, which compared to the bandwidth used in Aikman et al. (2015) is

√

slightly larger and emphasises our aim to have rather unbiased spectral density estimates; at the cost

of a higher variance. As is common, we only consider the frequency window 0 to π, which sufﬁces

to determine the cyclical properties of variables when considering the absolute value of the spectral

densities.

Conﬁdence intervals for spectral densities are bootstrapped (see Figure 15). As suggested in Croux

et al. (2001) and described in Franke and Härdle (1992) as well as in Berkowitz and Diebold (1998),

we bootstrap the individual (cross-)spectra, rather than the time series. For each cross-spectrum we

ECB Working Paper 1846, September 201510resample from a χ2
each periodogram.7

2-distribution using 5000 replications and use a Gaussian kernel for smoothing

We calibrate the frequency window around the peak of power cohesion using available knowledge

on business cycles. First and as is standard in the literature on turning points, we require that the

minimum cycle length considered is 5 quarters and the maximum cycle length remains unrestricted.

Not restricting the maximum cycle length may lead to ultra long cycles or trends being included in

the ﬁnal frequency window. However, we ascertain stationarity of indicators and, thus, argue not to

capture trend components; further, given that very long cycles are imprecisely estimated and ﬁltered
using spectral methods, upper limits should be interpreted with care.8 Second, capturing 2/3 of total

co-movements across indicators leads to frequency windows for business cycle indicators for which

the median of the highest frequencies is around 2 years, which is often used as an input to band pass

ﬁlters when smoothing business cycle indicators.

Speciﬁcally, we propose to endogenously select a frequency window by determining the maximum

(ω1) and minimum (ω2) cycle lengths (ω2, ω1 ∈ [0, 2π/5] ∧ ω2 ≥ ω1) through

(cid:82) ω2
PCohX (ω)dω
ω1
(cid:82) π
0 PCohX (ω)dω

min
ω2−ω1

≥ p.

(17)

where p is deﬁned to be in the range [0,1], such that the frequency band contains p · 100% of
common variation excluding variation with a frequency below 1.25 year.9 In our setup we assume

p = 2/3. By ﬁnding the maximum and minimum cycle length that minimises the distance ω2 − ω1,

we assure to pick the most important common ﬂuctuations across indicators around the peak.

At last, the frequency window, which we identify, serves as an input to the asymmetric speciﬁca-

tion of the band pass ﬁlter proposed by Christiano and Fitzgerald (2003) when smoothing composite

ﬁnancial cycles as well as individual series. In applying the band pass ﬁlter, we elect for the speciﬁca-

tion that does not correct for unit roots or drifts/time trends in the variables in order to keep distorting

effects of the ﬁlter to a minimum. To minimise endpoint problems, we forecast the composite index

as well as the indicators 10 years ahead using an AR(p) process with intercept where the maximum

lag length is set to 8 and the optimal number is selected via BIC. To further minimise endpoint prob-

lems we ﬁt the obtained ﬁltered series optimally to the unﬁltered series by transforming its mean and

variance such that squared deviations are minimised.

7This bootstrapping procedure assumes independence of cross-spectra, however, to the best knowledge of the authors,

research in this area is still ongoing and no solution for this exact problem has been proposed.

8We conduct a robustness analysis using the duration of Kondratiev waves as a maximum cycle length, which is 50 to 60
years. Excluding cycles of longer duration yields equivalent results. Findings are available from the authors upon request.
9An unrestricted range would select ultra-high frequencies, which can be related to the high ampliﬁcation that occurs

using the quarter-on-quarter ﬁlter.

ECB Working Paper 1846, September 2015112.2 Time-varying aggregation of indicators – Constructing a composite index of the ﬁ-

nancial cycle

The combination of indicators to a composite synthetic ﬁnancial cycle is obtained through time-

varying aggregation weights that exploit changing correlation structures between indicators. We re-

strict time-varying weights to emphasise alike (and therefore systemic) developments in the system.

Our approach is related to the methodology followed by Holló et al. (2012) for constructing an in-

dicator of systemic ﬁnancial stress. Apart from its advantage of time-varying weights in aggregation,
it emphasises robustness properties; also related to real-time updating.10

In a ﬁrst step, we pre-multiply indicators such that a rise in each contributing variable relates to

an upswing of the ﬁnal composite index.

In a second step and following Holló et al. (2012), we transform underlying indicators using their

empirical distribution function, i.e., each value of a single indicator is mapped into a unit free ordinal

scale in (0,1].

Third, we linearly combine indicators using time-varying weights, that exploit time-varying cor-

relations between indicator pairs. In capturing cyclical swings to construct a macroprudential notion

of the cycle, we would like to emphasise directional developments of a systemic nature, or put differ-

ently, movements of a set of indicators that are in a similar direction, i.e., indicators that are positively

correlated. In a situation in which there is a lack of models to describe the build-up of imbalances

in the ﬁnancial sector our procedure reﬂects an easy and tangible possibility. Technically we achieve

this by restricting correlations to be positive; negative correlations are assumed to be zero. While all

series enter the ﬁnal index by construction, it implies that movements of positively related series are
emphasised.11

More speciﬁcally, let (xi,[1], xi,[2], . . . , xi,[T ]) denote the ordered sample of variable xi,t. The

transformed indicators are derived by

10One alternative approach for aggregating common information contained in several variables is through principal com-
ponent analysis. This approach has, however, at least two drawbacks. First, cross-country comparability issues arise due to
a possible different selection of indicators across countries that explain most important contemporaneous movements. Sec-
ond, real-time updating is an issue in that new data points might alter the selection of indicators most relevant for common
ﬂuctuations. Indeed, a principal component analysis is static by deﬁnition and thus does not allow for capturing changing
trends in the interdependence between ﬁnancial indicators.

11To illustrate, consider the case of three indicators: if two of the series remain above (or below) their historical medians
and the third series is located below (or above) for an extended period of time, using our method, the ﬁnal signal tends to
reﬂect the location of the ﬁrst two series, since the third series is negatively related and negative correlations are assumed
to be zero. As a consequence, the overall aggregation weight of the third series is lower relative to the ﬁrst two; but still
larger than zero. Employing unrestricted correlations, negative and positive correlations would cancel each other out and the
aggregation would be similar to a simple average. In this case, the location of the ﬁnancial cycle would not emphasise the
build-up or correction of imbalances. Especially, for an early detection of imbalances or corrections visible in the majority
of indicators, we argue that our approach is the more favourable one.

ECB Working Paper 1846, September 201512yi,t = Fi,T (xi,t) =




r
T


1

for xi,[r] ≤ xi,t < xi,[r+1],

r = 1, 2, . . . , T − 1

(18)

for xi,t ≥ xi,[T ],

where Fi,T denotes the empirical cdf. Let Yt = (y1,t, . . . , yM,t) and ι be a vector of ones of dimension
1 × M . The single transformed indicators are aggregated in the following way

ζt =

1
ι(cid:48)Ctι

· ι(cid:48)CtY (cid:48)
t ,

where Ct is the time-varying cross-correlations matrix, i.e., the typical element of Ct, cij, is
σii,tσjj,t). We follow Holló et al. (2012), who propose to obtain the time-varying

ρij,t = σij,t/(

√

cross correlations on the basis of an exponentially-weighted moving average process, where

σij,t = λσij,t−1 + (1 − λ)(yi,t − 0.5)(yj,t − 0.5).

(19)

In this setup the transformed variables yi,t are centered using the median and λ represents the
decay factor. Due to the aggregation method ζt ∈ (0, 1] as well. ζt is then called the unﬁltered

composite indicator.

Updating ζt, similarly to Holló et al. (2012), is done by applying Equation (18) recursively over

expanding samples, i.e., “old” observations are ﬁxed and new ones are added to the existing distribu-

tion.

Time-varying correlations are modelled using a decay factor λ of 0.89. This is slightly smaller

than in Holló et al. (2012), who use 0.93. We employ a smaller decay factor since we have quarterly

(instead of daily) data with, thus, fewer observations. Using 0.89 starting conditions become negli-

gible at a faster rate. Further, covariances are initialised using the ﬁrst 8 quarters of observations for

each variable.

3 APPLICATION: EUROPEAN FINANCIAL CYCLES

This section contains an application of the methodology to a set of European Union countries. After

an exposition on data, their transformations, and descriptives on spectral properties, the application

of the methodology mirrors the two steps described in Section 2. First, the selection of ﬁnancial

cycle frequencies using power cohesion is detailed and, second, results for the composite indicators

of European ﬁnancial cycles are presented.

ECB Working Paper 1846, September 2015133.1 Data, transformations, and summary of cross-spectra

Data and transformations

Absent a single summary measure for the state of the ﬁnancial sector, we argue that a multivariate

approach that relies on a range of macro-ﬁnancial indicators provides the best-suited method for

obtaining a ﬁnancial cycle estimate.

In conceptualising the determinants of the ﬁnancial cycle suitable for macroprudential analysis,

we elect for a set of explanatory variables which build on the traditional set contributing to the build-

up and propagation of systemic risk. Studies to date have focused predominantly on various measures

of credit (generally transformations of total or bank based credit, either in changes in credit or ratios

to GDP), as well as prices for a subset of non-ﬁnancial sector balance sheet assets (real estate and

equity). Indeed, the choice of these variables can be thought of as corresponding to systemic ex-

ternalities underpinning the cycle such as those outlined in Claessens (2014) – that is, the scope for

strategic complementarities in asset allocations in ﬁnancial cycle upswings as well as ﬁre sale po-

tential for asset prices in cyclical downswings. At the same time, leverage (captured, for instance,

by the simple proxy of broad credit for which long time series of country data are available) plays

a key role in systemic risk propagation, the operationalisation of systemic risk monitoring (see, for

instance, European Systemic Risk Board (2014)). To include all main asset markets in our measure

of a synthetic ﬁnancial cycle, we amend this set of variables by benchmark government bond yields.

Thus, estimation is based on a parsimonious set of four variables relevant for the ﬁnancial cycle –

measuring credit, as well as prices in the main asset market segments (house prices, equity prices and

benchmark government bond yields). Further, we construct our measure of a reference business cycle

through indicators on economic activity (real GDP), labour markets (unemployment rate), consumer

price inﬂation, and the government benchmark bond yields as an available proxy for the price of

intertemporal substitution of real variables such as consumption and investment. The above variables

draw from a dataset covering 13 EU countries (AT, BE, DE, DK, ES, FI, FR, IE, IT, NL, PT, SE, and
UK) and the euro area aggregate, at a quarterly frequency spanning from 1970Q1 until 2013Q4.12

Variables are expressed in real terms (with the only exception of the unemployment rate). Long term

yields on government bonds are adjusted for inﬂation, i.e., they reﬂect real long term yields.

In this study, we analyse cycles in growth rates, rather than classical cycles or growth cycles (Hard-

ing and Pagan (2005)). So as to preserve cyclical turning points, a quarter-on-quarter differencing is

implemented – in keeping with the well-established NBER methodology (and CEPR in Europe) for

identifying peaks and troughs of the business cycle on the basis of quarterly changes in GDP. Thus,

total credit, house prices, equity prices, and GDP are measured in quarterly growth rates. bond yields,

unemployment, and inﬂation reﬂect quarterly percentage point changes. The exact details on the vari-

12Starting dates vary for BE and FI (1970Q4), ES (1971Q1), IE (1971Q2), AT (1986Q3), EA (1987Q1), and PT (1988Q1).

ECB Working Paper 1846, September 201514ables and their unit root properties are provided in Appendix A.1.13 Note that cycles identiﬁed by

Drehmann et al. (2012) are recovered from annual growth rates – however, this transformation lacks

precision for identifying turning points. We contrast the implications of both year on year (yoy) and
quarter-on-quarter (qoq) transformations for the resulting spectral properties in Appendix A.2.14

Table 1: Pre-multiplication of indicators: Financial cycle and business cycle index

Financial Cycle

Business Cycle

∆c ∆ph ∆pe ∆r ∆q ∆u ∆πp ∆r
−
×

−

×

−

×

×

×

Notes: − indicates that indicators have been multiplied by −1 before applying the transformation from Equation (18). × denotes no
pre-multiplication. ∆c refers to percentage changes in total credit, ∆ph to percentage changes in house prices, ∆pe to percentage changes
in equity prices, ∆r to percentage point changes in bond yields, ∆q to percentage changes in GDP, ∆u to percentage point changes of the
unemployment rate, and ∆πp to percentage point changes in inﬂation.

For deriving the composite indices, two further transformations are carried out. First, variables

are pre-multiplied to ensure that increases in their values correspond to an improvement of ﬁnancial

conditions. For the ﬁnancial cycle, this implies a pre-multiplication of benchmark government bond

yields by −1. An analogous pre-multiplication is also conducted for those business cycle indicators

which negatively relate to improving economic conditions, i.e. the unemployment rate in addition to

the bond yield – see Table 1 summarising all such restrictions. Second, indicators are transformed

using their ecdf-function as mentioned in Section 2.2 - thereby mapping series to a 0/0.5/1 scale.

Summary of cross-spectra

Figure 1 shows absolute cross-spectra across countries that are normalised, such that the maximum

value is one. Solid blue lines denote the median, lower dashed lines portray the 10th percentile and

the upper ones the 90th percentile. A small distance between the two dashed lines indicates that that

the cyclical properties of the respective indicator at that frequency is similar across countries, while a

long distance refers to the case where properties differ strongly.

The results indicate that there are strong cyclical commonalities between credit, house prices, and

equity prices for medium term frequencies that range between 8 and 20 years, that are consistent over

country cases, which can be seen by the relative small distance between the dashed lines. Considering

pairs involving bond yields, the evidence is not as strong, however, in the case of credit and house

prices, still, there are most important cycles located in the medium term region as the distribution is

most elevated compared to other part of the distribution. Co-movement of equity prices and bond

13Note that for ES and IE industrial production is employed. Details are provided in Appendix A.1.
14Summarising the results of this exercise, we draw the conclusion that the annual transformation removes the higher
frequency cycles, while the quarterly transformation emphasises them. Importantly, this does not change the relative signiﬁ-
cance of longer term cycles in the case of ﬁnancial indicators; however it does for the business cycle ones, i.e., transformation
of indicators matter for the business cycle but not for the ﬁnancial cycle. In contrast to ﬁnancial cycle indicators, business
cycle indicators have important variance located at short term frequencies, which vanish using the yoy ﬁlter.

ECB Working Paper 1846, September 201515Figure 1: Absolute normalised cross-spectra of indicators across countries
Notes: This panel shows the absolute and normalised cross-spectra of the ﬁnancial and business cycle indicators. The x-axis measures the
frequencies of cycles in radians from 0 - π/2. The blue area depicts business cycle frequencies, i.e., cycles with durations of 2.5-8 years
and the purple area marks medium term cycles (8-20 years). ∆c refers to percentage changes in total credit, ∆ph to percentage changes
in house prices, ∆pe to percentage changes in equity prices, ∆r to percentage point changes in bond yields, ∆q to percentage changes in
GDP, ∆u to percentage point changes of the unemployment rate, and ∆πp to percentage point changes in inﬂation.

yields are most important over short term cycles that range within 2.5 to 8 years. Considering the

respective univariate spectra (see Figure 13 in Appendix A.2), we note that for credit and house

prices the highest amount of variance is also located in the medium term where most co-movement

is located. Equity prices have the greatest amount of variance at cycles exactly around 8 years, i.e.,

at the border of short and medium term. Cycles contributing strongest to the overall variance of bond

0π/4π/200.51ΔcandΔph0π/4π/200.51ΔrandΔq0π/4π/200.51ΔcandΔpe0π/4π/200.51ΔrandΔu0π/4π/200.51ΔphandΔpe0π/4π/200.51ΔrandΔπp0π/4π/200.51ΔcandΔr0π/4π/200.51ΔqandΔu0π/4π/200.51ΔphandΔr0π/4π/200.51ΔqandΔπp0π/4π/200.51ΔpeandΔr0π/4π/200.51ΔuandΔπpECB Working Paper 1846, September 201516yields are located around 2.5 years, while part of the variable’s variance can also be allocated to

medium term frequencies.

The cross-spectra on business cycles suggest that most important co-movements are located in

the short term when compared to the medium term, except for unemployment and GDP, in which

case cycles are located in the region around 8 years. Bond yields and inﬂation have most important

common ﬂuctuations located at cycles shorter than 2.5 years. Again comparing cycle frequencies to

the variables’ variances (see Figure 13 in Appendix A.2), bond yields, GDP, and the unemployment

rate have important cycles in the short term, while unemployment has more important cycles at the

medium term. For GDP medium and short term cycles seem to be equally important.

Inﬂation,

however, has most variance located at movements of duration below one year.

Thus, while credit, house prices, and equity prices share cyclical frequencies that explain much

of their individual overall variances, benchmark bond yields exhibit a medium term component less

important relative to their overall variance. As cyclical ﬂuctuations in benchmark bond yields are,

in this way, attributable to both shorter and medium term frequencies, it can be justiﬁed that such

an indicator might be relevant for both (longer frequency) ﬁnancial and (shorter frequency) business

cycles. In the case of business cycle indicators most important co-movement is located in the short

term, while, still, some medium term cycles exist. At last, in contrast to all pairs, credit, house prices,

and equity prices have the strongest agreement of cyclical ﬂuctuations across countries as indicated

by the short distance between the dashed lines.

3.2 Selecting ﬁnancial cycle frequencies through power cohesion

Figure 2 shows power cohesion for the ﬁnancial and business cycle indicators for the euro area.

It suggests that co-movement of ﬁnancial indicators is higher for ﬁnancial cycle indicators in the

medium term than for business cycle variables, as, ﬁrst, the peak of power cohesion is located in the

purple region, while for the business cycle it is not; second, the distribution of power cohesion in this

frequency region is above the one of power cohesion for business cycle indicators.

Across countries and again compared to business cycles (see Figure 3), we ﬁnd that ﬁnancial

cycles have homogeneously an important medium term cyclical component, which is on average 1.94

times relatively more important (see Table 2); in 11 out of 13 country cases the most important cycle

even falls into the medium term range of 8 to 20 years (see purple region in Figure 3). In the case of

business cycles, all country cases are characterised by important short run ﬂuctuations; in 9 out of 13

country cases the most important cycle is shorter than 8 years. However, as suggested in the literature

(e.g., Comin and Gertler (2006) or A’Hearn and Woitek (2001)), we also ﬁnd in more than half of the

country cases important ﬂuctuations in the medium term.

The frequency windows identiﬁed using power cohesion cover short run as well as medium term

ECB Working Paper 1846, September 201517Figure 2: Power cohesion of ﬁnancial (black) and business (red) cycle indicators for the euro area
Notes: This graph shows the power cohesion of the ﬁnancial (black lines) and business cycle indicators (red lines). The dashed lines
indicate the 68% bootstrapped conﬁdence intervals. The x-axis measures the frequencies of cycles in radians from 0 to π/2. The blue area
depicts business cycle frequencies, i.e., cycles with durations of 2.5-8 years and the purple area marks medium term cycles (8-20 years).

ﬂuctuations for both ﬁnancial and business cycle indicators (see Table 2). In the case of ﬁnancial

cycles, however, this window tends to cover lower frequencies.

Figure 3: Highest density graph of power cohesion of ﬁnancial (black) and business (red) cycle
indicators
Notes: This graph depicts the 25% highest density region of power cohesion excluding cycles lower than 5 quarters for ﬁnancial and
business cycle indicators. The purple region marks medium term frequencies, i.e, in the range of 8 to 20 years, while the blue area short
term ﬂuctuations, i.e., 2.5 to 8 years. The white dash locates the peak of power cohesion.

The peak estimate of power cohesion for the ﬁnancial indicators reveals that most important cycles

range from 20.5 to 5.4 years. The median cycle is 11.6 (SE) and average 12.7 years indicating

a relatively symmetric distribution of cycle length peaks across countries, which however is quite

dispersed with a standard deviation of 4.2 years. There is a group of countries that has a relatively

0π/4π/200.51EAAT BE DE DK ES FI FR IE NL PT SE UK EA IT 20 8 2.5 Cyclical frequencies (years) ECB Working Paper 1846, September 201518long most important cycle which is in the range of 20.5 and 15.5 years (IE, ES, NL, BE, FR, IT).

DK is found to be slightly shorter than SE with 11.4 years. FI (10.7 years), AT (9.3 years), PT (8.8

years), and DE (7.9) have shorter most important ﬁnancial cycles. UK has the shortest most important

ﬁnancial cycle that is reported to be 5.4 years. However looking at the UK highest density region in

Figure 3, we see that for the UK important cycles are also located in the medium term.

For a group of countries (BE, DE, ES, FI, IE, NL, and PT), Figure 3 suggests that important

business cycles are located in the medium term. Further and in the business cycle case, in nine out

of 13 countries there are at least two separate regions of most important frequencies, whereas for

ﬁnancial cycles in only two country cases (AT and UK). Thus, ﬁnancial cycle characteristics tend

to be more homogeneous across countries compared to business cycle characteristics. The relevant

country graphs of power cohesion for the ﬁnancial and business cycles are reported in Appendix A.3.

Table 2: Importance of cyclical variation (left) and frequency band in years (right)

Variance ﬁnancial/business
Country Medium term Short term
3.79
EA
3.19
AT
2.36
BE
1.43
DE
2.15
DK
1.95
ES
1.29
FI
2.07
FR
1.65
IE
1.96
IT
1.57
NL
1.39
PT
2.78
SE
1.38
UK
Mean
1.94
Median
1.93

0.58
0.97
0.82
0.83
0.80
0.60
0.85
0.73
0.95
0.73
0.96
0.87
0.85
0.93
0.84
0.88

Financial cycle Business cycle
ωhigh
2.0
1.5
1.8
2.0
2.3
2.6
2.9
2.1
2.2
1.8
2.3
2.2
1.7
2.1
2.2
2.1

ωlow
8.4
4.4
14.2
11.9
26.9
512.0
24.4
30.1
∞
7.0
∞
46.5
6.0
17.1
∞
24.4

ωlow
∞
512.0
∞
128.0
30.0
∞
39.4
512
∞
42.7
∞
128.0
34.1
128.0
∞
128.0

ωhigh
4.6
1.9
3.0
2.3
2.5
4.4
3.1
2.6
3.2
2.1
4.2
2.4
2.6
2.5
2.8
2.6

Notes: Columns two and three report the relative share of co-movement of the ﬁnancial cycle indicators in comparison to the
co-movement of business cycle indicators scaled to the same total amount of co-variance over all cycle frequencies. Shares are
reported for medium term cycles (20-8 years) and short term cycles (8-2.5 years). More speciﬁcally, ﬁgures reﬂect the ratio:
PCohBusiness(ω)dω/ (cid:82) π
((cid:82) f2
0 PCohBusiness(ω)dω)−1, where f1 and f2 reﬂect the
f1
lower and upper frequencies for the medium and short term cycles.
Columns four to seven report the frequency band around the peak of power cohesion that is obtained by capturing 2/3 of the common
variance as described in Section 2.1.

0 PCohFinancial(ω)dω)((cid:82) f2
f1

PCohFinancial(ω)dω/ (cid:82) π

In support of results from Figure 3, statistics in Table 2 indicate that the variance located in the

medium term is on average 1.94 times more important for ﬁnancial than for business cycles indica-

tors, with 3.19 (AT) and 1.38 (UK) times being the maximum and minimum of the analysed country

cases. Within the short term range, business cycle indicators have on average 1.19 times more im-

portant variances, with 1.67 (ES) and 1.03 (AT) being the maximum and minimum respectively.

ECB Working Paper 1846, September 201519Conclusively, the medium term component for ﬁnancial cycle indicators is by far more distinct from

business cycle characteristics than is the short term one, as share for the short term do not differ as

strongly.

The identiﬁed frequency window ranges from 128 to 2.6 years for ﬁnancial cycle indicators (see

median Table 2) and, thus, covers longer cycles when compared to the one for business cycle indica-

tors, which is 24.4 to 2.1 years. The highest frequencies included in the window are quite homoge-

nously spread for the business cycle case, where the minimum is 1.5 (AT) and maximum 2.9 (FI)

years. In contrast, there is more heterogeneity reported for ﬁnancial indicators as the minimum is

1.9 (AT) and maximum 4.4 (ES) years. For the lower frequencies included in the frequency window,

ﬁnancial cycle ﬁgures are by far larger, with the exceptions of DK, IE, and NL. In IE and NL both

endpoints are ∞ and in the case of DK the difference is only 3.1 years – 30 (ﬁnancial cycle) and 26.9

(business cycle) years.

3.3 A composite index of the ﬁnancial cycle

This section ﬁrst discusses the early warning properties of ﬁnancial cycles for systemic banking crises.

Second, the euro area ﬁnancial cycle and individual European country ﬁnancial cycles are discussed.

Third, we provide a comparison of ﬁnancial and business cycles. The last part offers several robust-

ness checks.

For the analyses in this section we use among other things the method on turning points as sug-

gested by Bry and Boschan (1971) and extended to quarterly frequency by Harding and Pagan (2002).
The turning point analysis is conducted on the aggregated composite cycle indices.15

3.3.1 Early warning exercise

This section motivates the construction of a ﬁnancial cycle index by analysing its early warning

properties of ﬁnancial crises. In this, we build on the seminal work by Frankel and Rose (1996),

Kaminsky and Reinhart (1999), and Schularick and Taylor (2012). We ﬁnd that the ﬁltered composite

ﬁnancial cycle outperforms the single indicators and the credit-to-GDP gap in predicting systemic

banking crises at a horizon of one to three years ahead, while it also enhances the predictability of

crises at longer horizons.

More speciﬁcally, we use a logit model estimated on a pooled data set to explain two vulnerabil-
ity horizons preceeding systemic banking crises as deﬁned by Laeven and Valencia (2012).16 The

15The Matlab code has been gratefully adapted from Canova and Schlaepfer (2015). Since turning points are deﬁned by
local minima and maxima in the level of series we aggregate our composite cycles. To this end, we ﬁrst subtract the median
from each composite cycle and then cumulatively sum up the respective index.

16As is common in the early warning literature, we focus on predicting vulnerable periods preceding systemic banking
crises instead of the banking crises themselves. This is because vulnerabilities can be triggered into crises by hardly pre-
dictable or unforeseen events. Further, note that crisis dummies can only be deﬁned on a yearly basis using dates provided
in Laeven and Valencia (2012). It implies that the link of a starting date of a crisis and vulnerability period cannot be exact

ECB Working Paper 1846, September 201520Table 3: Early warning exercise

Financial indicators Vulnerability horizon: 4 to 12 quarters Vulnerability horizon: 12 to 20 quarters

∆c

∆ph

∆pe

∆r

Filt. ﬁnancial cycle

Credit-to-GDP gap

McFadden adj. R2
AUROC
Type I error
Type II error
Observations

(i)
0.21
[0.07]
0.14
[0.05]
0.03
[0.01]
-0.09
[0.07]

0.05
0.72
0.19
0.42
2030

(ii)

(iii)

(iv)

3.30
[0.80]

0.09
0.73
0.25
0.33
2030

0.03
[0.01]
0.03
0.64
0.71
0.07
2030

3.24
[0.85]
0.03
[0.01]
0.12
0.79
0.27
0.27
2030

(v)
0.07
[0.07]
0.18
[0.06]
0.00
[0.01]
-0.01
[0.07]

0.03
0.67
0.21
0.53
2030

(vi)

(vii)

(viii)

2.04
[0.81]

0.04
0.65
0.35
0.36
2030

0.03
[0.01]
0.02
0.68
0.25
0.43
2030

1.98
[0.80]
0.03
[0.01]
0.06
0.74
0.40
0.24
2030

Notes: Country clustered standard errors are reported in square brackets. Coefﬁcients in bold indicate signiﬁcance at least at the 10%
signiﬁcance level. Filt. denotes ﬁltered and adj. to adjusted. Type I/II errors are derived by minimising the policy makers loss function using
equal preferences for missing a crises (no signal but crisis, type I error) and false alarms (signal but no crisis, type II error) with respect to
some signalling threshold level separating predicted crises and non-crises. Loss is deﬁned as L = Quarters no signal
Quarters no crisis . Sample
lengths have been equalised at the country level for comparative purposes.

Quarters crisis + Quarters signal

vulnerability horizons explored are 4 to 12 as well as 12 to 20 quarters. Variables considered are the

unﬁltered indicators as well as the ﬁltered ﬁnancial cycle that has been derived on an expanding sam-
ple.17 These are contrasted with the credit-to-GDP gap that is constructed employing the HP-ﬁlter
with a smoothing parameter of 400000, again, on an expanding sample.18 We choose to compare

our ﬁnancial cycle measure with the credit-to-GDP gap measure, as the latter has been assigned a

prominent role for setting countercyclical capital buffers in the Basel III regulations and the EU Cap-

ital Requirements Directive (CRD IV). Further, studies have suggested that the latter variable ranks

among the variables with the best early warning properties for banking crises (see e.g., Behn et al.
(2013)). To assess early warning properties, we report the adjusted R2 suggested by McFadden, the

area under the receiver operator curve (AUROC) and the type I and II errors derived by equal prefer-

ences of a policy maker between type I and II errors. For further details please refer to the caption of

Table 3 or Behn et al. (2013).

Within the vulnerability horizon of one to three years the ﬁltered ﬁnancial cycle is found to have

the best early warning properties among the selected variables in at least three dimensions (see Equa-

when using quarterly data. This, however, does not impair the comparison of indicators provided.

17The standardisation using the ecdf is carried out employing the complete data set, as such a standardisation is only

reasonable for a large number of observations.

18This reﬂects the exact speciﬁcation as laid down in the Ofﬁcial Journal of the European Union (2014/C 293) “Recom-

mendation of the European Systemic Risk Board of 18 June 2014 on guidance for setting countercyclical buffer rates”.

ECB Working Paper 1846, September 201521tion (ii) in Table 3). First, the AUROC is 0.73, which is higher than the one for the single indicators

(Equation (i)) and by far larger than the AUROC reported for the credit-to-GDP gap (0.64, Equation
(iii)). Further, the R2 suggests that Equation (ii) has the best model ﬁt. Second, besides having a rel-

atively low type I error of 25%, the sum of both type I and II errors is lowest for Equations (i) to (iii).

The credit-to-GDP gap has the highest type I error of 0.71, i.e., it misses 71% of economically costly

crises. Third, the ﬁnancial cycle improves the AUROC of the credit-to-GDP gap by 15 percentage

points (Equation (iv)).

Considering the longer horizon of three to four years, the credit-to-GDP gap slightly outperforms

the ﬁnancial cycle measure (Equation (vi) vs. (vii)). Still, the ﬁnancial cycle improves the AUROC

of the credit-to-GDP gap by 6 percentage points (Equation (viii)).

The estimated signs of statistically signiﬁcant coefﬁcients are in line with theoretical considera-

tions. An increase in the ﬁltered ﬁnancial cycle, similarly to a rise in the credit-to-GDP gap, elevates

the predicted probability of systemic banking crises at both vulnerability horizons. In the models with

individual unﬁltered series, an increase in credit, residential property prices, or equity prices predicts

a rise of the crisis probability. In contrast, a decrease in bond yields, which mirrors an increase in

bond prices, predicts an elevation of the crisis probability. At last, while the coefﬁcients of credit,

equity prices, and bond prices are not found to be statistically signiﬁcant in all of the speciﬁcations,

the ones for residential property prices are.

In sum, results provide strong support for our proposed ﬁnancial cycle measure, which can help

policy makers to predict systemic banking crises also beyond the credit-to-GDP gap measure promi-

nent in the Basel III and the equivalent European legislation.

3.3.2 Financial cycles

An examination of the ﬁnancial cycle for an euro area aggregate suggests a particularly pronounced

boom-bust phase around the onset of global ﬁnancial crisis in 2008. This notably includes an unusu-

ally stark suppressed phase of the cycle since the outbreak of the global ﬁnancial crisis. This down

phase follows a pronounced up phase prior to its onset (Figure 4a). Both phases are mainly explained

by movements in credit, house, and equity price variables, as indicated by the higher aggregation

weights (Figure 4c).

This latter ﬁnding is consistent with the ﬁnding over the entire sample period, whereby the unﬁl-

tered ﬁnancial cycle index correlates highest with house prices (0.76), then credit (0.72), equity prices

(0.43), and bond yields (-0.30).

Indeed, credit appears to also account for the other two prior downturns since 1987 – in conjunc-

tion with house prices in the early 1990s in contrast to equity prices in the early 2000s. Looking at

the graph of ﬁltered indicators (Figure 4b) and the time-varying weights (Figure 4c), both credit and

ECB Working Paper 1846, September 201522(a) Unﬁltered (blue) and ﬁltered (black) composite ﬁnancial cycle

(b) Filtered indicator series: ∆c (blue), ∆ph (green), ∆pe (red), and −∆r (purple)

(c) Time-varying aggregation weights: ∆c (blue), ∆ph (green), ∆pe (red), and −∆r (purple)

Figure 4: Euro area ﬁnancial cycle, 1987Q2-2013Q4
Notes: The upper (a) and middle (b) panel show the unﬁltered and ﬁltered composite ﬁnancial cycle as well as its indicators using the
frequency band presented in Table 2. The x-axis measures the date and the y-axis the relative historical position, where 0/1 represents
the min/max and 0.5 is the historical median. The lower panel (c) depicts the time-varying aggregation weights exploiting time-varying
correlations between indicators. The 0.25 line indicates equal weighting. Date is indexed on the x-axis and the aggregation weight on the
y-axis. The grey shaded area marks a systemic banking crisis as identiﬁed by Laeven and Valencia (2012).

8890929496980002040608101200.51YearHistorical positionEA8890929496980002040608101200.51YearHistorical position889092949698000204060810120.150.20.250.3YearAggregation weightECB Working Paper 1846, September 201523Table 4: Correlation of unﬁltered indicators with unﬁltered composite ﬁnancial cycle

Country
AT
BE
DE
DK
ES
FI
FR
IE
IT
NL
PT
SE
UK
Mean

∆c ∆ph ∆pe
0.47
0.39
0.41
0.52
0.61
0.53
0.35
0.57
0.59
0.66
0.77
0.63
0.56
0.65
0.70
0.74
0.72
0.38
0.47
0.62
0.46
0.58
0.70
0.54
0.42
0.50
0.59
0.37
0.65
0.65
0.54
0.56
0.61
0.44
0.72
0.50
0.44
0.65
0.60
0.50
0.62
0.55

∆r
-0.27
-0.22
-0.23
-0.11
-0.26
-0.24
-0.40
-0.10
-0.30
-0.13
-0.26
-0.16
-0.09
-0.21

Notes: Table shows the correlation between each unﬁltered indicator and the unﬁltered composite ﬁnancial cycle across the longest available
sample in each country case. ∆c refers to percentage changes in total credit, ∆ph to percentage changes in house prices, ∆pe to percentage
changes in equity prices, ∆r to percentage point changes in bond yields.

house prices are below their historical median and second, the weight attached to both series is higher

than the one to equity prices and bond prices. The second suppression of the euro area ﬁnancial cycle

commences in 2001Q2 and is explained by movements in equity prices as well as credit. The weight

for credit is high throughout this period and equity is second highest beginning in 2002Q2.

It is also striking to what extent the unﬁltered composite euro area ﬁnancial cycle exhibits a strong

cyclical tendency (Figure 4a). Indeed, its movement is well described by the ﬁltered ﬁnancial cycle,

that follows closely the unﬁltered index’ low frequency variation. There is some volatility around this

low frequency ﬂuctuations, as exempliﬁed for instance in the rapid upward spike in 2010 that is not

reﬂected in the ﬁltered series – though the endpoint of the ﬁltered index respects that of the unﬁltered

series in this case.

For single country cases (see Table 4), ∆c is represented strongest in the composite index of DE,

ES, IT, NL (of similar magnitude as ∆ph), and PT. ∆ph is most important in the case of BE, DK,
FR, IE, NL, SE, and UK. In the case of AT and FI, ∆pe is found to be most important. In contrast, in
none of the country cases is bond yield series the most important one.19

Concordance across countries

Concordance of ﬁnancial cycles ranges from 0.42 (DE with UK and FR) to 0.91 (ES with UK) sug-

gesting important differences in cycle synchronisation across countries (see Table 9 in Appendix

A.4.1). In general, DE has the lowest concordance with 0.53 and BE the highest with 0.75 both on

average. The heterogeneity of cycle synchronisation is illustrated by the differing colours in Fig-

19The individual country ﬁnancial cycles, their indicators, and aggregation weights are depicted in Appendix A.4.1.

ECB Working Paper 1846, September 201524Figure 5: Concordance of ﬁnancial cycles
Notes: Concordance is obtained on the maximum common sample, i.e., 1988Q1-2013Q4, using the turning point algorithm on the aggre-
gated ﬁltered ﬁnancial cycles as indicated in Section 3.3.

ure 5, in which countries are ordered from top to bottom by highest to lowest average concordance
respectively.20

3.3.3 A comparison to business cycles

As inherent in the data, the composite euro area ﬁnancial cycle is longer than its business cycle coun-
terpart constructed on a conceptually equivalent basis (see Figure 6).21 Moreover, the ﬁnancial cycle

appears to have leading properties ahead of the global ﬁnancial crisis, whereby subsiding ﬁnancial

cycle vigour occurs well in advance of the turning point in the business cycle (2005Q4 vs. 2007Q3).

In contrast, the business cycle recovers strongly after the ﬁrst trough in response to the ﬁnancial crisis,

while the ﬁnancial cycle remains suppressed for a prolonged period of time.

These observations are consistent with more formalised turning point analysis across countries,

20In support of these results, a principal component analysis (not reported in this study) of ﬁltered ﬁnancial cycles from
2000-2013 suggests that 12 out of 13 country ﬁnancial cycles, i.e., all but DE, correlate strongly and positively with the ﬁrst
principal component that explains 67% of total variation. The second principal components captures a factor related strongly
and positively to the DE ﬁnancial cycle, but not the other countries. Interestingly this second principal component relates
negatively to UK and ES, which showed strongest concordance of country cycles. A rise in the second principal component
is likely to be followed by rise of the DE ﬁnancial cycle, but a fall in the cycle of ES or UK, which have a correlation
of -0.55 and -0.58 respectively. Of course, a principal component analysis does not offer a structural interpretation of
interdependencies, nonetheless, common sources of variation may be described.

21The respective charts for the individual countries and the unﬁltered business cycle composite indices can be found in

Appendix A.4.2.

BEUKSEFIESIEFRDKITNLPTATDEBEUKSEFIESIEFRDKITNLPTATDE0.450.50.550.60.650.70.750.80.850.9ECB Working Paper 1846, September 201525Figure 6: Euro area ﬁnancial (black) versus business (red) cycle
Notes: The x-axis measures the date and the y-axis the relative historic position, where 0/1 represents the min/max and 0.5 is the historic
median. The grey shaded area indicates a systemic banking crisis as identiﬁed by Laeven and Valencia (2012).

which suggests longer and less symmetric ﬁnancial cycles.

First, ﬁnancial cycles tend to be longer than their business cycle analogue (Table 5). The average

ﬁnancial cycle length derived from the unﬁltered indicator is 7.2 years versus an average business

cycle length of 4.7 years in the case of the ﬁltered business cycle indicator. While the comparison of

the means for the unﬁltered indicators does not provide as strong evidence (4.5 versus 4.1 years) we

ﬁnd that ﬁnancial cycles are longer in nine out of 13 country cases.

Second, ﬁnancial cycles also tend to be much more asymmetric than their equivalently calculated

business cycle counterparts (see Figure 7). In particular, the distribution of upturns in ﬁnancial cycles,

i.e, trough to peak, has a fatter tail with respect to downturns. Further, the median and the upper

quantile of the ﬁltered composite ﬁnancial cycle index is above that of downturns – and the mean

for upturns is larger than for downturns (see Table 5). In contrast, distributions of durations of the

composite business cycle indicator for up- and downturns appear to be rather symmetric – and the

median is slightly higher for upturns, while the mean of the upper quantile is about equal (or even

smaller, for that matter).

Regarding synchronisation of business with ﬁnancial cycles (see Table 5), on average 67% of the

country cases are in phase. Above average concordance is found for DK (0.74), ES (0.79), FI (0.73),

FR (0.72), and IE (0.81). Lowest concordance exists between the ﬁnancial and business cycle in NL

(0.59) and SE (0.59), closely followed by DE (0.60).

Turning to the cross-country distributions of ﬁnancial and business cycles synchronisation re-

spectively (Figure 8), results suggest greater ﬁnancial than real economy heterogeneity, albeit with

correlated ﬁnancial cycle peaks. The concordance of ﬁnancial cycles across the European Union

countries analysed is more heterogeneous than that of business cycles (inherent in the variance of the

distributions). That said, for most countries the synchronisation of ﬁnancial cycles is higher than for

99000102030405060708091011121300.51YearHistorical positionEAECB Working Paper 1846, September 201526Financial cycle:

Business cycle:

(a) Filtered

(b) Unﬁltered

Figure 7: Duration of cyclical phases across European countries in years
Notes: The upper panel (a) shows boxplots describing the distribution of duration from peak to trough and trough to peak for the ﬁltered
composite ﬁnancial and business cycle in years. The lower panel (b) depicts the latter statistics for the unﬁltered composite indices. The
statistics are derived by excluding the euro area aggregate and using the turning point algorithm as indicated in Section 3.3.

Figure 8: Synchronisation of ﬁnancial cycles (black) versus synchronisation of business cycles (red)
Notes: Figure shows smoothed histogram depicting distribution of bilateral concordance of ﬁnancial versus business cycles for all analysed
EU countries (excluding euro area aggregate). Concordance is obtained on the maximum common sample, i.e., 1988Q1-2013Q4. Statistics
are produced using the turning point algorithm as indicated in Section 3.3.

01234567891011Peak to troughTrough to peak01234567891011Peak to troughTrough to peak01234567891011Peak to troughTrough to peak01234567891011Peak to troughTrough to peak0.40.50.60.70.80.910510152025Concordance# of casesECB Working Paper 1846, September 201527Table 5: Duration of down- and upturns (P-T and T-P) and concordance (Conc.) of ﬁnancial and
business cycles in years

Filtered:
Financial cycle Business cycle
P-T

P-T

T-P

T-P

EA

AT

BE

DE

DK

ES

FI

FR

IE

IT

NL

PT

SE

UK

Mean

3.4
(0.9)
[2]
2.4
(1.1)
[5]
2.9
(2.2)
[5]
3.3
(3.2)
[6]
2.6
(1.9)
[9]
7.9
(4.4)
[2]
2.8
(1.2)
[6]
4.0
(2.4)
[5]
4.3
(2.3)
[5]
2.4
(1.8)
[6]
3.8
(2.9)
[3]
2.0
(0.7)
[6]
2.5
(1.7)
[8]
3.3
(2.4)
[4]
3.4
[70]

4.4
(1.2)
[2]
1.8
(1.4)
[5]
4.0
(1.3)
[5]
3.7
(2.2)
[5]
2.1
(1.2)
[9]
8.6
(4.4)
[2]
3.3
(1.5)
[7]
3.4
(3.4)
[6]
4.9
(2.7)
[4]
3.2
(1.9)
[7]
5.6
(4.3)
[3]
1.7
(1.9)
[6]
2.7
(1.7)
[8]
5.1
(2.7)
[4]
3.8
[71]

2.5
(1.4)
[2]
1.2
(0.5)
[16]
2.4
(1.3)
[10]
1.9
(0.8)
[9]
2.3
(1.9)
[9]
3.3
(2.4)
[5]
2.4
(1.2)
[7]
2.5
(1.8)
[8]
3.2
(1.3)
[5]
1.5
(0.6)
[11]
2.8
(1.3)
[7]
2.3
(1.3)
[9]
1.4
(0.6)
[13]
1.6
(1.1)
[12]
2.2
[121]

2.6
(1.2)
[2]
1.3
(0.5)
[17]
1.7
(0.8)
[9]
2.6
(1.6)
[9]
2.4
(1.5)
[9]
4.3
(3.0)
[5]
3.4
(1.9)
[7]
2.1
(1.3)
[8]
3.8
(2.9)
[4]
1.9
(0.9)
[12]
2.9
(2.1)
[7]
2.3
(2.0)
[8]
1.8
(1.1)
[13]
2.0
(0.8)
[11]
2.5
[119]

Conc.

0.79

0.64

0.63

0.60

0.74

0.79

0.73

0.72

0.81

0.62

0.59

0.63

0.59

0.63

0.67

Unﬁltered:
Financial cycle Business cycle
P-T

P-T

T-P

T-P

1.4
(0.7)
[4]
2.1
(1.5)
[6]
2.4
(2.0)
[7]
2.3
(1.8)
[9]
2.0
(2.0)
[9]
2.6
(1.2)
[6]
2.3
(1.6)
[8]
1.9
(1.3)
[10]
1.7
(1.6)
[12]
1.8
(1.6)
[7]
1.8
(1.4)
[8]
2.0
(1.1)
[7]
3.3
(2.9)
[7]
2.3
(1.6)
[7]
2.2
[103]

2.6
(2.1)
[4]
2.1
(1.1)
[6]
2.8
(1.7)
[8]
2.1
(1.5)
[9]
2.1
(1.6)
[9]
3.0
(4.4)
[6]
2.3
(1.2)
[9]
1.9
(1.2)
[11]
1.7
(1.8)
[12]
3.0
(2.8)
[8]
2.2
(1.7)
[8]
1.7
(2.1)
[6]
2.7
(2.2)
[7]
2.9
(3.1)
[7]
2.3
[106]

1.4
(0.6)
[3]
1.6
(0.8)
[13]
2.3
(1.8)
[8]
2.3
(1.7)
[10]
1.8
(0.8)
[13]
2.3
(2.7)
[8]
2.4
(1.6)
[8]
2.1
(1.9)
[8]
1.7
(1.1)
[10]
1.6
(1.3)
[11]
2.5
(1.2)
[7]
2.1
(1.6)
[10]
2.1
(1.3)
[8]
1.9
(1.4)
[11]
2.0
[125]

1.8
(1.0)
[3]
1.5
(1.1)
[14]
2.3
(1.2)
[8]
1.9
(1.8)
[10]
1.5
(1.4)
[13]
2.4
(2.3)
[8]
2.5
(2.0)
[8]
2.5
(1.4)
[8]
1.4
(0.7)
[10]
1.7
(1.1)
[11]
3.2
(1.9)
[7]
2.1
(1.7)
[9]
2.5
(1.3)
[9]
2.1
(1.5)
[10]
2.1
[125]

Conc.

0.79

0.77

0.66

0.58

0.61

0.77

0.70

0.71

0.65

0.68

0.65

0.76

0.63

0.66

0.68

Notes: This table shows the mean of durations for downturns denoted by P-T (peak to trough) and upturns denoted by T-P (trough to peak).
Standard deviations are reported in round brackets and number of events in square brackets. Conc. refers to concordance and measure
the synchronicity of phases of country composite ﬁnancial and business cycles and is obtained on the maximum common sample, i.e.,
1988Q1-2013Q4. Mean is derived by averaging all country means and counting all events excluding the euro area aggregate. Statistics are
produced using the turning point algorithm as indicated in Section 3.3.

ECB Working Paper 1846, September 201528business cycles (peak of distribition).

At last, there is evidence that the output of the turning point algorithm should be adapted for the

analysis of unﬁltered ﬁnancial cycle indicators, as, e.g., is done by Claessens et al. (2012) by reporting

time of recoveries, i.e., the time it takes for a variable to attain the level of the previous peak after

a trough. While the algorithm does not produce largely differing results for ﬁltered and unﬁltered

business cycles (see Table 5), it does in the case of the ﬁnancial cycle. For business cycles, the total

average length differs by 0.6 years while for ﬁnancial cycles it extends to 4.7 years.

3.4 Robustness Analysis

In this section, we perform several robustness checks; ﬁrst, we analyse cycles based on subsets of

ﬁnancial cycle indicators. Second, we highlight the effect of varying the parameter determining the

frequency window. And third, we show the effect of setting a different parameter λ that controls the

persistence of time-varying correlations.

3.4.1 Cycles using subsets of indicators

In this part we consider two subsets of indicators and compare outcomes of the different analyses.

As the emerging literature on ﬁnancial cycles has mainly focussed on measures of credit, residential

property prices, and equity prices, we focus on these variables in our ﬁrst subset. Further, to derive

a synthetic ﬁnancial cycle measure Drehmann et al. (2012) suggest to ﬁlter credit measures as well

as residential property prices using a frequency window of 8 to 30 years before linearly aggregating.

Therefore, we consider only credit and residential property prices for our second subset of indicators.

Three important results emerge: First, most relevant cycles are rather consistently located at simi-

lar frequencies across the different sets of indicators. Second, cycle length estimates are rather robust

when excluding bond yields, but rather not when focussing only on credit and residential property

prices. That is, for half of the country cases (seven out of 14) the lengths of extracted ﬁnancial cycles

only differ marginally, i.e., by up to one year, when only bond yields are excluded. In three country

cases, cycle lengths differences are marginal for the two subsets, while more pronounced when each

compared to the benchmark setup. Notably, in the case of ES, the cycle length is robust across all

speciﬁcations. In further four country cases, estimates of cycle length differ across all sets. Third,

when only considering credit and residential property prices for identifying ﬁnancial cycles, our re-

sults suggest that shortest cycles that should be considered are well below 8 years, contrary to the

argument of Drehmann et al. (2012).

The highest density graph (Figure 9) suggests that – with respect to the exclusion of bond yields

and equity prices – the agreement of indicators for identiﬁed cycles that contribute strongest to the

overall co-variance is rather stable, with the only major exception of PT. Further, in the case of DE

ECB Working Paper 1846, September 201529Figure 9: Highest density graph of power cohesion of all ﬁnancial indicators (black), ∆c, ∆ph, and
∆pe (blue), and ∆c and ∆ph (orange)
Notes: This graph depicts the 25% highest density region of power cohesion excluding cycles lower than 5 quarters for ﬁnancial and subsets
of ﬁnancial cycle indicators. The purple region marks medium term frequencies, i.e, in the range of 8 to 20 years, while the blue area short
term ﬂuctuations, i.e., 2.5 to 8 years. The white dash locates the peak of power cohesion.

and IE, longer cycles are suggested when considering only credit and residential property prices

(orange bar), while in the case of AT (blue and orange bar) and UK (orange bar), important short

term ﬂuctuations disappear. Also, we ﬁnd that the more asset prices dropped the denser is the region

where 25% of most important cycles are located, i.e., compared to the black bars, the blue bar is

shorter across country cases. Shortest is the orange bar.

The identiﬁed frequency window allows for similar conclusions (Table 6). The window identiﬁed

using only credit and residential property prices is shorter than the one including equity prices as

both the low and high frequency limits are include in the latter set. As stressed, while the long cycles

included differ much in years, their importance with respect to cycle selection is minor. However,

important differences emerge with respect to the shortest cycle length included. The mean of the

shortest cycles included is 6.2 for credit and residential property prices and 4.1 years by additional

considering equity prices. This is in contrast to 2.6 years employing all indicators. This result is also

mirrored in the turning point analysis (Table 7), for which we ﬁnd that credit and residential property

price cycles last on average 10.8 years, while including equity prices leads to an average length of 8.8

years. This is in contrast to our benchmark scenario that identiﬁes cycles of an average length of 7.2

years. However, taking a country perspective, we note that in half of the country (and region) cases

the differences are only marginal, i.e., up to one year, when excluding bond yields. In four cases cycle

AT BE DE DK ES FI FR IE IT NL PT SE UK EA AT BE DE DK ES FI FR IE IT NL PT SE UK EA 20 8 2.5 Cyclical frequencies (years) 20 8 2.5 Cyclical frequencies (years) ECB Working Paper 1846, September 201530Table 6: Frequency band of power cohesion identiﬁed using subsets of variables

∆c, ∆ph,
and ∆pe
ωlow
256.0

ωhigh
6.7
∞ 2.8
∞ 5.3
∞ 3.1
2.7
8.3
4.3
∞ 4.2
5.6
2.3
5.6
∞ 3.0
∞ 4.1
4.0
∞ 4.3
4.1

28.4
170.7
56.9

512.0
64.0
73.1

128.0

512.0

512.0

32.0
85.3
85.3
102.4

∆c and ∆ph
ωhigh
ωlow
8.5
56.9
∞ 5.2
7.8
∞ 4.9
5.6
9.5
6.1
6.4
∞ 8.1
2.0
7.1
∞ 6.2
6.8
5.2
∞ 6.2
6.2

85.3
512.0

46.5
36.6

102.4

Country
EA
AT
BE
DE
DK
ES
FI
FR
IE
IT
NL
PT
SE
UK
Mean
Median

Notes: Table reports the frequency band around the peak of power cohesion that is obtained by capturing 2/3 of the common variance as
described in Section 2.1.

lengths are only marginally different for the two subset of indicators, while in 4 cases all estimates are

found to be different. Most robust is our ﬁnding for ES, in which case the cycle length consistently

found to be around 15 to 16 years. At last and as found previously, cycles tend to be asymmetric as

the upturn lasts on average 4.7 years (6 years excluding equity) and the down turn only 4.1 years (4.8

years excluding equity). The statistics for the unﬁltered series provide weaker evidence.

More speciﬁcally concerning credit and residential property prices, highest frequencies selected

by our frequency window are below 8 years and the lowest well above 30 years, indicating that –

using credit and residential property prices – important cycle frequencies are located in this part of

the spectrum and, thus, outside of the region suggested by Drehmann et al. (2012). Even the highest

density chart (see Figure 9) suggests that there are country cases in which, considering only the 25%

of most important cycles, ﬂuctuations are located outside of this 8 to 30 year window (AT, DE, IE,

PT). Thus, also when considering measures of credit and house prices the latter frequency window

potentially leads to a serious bias of ﬁnancial cycles as ﬂuctuations that contribute strongest to the the

overall co-variance are neglected.

3.4.2 Varying the frequency window parameter

We conduct this robustness analysis for illustrative purposes on the euro area ﬁnancial cycle. Next to

the benchmark frequency window of 2/3, Figure 10 also shows the ﬁltered composite ﬁnancial cycle

when using a window that is 10 percentage points (p.p.) larger or smaller.

ECB Working Paper 1846, September 201531Table 7: Duration of down- and upturns (P-T and T-P) of subsets of indicators in years

∆c, ∆ph, and ∆pe
Filtered:
P-T

T-P

Unﬁltered:
P-T

T-P

∆c and ∆ph
Filtered:
P-T

T-P

Unﬁltered:
P-T

T-P

EA

AT

BE

DE

DK

ES

FI

FR

IE

IT

NL

PT

SE

UK

Mean

3.0
(1.4 )
[2 ]
2.8
(1.4 )
[3 ]
4.2
(2.3 )
[4 ]
3.8
(4.3 )
[6 ]
4.2
(2.9 )
[6 ]
7.5
(3.9 )
[2 ]
4.4
(3.0 )
[4 ]
3.8
(2.5 )
[5 ]
5.3
(1.8 )
[2 ]
3.6
(2.4 )
[4 ]
3.7
(2.3 )
[3 ]
2.0
(0.8 )
[6 ]
3.6
(2.6 )
[3 ]
4.3
(1.9 )
[3 ]
4.1
[51]

4.9
( 0.2 )
[ 2 ]
2.3
( 1.0 )
[ 3 ]
4.4
( 0.7 )
[ 4 ]
3.3
( 1.1 )
[ 5 ]
2.8
( 1.4 )
[ 6 ]
9.3
( 3.9 )
[ 2 ]
3.9
( 0.2 )
[ 4 ]
3.8
( 2.0 )
[ 5 ]
6.7
( 5.5 )
[ 3 ]
5.0
( 4.5 )
[ 4 ]
5.8
( 2.9 )
[ 3 ]
1.8
( 1.9 )
[ 6 ]
5.5
( 1.3 )
[ 3 ]
6.8
( 4.1 )
[ 3 ]
4.7
[51]

3.3
( 1.8 )
[ 2 ]
2.4
( 1.1 )
[ 4 ]
2.6
( 1.8 )
[ 6 ]
2.2
( 2.1 )
[ 11 ]
1.9
( 0.8 )
[ 10 ]
3.9
( 2.4 )
[ 4 ]
2.1
( 1.8 )
[ 8 ]
2.4
( 2.3 )
[ 8 ]
1.6
( 1.1 )
[ 12 ]
2.0
( 1.6 )
[ 8 ]
1.6
( 1.2
[ 9 ]
1.5
( 1.0 )
[ 7 ]
2.6
( 1.7 )
[ 8 ]
2.0
( 1.8 )
[ 8 ]
2.2
[103]

4.5
( 0.0 )
[ 2 ]
2.1
( 1.1 )
[ 4 ]
3.2
( 1.6 )
[ 7 ]
1.6
( 1.2 )
[ 10 ]
1.8
( 1.4 )
[ 10 ]
4.4
( 4.9 )
[ 4 ]
2.4
( 1.7 )
[ 9 ]
2.3
( 1.7 )
[ 9 ]
1.8
( 1.9 )
[ 12 ]
2.4
( 2.5 )
[ 9 ]
2.2
1.8 )
[ 10 ]
2.0
( 1.9 )
[ 7 ]
2.5
( 2.0 )
[ 8 ]
2.5
( 2.0 )
[ 9 ]
2.4
[108]

4.5
( 0.0 )
[ 1 ]
4.5
( 0.0 )
[ 2 ]
5.4
( 2.3 )
[ 2 ]
5.8
( 4.2 )
[ 4 ]
3.9
( 2.8 )
[ 4 ]
7.3
( 1.8 )
[ 2 ]
4.0
( 2.8 )
[ 3 ]
5.5
( 1.8 )
[ 3 ]
5.1
( 2.3 )
[ 2 ]
4.3
( 2.2
[ 4 ]
4.4
( 2.7 )
[ 2 ]
3.9
( 0.9 )
[ 2 ]
4.3
( 3.3 )
[ 3 ]
4.8
( 2.6 )
[ 3 ]
4.8
[36]

9.1
( 4.1 )
[ 2 ]
3.3
( 0.4 )
[ 2 ]
8.8
( 4.0 )
[ 3 ]
5.2
( 3.1 )
[ 3 ]
4.3
( 1.4 )
[ 4 ]
8.4
( 3.0 )
[ 2 ]
7.7
( 2.8 )
[ 3 ]
5.8
( 5.3 )
[ 3 ]
6.9
( 5.9 )
[ 3 ]
4.6
4.2 )
[ 4 ]
7.1
( 1.9 )
[ 2 ]
3.5
( 3.9 )
[ 2 ]
6.0
( 0.2 )
[ 4 ]
6.3
( 3.3 )
[ 3 ]
6.0
[38]

2.5
( 2.8 )
[ 2 ]
1.7
( 1.5 )
[ 7 ]
3.1
( 2.1 )
[ 6 ]
2.8
( 2.3 )
[ 8 ]
2.5
( 2.2 )
[ 6 ]
2.9
( 1.6 )
[ 5 ]
3.2
( 2.9 )
[ 5 ]
3.7
( 2.2 )
[ 5 ]
1.7
( 2.0 )
[ 8 ]
2.8
( 2.1 )
[ 6 ]
2.3
( 2.3 )
[ 6 ]
1.2
( 0.5 )
[ 7 ]
4.4
( 2.4 )
[ 4 ]
2.6
( 2.0 )
[ 7 ]
2.7
[80]

5.5
( 1.0 )
[ 3 ]
1.1
( 0.7)
[ 7]
3.1
( 2.0)
[ 7 ]
2.3
( 1.5)
[ 7 ]
3.2
( 2.5)
[ 6 ]
3.6
( 4.1)
[ 6 ]
3.8
( 2.0)
[ 6 ]
3.9
( 3.6)
[ 5 ]
2.3
( 2.3)
[ 9]
2.9
( 3.5 )
[ 7 ]
3.1
( 2.4 )
[ 6 ]
1.4
( 1.9)
[ 8 ]
5.4
( 5.7)
[ 4 ]
2.8
( 2.5)
[ 8 ]
3.0
[86]

Notes: This table shows the mean of durations for downturns denoted by P-T (peak to trough) and upturns denoted by T-P (trough to peak).
Standard deviations are reported in round brackets and number of events in square brackets. Mean is derived by averaging all country
means and counting all events excluding the euro area aggregate. Statistics are produced using the turning point algorithm as indicated in
Section 3.3.

ECB Working Paper 1846, September 201532Figure 10: Filtered ﬁnancial cycles using a frequency window covering 10 p.p. more and less than
the benchmark setup
Notes: The x-axis measures the date and the y-axis the relative historical position, where 0/1 represents the min/max and 0.5 is the historical
median. The grey shaded area indicates a systemic banking crisis as identiﬁed by Laeven and Valencia (2012).

The ﬁltered series with the smallest parameter, i.e., 10 p.p. less, is naturally the smoothest one,

only capturing an upward trend at the end of global ﬁnancial crisis. The endpoints of the unﬁltered

series and this ﬁltered one deviate more strongly than the other ﬁltered cycle estimates. The speciﬁ-

cation using a larger frequency window, i.e., covering 10 p.p. more of common variation, follows the

unﬁltered series more closely, but has also more noise added to it. Endpoints do not deviate strongly

and are similar to the benchmark setup.

Note that while we ﬁnd that the peaks and troughs of growth rates differ for all frequency window

speciﬁcations, we do not ﬁnd such evidence for turning points, i.e., when the series passes from below

median to above or vice versa. In this case the benchmark speciﬁcation follows almost exactly the

less smooth one. Some small bias exists for the smoother one.

In sum, we argue that 2/3 represents a good trade-off for balancing smoothness and bias.

3.4.3 Varying the correlation persistence parameter

In this section, we vary the persistence parameter, λ using 0.89 and 0.95 instead of 0.93. Further, we

plot the simple average, i.e, without employing time-varying weights. Figure 11 shows the result for

the unﬁltered euro area ﬁnancial cycle.

First, the simple average adds noise to the location of the ﬁnancial cycle and, thus, time-varying

weights should be preferred. In the latter case, booms and busts are well more deﬁned, i.e., the un-

ﬁltered indicator remains above the historical median, as e.g., can be seen by the ﬁrst boom phase on

the sample, the upswing the before the ﬁnancial crisis, and also the downturn following the ﬁnancial

crisis shock, where the signal has less variance. Further, the global ﬁnancial crisis shock leads to a

downturn before the simple average.

8890929496980002040608101200.10.20.30.40.50.60.70.80.91YearEA+10p.p.-10p.p.ECB Working Paper 1846, September 201533Figure 11: Unﬁltered ﬁnancial cycle indicator using different correlation persistence parameters and
the simple average
Notes: The x-axis measures the date and the y-axis the relative historical position, where 0/1 represents the min/max and 0.5 is the historical
median. The grey shaded area indicates a systemic banking crisis as identiﬁed by Laeven and Valencia (2012).

Second, the difference using the different persistence parameters is seen to be negligible.22

4 CONCLUSIONS

Beyond enhancing ﬁnancial system resilience, one of the key objectives of macroprudential policy is

to attenuate ﬁnancial cycles. This paper presents an empirical methodology to characterise and extract

ﬁnancial cycles, which is based on a novel multivariate spectral method of deriving common cyclical

frequencies for ﬁnancial aggregates. Further, a time-varying aggregation method is presented which

allows for a unique composite cycle constructed from constituent indicators capturing economic ﬂuc-

tuations of a systemic nature. We apply this method to selected European Union countries and the

euro area aggregate using total credit and measures for different asset markets (residential property

prices, equity prices, and benchmark bond yields) as aggregates. Quarterly cycles for credit and the

above main asset prices are derived for the period of 1970-2013. The resulting synthetic country

ﬁnancial cycles are calculated in such a way that they summarise the (co-)movements over time of

a range of ﬁnancial sector variables, while still retaining information on each constituent variable

relevant for informed policymaking.

The methodology introduced in this paper to construct composite ﬁnancial cycles strengthens the

basis for countercyclical macroprudential mandates currently being implemented around the world.

The empirical application to a broad set of the EU countries emphasises how a consistent summary

representation of credit and asset market developments can help in predicting ﬁnancial stress, while

22Compared to an index using unrestricted correlations, our methodology identiﬁes more clearly swings in the ﬁnancial

cycle, which, e.g., can be noted by a higher degree of persistence.

8890929496980002040608101200.10.20.30.40.50.60.70.80.91YearEAsimpleaverage0.950.89ECB Working Paper 1846, September 201534at the same time allowing for country-speciﬁc cycles drawing from frequency domain analysis of

ﬁnancial cycle characteristics. On the one hand, the results support the notion that countercyclical

macroprudential policies in the EU need to be tailored to country-speciﬁc phases. On the other hand,

considerable co-movement of ﬁnancial cycles across the countries analysed suggests a strong need for

coordination and reciprocity in the implementation of country-speciﬁc measures. Further, ﬁnancial

cycles’ interaction with their business cycle counterparts – and the potential for divergence – un-

derscores the need for policy specialisation, notably across the macroeconomic and macroprudential

space.

The methodology and geographic coverage in this way contribute to a small and growing litera-

ture on ﬁnancial cycles. Notwithstanding its contribution, several areas of further research remain.

These include methodologies suited to structural breaks and nonlinearities inherent in underlying se-

ries, a more structural analysis of the interplay of composite ﬁnancial cycles across countries, and

exploration of other variables that could further enhance the precision of ﬁnancial frequencies and

cycles.

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A.1 Data, transformations, and tests on unit roots

A APPENDIX

The data are from the Bank of International Settlements (BIS), Datastream (DS), Global Financial

Data (GFD), the Statistical Data Warehouse (SDW), or the OECD.

In case data is available at the yearly frequency only, it is converted to quarterly frequency using

the approach suggested in Bernanke et al. (1997), which exploits state-space methods. Further, some

series are backcasted using similar variables which have a longer history, chained back in time on the

basis of growth rates.

All series, except for inﬂation and unemployment, are measured in real terms. GDP and house

prices are directly obtained in real terms, while real total credit and real equity prices are deﬂated with

the respective country consumer price index (CPI). Total credit, house prices, equity prices, and GDP

are transformed to log quarter-on-quarter (or year-on-year), i.e., percentage, changes. Bond yields and

unemployment are quarter-on-quarter (or year-on-year), i.e., percentage point, changes. Inﬂation is

the ﬁrst difference of log quarter-on-quarter (or year-on-year) changes in the CPI (percentage points).

The resulting sample period is 1970Q3 until 2013Q4 for the quarter-on-quarter transformation

(and 1971Q2 until 2013Q4 for all results in the appendix using annual transformations), except where

denoted for speciﬁc variables below.

Total Credit: Total credit is taken from the BIS data set and reﬂects total loans and debt securities

provided by domestic banks, all other sectors of the economy and non-residents to the private non-

ﬁnancial sector (non-ﬁnancial corporations, households, and non-proﬁt institutions serving house-

ECB Working Paper 1846, September 201537holds). Exceptions to the above starting dates are BE (1970Q4), FI (1970Q4), and IE (1971Q2).

Credit for the euro area, based on a synthetic aggregation available since 1980Q1, reﬂects loans to

households and non-ﬁnancial corporations and is taken from the balance sheet items data set (SDW:

BSI.Q.U2.N.A.A20.A.1.U2.2250.Z01.E and BSI.Q.U2.N.A.A20.A.1.U2.2240.Z01.E).

House prices: This measure reﬂects real residential property prices as compiled by the ECB using

national sources, backcasted using growth rates from OECD data. For Austria up to 2000Q1 the

series only reﬂects house prices in Vienna. Starting dates vary for AT (1986Q3), ES (1971Q1) and

PT (1988Q1). The euro area aggregate is a synthetic euro area aggregate for 17 countries (SDW:

RPP.Q.I6.N.TD.00.3.00), with start date 1980Q1.

Equity prices: We employ the index from OECD main economic indicators. In the case of BE

(before 1985Q2), DK (before 1983Q1), ES (before 85Q1), and PT (before 1988Q1) we use an equity

index provided by GFD. The respective GFD codes are _BSPTD, _OMXCPID, _SMSID, _PSI20D.

Starting date varies for PT (1977Q2). The euro area aggregate commences in 1987Q1.

Bond yields: Bond yields are measured by long term government bonds with a maturity of around

10 years and are obtained through SDW (ﬁnancial market data). For DK, FI, SE we employ the

relevant series of the BIS Macro-economic series database. Series for DK, FI, SE, and UK are back-

casted using data form the international ﬁnancial statistics database. Further, in the case of ES (before

1987Q2) and FI (before 1988Q1) we use the respective series provided by GFD: codes are IGESP10D

and IGFIN10D. In the case of PT (1974Q2 - 1975Q5) and SE (1986Q1 - 1986Q2), because of miss-

ing data, we use the GFD series as a way to circumvent these data issues. Codes are IGPRT10D and

IGSWE10D. The euro area aggregate commences in 1980Q1.

GDP: Real GDP is obtained from SDW and reﬂects the OECD/Eurostat series. In the case of

IE we use industrial production, given a yearly frequency for Irish GDP most part of our sample

(before 1996). DS code is IRQ66..CE. For ES, on the basis of the unit root test (see Table 8), we

employ industrial production instead of GDP. The DS code is ESIPTOT.G. The euro area aggregate

commences in 1995Q1.

Unemployment: Country unemployment indices are taken from the OECD Economic Outlook

database and retrieved trough SDW. In the case of IE (before 1983Q1) and ES (before 1976Q3)

we convert from annual to quarterly frequency. In IE, as an indicator for quarterly changes we use

the persons on the life register series (DS: IRUNPBENO) and convert the annual unemployment

series using GFD (GFD: UNIRLM). For ES we relate the yearly GFD (GFD: UNESPM) series to

the number of registered unemployed by the relevant Spanish Ministry (DS: ESUNPTOTP). In the

case of Finland we use the series by GFD (GFD: UNFINM) before 1975Q1. For DE we use the

OECD Main Economic Indicators’ series (DS: BDQLRT28Q). The euro area aggregate commences

in 1998Q1.

ECB Working Paper 1846, September 201538Table 8: Unit root tests

Country

c

ph

pe

r

y

u

πp

c

ph

Augmented Dickey Fuller (ADF) Test

Philips-Perron (PP) Test
y
pe

r

u

πp

Level
EA
AT
BE
DE
DK
ES
FI
FR
IE
IT
NL
PT
SE
UK

Yoy Filter
EA
AT
BE
DE
DK
ES
FI
FR
IE
IT
NL
PT
SE
UK

Qoq Filter
EA
AT
BE
DE
DK
ES
FI
FR
IE
IT
NL
PT
SE
UK

0.725
0.966
0.999
0.633
0.836
0.541
0.999
0.998
0.905
0.791
0.890
0.794
1.000
0.948

0.280
0.007
0.105
0.401
0.023
0.043
0.037
0.000
0.258
0.134
0.038
0.186
0.066
0.644

0.341
0.000
0.000
0.004
0.036
0.244
0.000
0.000
0.003
0.000
0.003
0.086
0.000
0.000

0.567
0.001
0.879
0.574
0.551
0.446
0.423
0.725
0.356
0.456
0.403
0.872
0.976
0.708

0.209
0.123
0.116
0.012
0.001
0.111
0.004
0.184
0.186
0.003
0.072
0.075
0.023
0.002

0.090
0.000
0.014
0.000
0.000
0.000
0.000
0.011
0.005
0.000
0.054
0.001
0.006
0.001

0.320
0.216
0.482
0.445
0.911
0.412
0.179
0.490
0.371
0.109
0.520
0.109
0.767
0.645

0.018
0.000
0.008
0.000
0.000
0.049
0.003
0.000
0.000
0.000
0.010
0.004
0.000
0.001

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.627
0.572
0.469
0.510
0.056
0.533
0.814
0.610
0.113
0.470
0.553
0.294
0.209
0.001

0.037
0.008
0.000
0.000
0.009
0.003
0.001
0.003
0.000
0.001
0.001
0.000
0.019
0.001

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.441
0.936
0.872
0.898
0.758
0.835
0.827
0.768
0.933
0.168
0.812
0.396
0.999
0.970

0.015
0.015
0.000
0.000
0.015
0.131
0.049
0.012
0.462
0.010
0.016
0.007
0.000
0.018

0.000
0.000
0.000
0.000
0.000
0.004
0.000
0.000
0.021
0.000
0.000
0.000
0.000
0.000

0.209
0.542
0.058
0.194
0.162
0.518
0.154
0.356
0.254
0.534
0.051
0.329
0.599
0.185

0.006
0.001
0.003
0.041
0.004
0.005
0.040
0.018
0.008
0.097
0.038
0.037
0.000
0.007

0.083
0.000
0.000
0.001
0.000
0.000
0.001
0.000
0.000
0.001
0.015
0.001
0.000
0.000

0.850
0.020
0.030
0.096
0.128
0.756
0.386
0.363
0.249
0.738
0.393
0.580
0.253
0.060

0.000
0.000
0.001
0.000
0.000
0.001
0.000
0.000
0.000
0.002
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.869
0.967
1.000
0.321
0.983
0.932
0.999
1.000
0.997
0.979
0.971
0.978
1.000
0.951

0.373
0.059
0.007
0.115
0.209
0.460
0.001
0.006
0.048
0.076
0.167
0.010
0.011
0.012

0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.794
0.094
0.987
0.715
0.632
0.646
0.730
0.927
0.665
0.424
0.688
0.944
0.991
0.737

0.262
0.007
0.045
0.004
0.010
0.027
0.011
0.037
0.045
0.138
0.059
0.050
0.112
0.009

0.027
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000

0.352
0.305
0.515
0.565
0.940
0.239
0.294
0.562
0.427
0.124
0.518
0.255
0.847
0.685

0.025
0.002
0.006
0.012
0.015
0.029
0.002
0.005
0.013
0.001
0.011
0.002
0.017
0.013

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.383
0.300
0.237
0.259
0.062
0.310
0.680
0.413
0.062
0.220
0.255
0.035
0.135
0.085

0.044
0.018
0.026
0.003
0.000
0.000
0.141
0.016
0.001
0.045
0.000
0.000
0.002
0.032

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.342
0.919
0.848
0.842
0.758
0.856
0.836
0.703
0.981
0.120
0.830
0.386
0.997
0.971

0.078
0.001
0.035
0.000
0.000
0.054
0.003
0.003
0.001
0.037
0.000
0.006
0.000
0.006

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.640
0.577
0.181
0.307
0.162
0.772
0.342
0.362
0.420
0.745
0.234
0.895
0.007
0.275

0.154
0.000
0.009
0.037
0.004
0.043
0.022
0.003
0.018
0.011
0.037
0.004
0.000
0.016

0.061
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.009
0.000
0.000
0.000

0.914
0.001
0.008
0.000
0.000
0.004
0.064
0.277
0.001
0.110
0.004
0.000
0.000
0.007

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

Notes: Table depicts p-values for indicated tests on unit roots. Bold numbers indicate that test rejects the H0 of a unit root at least at the 5%
level. Red numbers in the case of yoy and qoq indicate that both the ADF and PP tests indicate that for the respective series the H0 cannot
be rejected given a 5% level. All tests include a constant term. Maximum lag length is 13 for the ADF test and the Schwarz Info Criterion
used. In the case of the PP test the bandwidth is chosen via Newey-West. c refers to total credit, ph to house prices, pe to equity prices, r
to bond yields, y to gdp, u to unemployment rate, and πp to inﬂation.

Inﬂation: CPI is from OECD/Eurostat and obtained through SDW. In order to maximise our

sample period we obtain this measure for IE from the national statistics ofﬁce (DS: IRCONPRCF).

The euro area aggregate commences in 1996Q1.

Unit root tests, as presented in the Table 8, indicate that – taking both the augmented Dickey-

Fuller (ADF) and Phillips-Perron (PP) test into account (5 % signiﬁcance level) – there is evidence of

unit roots in the levels of the variables. This can only be rejected in the case of inﬂation for AT and

BE. For the quarter-on-quarter ﬁlter tests results suggest compelling evidence against unit roots in all
cases, with the only exception being the aggregate euro area unemployment series. 23 For ES we ﬁnd

23For the year-over-year ﬁlter the tests indicate stationarity for most variables. However there are six cases, in which both
tests cannot reject the null hypothesis of a unit root: credit for the euro area, DE, IT, and the UK as well as house prices for

ECB Working Paper 1846, September 201539evidence in the case of GDP of a unit root.24

A.2 Spectral properties of indicators and indicator pairs

This Appendix discusses the implications of the quarter-on-quarter and year-on-year transformations

for the cyclical characteristics of the underlying indicators. First, we discuss the theoretical effects of

transformations and following, we compare the estimated spectral densities across indicators.

A.2.1 The effects of transforming indicators

The spectral approach requires a stationary process, thus, raising the important task to correctly de-
trend the data.25 The method for correctly detrending, i.e., without distorting the cyclical pattern of

interest, depends on the nature of the non-stationarity. In the absence of a commonly agreed deﬁnition

of a ﬁnancial or even business cycle it is impossible to deﬁne the cyclical pattern of interest. Further,

one does not know the source of non-stationarity, which further hinders a correct analysis. In this re-

spect tests on unit roots might give an indication whether a transformation renders a series stationary,

however these are known to be ﬂawed by low power. In light of these observations we follow the

procedure suggested in A’Hearn and Woitek (2001) which is to compare the power transfer functions
of the ﬁlters and learn about the distortions that these ﬁlters induce into the data.26

To stationary transform indicators we compare two different ﬁlters. The ﬁrst one reﬂects the

standard ﬁrst difference ﬁlter (∆yt = yt − yt−1) which we call qoq ﬁlter as we use quarterly series.

The second one is similar but represents a seasonal ﬁlter in order to, among other things, mute yearly

seasonal cycles (∆4yt = yt − yt−4). We call this ﬁlter yoy ﬁlter. In the context of quarterly data,
the qoq ﬁlter is the standard one applied in business cycle studies (e.g. Comin and Gertler (2006)).27

The yoy ﬁlter is less standard but has been used, for instance, in the study of the ﬁnancial cycle by

Drehmann et al. (2012).

The power transfer functions (PTFS) in Figure 12 depict the squared gain induced by each ﬁlter

across frequencies. The area in blue marks business cycle frequencies (2.5-8 years) and the purple

area medium term cycle periods which have been argued to be important for the ﬁnancial cycle (8-20

years). The ideal ﬁlter – for the purpose of detrending – would remove the permanent ﬂuctuations at

the euro area and NL.

24On the basis of the test results we decide to substitute real GDP in ES with industrial production that could have led
to the evidence of unit roots. The p-values of the unit root tests for ES industrial production are – for the ADF and PP
test respectively: 0.39 & 0.45 (level); 0.21, 0.00 (yoy); 0.00, 0.00 (qoq). Unfortunately, a substitute is not apparent for the
ﬁnancial variables or EA unemployment.

25For a thorough discussion on detrending in relation with business cycle analyses, please refer to Canova (1998).
26Note, the distortions depend on the type of non-stationarity, the following example reﬂects the distortion induced to a

trend stationary or white noise series.

27There are also studies using yearly data (e.g. A’Hearn and Woitek (2001) or Aikman et al. (2015)) and applying the
ﬁrst difference transformation. The discussion provided here, however, exclusively depicts an exposition for quarterly data
as the windows of interest (short and medium term) would vary using a different data frequency

ECB Working Paper 1846, September 201540Figure 12: Power transfer function of quarter-on-quarter and year-on-year ﬁlter
Notes: The yoy ﬁlter is depicted by the solid black line; the qoq ﬁlter by the blue dashed line. The blue area marks business cycle
frequencies (2.5-8 years) and the purple area medium term cycles (8-20 years).

frequency zero and leave the others untouched (meaning a squared gain of 1).28 However, no such

ﬁlter exists for all processes. The qoq ﬁlter is optimal for difference stationary processes. The yoy

ﬁlter removes yearly cycles in the case of quarterly data, i.e. at frequency π/2. Further, the qoq

ﬁlter dampens the frequencies which are actually suspected to drive business and ﬁnancial cycles, as

their gain is below one in that region. High frequency components (e.g., < one year) are intensiﬁed.

In contrast, the yoy ﬁlter reduces the variance of cycles to a lesser extent and even ampliﬁes some

regions of business cycle frequencies. Moreover, the yoy ﬁlter rather suppresses high frequency
components, except for cycles around 2.¯6 quarters. In this light, it can be argued that the yoy ﬁlter

should be preferred as the actual frequencies of interest are not muted as strongly as in the case of

the qoq ﬁlter. However it also induces distortions, i.e. overemphasises business cycle frequencies

and biases the turning points properties of a series. In evaluating the spectral densities and power

cohesion it is important to keep in mind at which frequencies a ﬁlter induces distortions. In the case
of the yoy ﬁlter peaks around 2 years and 2.¯6 quarters could be induced by the ﬁlter. In contrast high

frequency movements (< one year) for the qoq ﬁlter could be induced by the latter.

A.2.2 Univariate spectra

We use our large country setup to discuss similarities of cycle characteristics of variables across coun-

tries. The following Figure 13 reports the distribution of important cycles for all indicators considered

in this study (ﬁnancial and business cycle) across countries, excluding the euro area aggregate series.

Spectral densities are normalised, such that the maximum value is one. Black lines depict the results

28The HP-ﬁlter is close the ideal one when applied to trend stationary data. However, the ﬁlter is known to induce spurious
cycles when applied to the wrong data type. A’Hearn and Woitek (2001) even show that there is the potential danger that it
induces a long cycle.

0π/4π/23π/4π01234PTFRadiansECB Working Paper 1846, September 201541for the year-on-year transformation and blue line the quarter-on-quarter. Lower dashed lines portray

the 10th percentile and the upper ones the 90th percentile. A small distance between the two dashed

lines indicates that that the cyclical properties of the respective indicator at that frequency is simi-

lar across countries, while a long distance refers to the case where properties differ strongly across

countries.

The graph conﬁrms the result that credit and house prices are characterised by medium term

cycles. Further, variables across countries seem to have similar cyclical properties as the distance

between the dashed lines is small. Similarly, for equity prices the graph depicts homogeneous results

across countries, however equity prices seem to have important ﬂuctuations both at the medium as

well as short term cycle frequencies.

In the case of business cycle indicators and r there is less evidence that variables have the same

cyclical properties across countries. However, bond yields have most important cycles located within

the window of the short term cycles skewed to 2.5 years. The qoq analysis also depicts important

cycle frequencies for higher frequency components. This is also true for y, in which case the dis-

tribution of power is distributed quite equally for the qoq ﬁlter. Both transformations suggest that

important ﬂuctuations are in the short and medium term frequencies, which is in line with previous

studies. In the case of the yoy ﬁlter most important cycles even appear towards longer term cycles,

i.e. skewed towards the zero frequency, which would indicate that the variable is still driven by a
trend.29 Regarding u, the spectra indicate for both qoq and yoy transformations that most important

cyclical variations are located in the medium term region. Nonetheless and similar to y, there are

important cycle frequencies in the short term range as well. Again the yoy transformation cancels out

the short term movements, while the qoq shows variation located in the higher frequency region for

some countries. In the case of πp differences between the resulting yoy and qoq spectra are strongest.

Medium and short term cycles are relatively not important in the qoq case but highly in the yoy one.

Contrasting the spectra using different transformations two conclusions can be drawn: First, the

yoy transformation removes the variation in the higher frequencies of the spectrum relative to the qoq

ﬁlter, except for πp. Second, the importance of the medium and short term cycle periods is robust for
ﬁnancial indicators (also r) with respect to the transformation across countries. Just for pe the graph

depicts that short term cycles for the qoq ﬁlter are more important relative to the short term cycles

employing the yoy ﬁlter, nonetheless indicating that the cycle length on the border of medium and

short term is most important. This is in contrast to the exclusive business cycle indicators (y, πp, and
u), in which case we note differences across ﬁlters within the short and medium term frequencies.

29Looking more speciﬁcally at the single spectra of y for each country, we note that for AT, BE, DE, DK, and SE most
important cycle frequencies are located in the short term. For ES, FR, IE, IT, and NL we note that the zero frequency is most
important, i.e., there is evidence that the transformed series is still governed by a long-term trend or a structural break may
be present. Next to this zero frequency, however, the short term still contains the second most important cycle frequencies,
except for PT. For FI and UK there is evidence of most important cycles being in the medium term.

ECB Working Paper 1846, September 201542Figure 13: Normalised univariate spectra of indicators across countries
Notes: The left column depicts the graphs for qoq transformations and the right one for the yoy transformations. The x-axis measures the
frequencies of cycles in radians. The maximum value of the spectral densities is normalised to one (y-axis). The blue area depicts business
cycle frequencies, i.e., cycles with durations of 2.5-8 years and the purple area marks medium term cycles (8-20 years). ∆ = 1 − L and
∆4 = 1 − L4, where L denotes the lag operator. c refers to the log of total credit, ph to the log of residential property prices, pe to the log
of equity prices, r to bond yields, q to the log of GDP, u to the unemployment rate, and πp to the ﬁrst log difference of the price level.

0π/4π/23π/4π00.51Δc0π/4π/23π/4π00.51Δ4c0π/4π/23π/4π00.51Δph0π/4π/23π/4π00.51Δ4ph0π/4π/23π/4π00.51Δpe0π/4π/23π/4π00.51Δ4pe0π/4π/23π/4π00.51Δr0π/4π/23π/4π00.51Δ4r0π/4π/23π/4π00.51Δq0π/4π/23π/4π00.51Δ4q0π/4π/23π/4π00.51Δu0π/4π/23π/4π00.51Δ4u0π/4π/23π/4π00.51Δπp0π/4π/23π/4π00.51Δ4πpECB Working Paper 1846, September 201543A.2.3 Cross-spectra

The previous subsection sheds light on the univariate spectra. For identifying economic cycles we,

however, advance the idea of exploiting the co-variation between several indicators. Thus, the follow-

ing analyses in detail at which cycle frequencies there is most co-movement for all pairs of indicators

neglecting phase shifts. These cross-spectra are reported in Figure 14. Again, a relatively short

(long) distance between the dashed lines indicates homogeneous (heterogeneous) cyclical properties

of indicator pairs across countries.

We ﬁnd that co-movement across indicators for the ﬁnancial cycle is generally located in the

medium term cycle region, while business cycle indicators are co-move in the short term as well as

in the medium term region. Furthermore while ﬁnancial indicators relatively agree in their cyclical

properties across countries, this is less evident for business cycle indicators.

More speciﬁcally and regarding the ﬁnancial indicators, we note that c shares important co-

movements at the medium term cycle with ph or pe. This is a homogeneous result across countries.
Co-movements of ph and pe are also most important within the medium term region which is a ho-
mogeneous result across countries. In contrast to the co-variation with credit, these graphs also depict

important cyclical movements at the short term, however with less agreement across countries. The

joint movement of c and ph with r is most important towards the medium term frequencies while
there exist important cycles also in the short term. For pe and benchmark bond yields (r) important
co-variation lies within the short and medium term. In all cross spectra that involve r we see that re-

sults differ relatively strong across countries. Moreover, the qoq transformation emphasises relatively

strongly high frequency movements.

With respect to the business cycle indicators the yoy transformation supports common ﬁndings

that important cyclical ﬂuctuations are located within the short term, but also in the medium term

region. However compared to the agreement of cyclical properties of the ﬁnancial indicators (except

for r), the business cycle cross spectra are relatively heterogeneous across countries. For the cross

spectra that involve πp high frequency movements are relatively more important in the qoq case.

Contrasting the yoy and qoq transformation, again, we draw the conclusion that the yoy transfor-

mation removes the higher frequency cycles, while the qoq emphasises them. This does not change

the importance of longer term cycles in the case of ﬁnancial indicators, however it does for the busi-

ness cycle ones. This is especially evident in the cross spectra that involve inﬂation. We conclude

from this section that the transformation of indicators matter for the business cycle but not for the

ﬁnancial cycle. The yoy ﬁlter has the nice property to reduce noise in the higher frequency regions,

while the qoq ﬁlter emphasises those.

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i
F

0π/4π/23π/4π00.51ΔcandΔph0π/4π/23π/4π00.51Δ4candΔ4ph0π/4π/23π/4π00.51ΔrandΔq0π/4π/23π/4π00.51Δ4randΔ4q0π/4π/23π/4π00.51ΔcandΔpe0π/4π/23π/4π00.51Δ4candΔ4pe0π/4π/23π/4π00.51ΔrandΔu0π/4π/23π/4π00.51Δ4randΔ4u0π/4π/23π/4π00.51ΔphandΔpe0π/4π/23π/4π00.51Δ4phandΔ4pe0π/4π/23π/4π00.51ΔrandΔπp0π/4π/23π/4π00.51Δ4randΔ4πp0π/4π/23π/4π00.51ΔcandΔr0π/4π/23π/4π00.51Δ4candΔ4r0π/4π/23π/4π00.51ΔqandΔu0π/4π/23π/4π00.51Δ4qandΔ4u0π/4π/23π/4π00.51ΔphandΔr0π/4π/23π/4π00.51Δ4phandΔ4r0π/4π/23π/4π00.51ΔqandΔπp0π/4π/23π/4π00.51Δ4qandΔ4πp0π/4π/23π/4π00.51ΔpeandΔr0π/4π/23π/4π00.51Δ4peandΔ4r0π/4π/23π/4π00.51ΔuandΔπp0π/4π/23π/4π00.51Δ4uandΔ4πpECB Working Paper 1846, September 201545A.3 Appendix to selecting ﬁnancial cycle frequencies through power cohesion

Figure 15: Power cohesion of ﬁnancial (black) and business (red) cycle indicators
Notes: This panel shows the power cohesion of the ﬁnancial (black lines) and business cycle indicators (red lines). The dashed lines indicate
the 68% bootstrapped conﬁdence interval. The x-axis measures the frequencies of cycles in radians from 0 to π/2. The y-axis shows the
value of PCoh.The blue area depicts business cycle frequencies, i.e., cycles with durations of 2.5-8 years and the purple area marks medium
term cycles (8-20 years).

0π/4π/200.10.20.3AT0π/4π/200.20.40.60.8BE0π/4π/200.20.4DE0π/4π/200.20.40.6DK0π/4π/200.51ES0π/4π/200.20.40.60.8FI0π/4π/200.20.40.6FR0π/4π/200.20.40.6IE0π/4π/200.20.40.6IT0π/4π/200.20.40.60.8NL0π/4π/200.20.4PT0π/4π/200.20.40.60.8SE0π/4π/200.20.40.6UKECB Working Paper 1846, September 201546A.4 Appendix to a composite index of the ﬁnancial cycle

A.4.1 Financial cycles

Figure 16: For each country:
1. Unﬁltered (blue) and ﬁltered (black) composite ﬁnancial cycle,
2. Filtered indicator series: ∆c (blue), ∆ph (green), ∆pe (red), and −∆r (purple),
3. Time-varying aggregation weights: ∆c (blue), ∆ph (green), ∆pe (red), and −∆r (purple)
Notes: The x-axis measures the date. For each country the y-axis of the upper two graphs shows the relative historical position, where
0/1 represents the min/max and 0.5 is the historical median. The y-axis of the lower graph depicts the time-varying aggregation weights
exploiting time-varying correlations between indicators, where the 0.25 line indicates equal weighting. Filtered indices use the respective
frequency window as depicted in Table 2. The grey shaded area indicates a systemic banking crisis as identiﬁed by Laeven and Valencia
(2012).

889092949698000204060810121400.51YearHistorical positionAT889092949698000204060810121400.51YearHistorical position88909294969800020406081012140.20.250.3YearAggregation weightECB Working Paper 1846, September 201547Figure 17: For each country:
1. Unﬁltered (blue) and ﬁltered (black) composite ﬁnancial cycle,
2. Filtered indicator series: ∆c (blue), ∆ph (green), ∆pe (red), and −∆r (purple),
3. Time-varying aggregation weights: ∆c (blue), ∆ph (green), ∆pe (red), and −∆r (purple)
Notes: The x-axis measures the date. For each country the y-axis of the upper two graphs shows the relative historical position, where
0/1 represents the min/max and 0.5 is the historical median. The y-axis of the lower graph depicts the time-varying aggregation weights
exploiting time-varying correlations between indicators, where the 0.25 line indicates equal weighting. Filtered indices use the respective
frequency window as depicted in Table 2. The grey shaded areas indicate systemic banking crises as identiﬁed by Laeven and Valencia
(2012).

758085909500051000.51YearHistorical positionBE758085909500051000.51YearHistorical positionDE758085909500051000.51YearHistorical position758085909500051000.51YearHistorical position75808590950005100.150.20.250.3YearAggregation weight75808590950005100.150.20.250.3YearAggregation weight758085909500051000.51YearHistorical positionDK758085909500051000.51YearHistorical positionES758085909500051000.51YearHistorical position758085909500051000.51YearHistorical position75808590950005100.150.20.250.3YearAggregation weight75808590950005100.150.20.250.3YearAggregation weightECB Working Paper 1846, September 201548Figure 18: For each country:
1. Unﬁltered (blue) and ﬁltered (black) composite ﬁnancial cycle,
2. Filtered indicator series: ∆c (blue), ∆ph (green), ∆pe (red), and −∆r (purple),
3. Time-varying aggregation weights: ∆c (blue), ∆ph (green), ∆pe (red), and −∆r (purple)
Notes: The x-axis measures the date. For each country the y-axis of the upper two graphs shows the relative historical position, where
0/1 represents the min/max and 0.5 is the historical median. The y-axis of the lower graph depicts the time-varying aggregation weights
exploiting time-varying correlations between indicators, where the 0.25 line indicates equal weighting. Filtered indices use the respective
frequency window as depicted in Table 2. The grey shaded areas indicate systemic banking crises as identiﬁed by Laeven and Valencia
(2012).

758085909500051000.51YearHistorical positionFI758085909500051000.51YearHistorical positionFR758085909500051000.51YearHistorical position758085909500051000.51YearHistorical position75808590950005100.150.20.250.3YearAggregation weight75808590950005100.20.250.3YearAggregation weight758085909500051000.51YearHistorical positionIE758085909500051000.51YearHistorical positionIT758085909500051000.51YearHistorical position758085909500051000.51YearHistorical position75808590950005100.150.20.250.3YearAggregation weight75808590950005100.150.20.250.3YearAggregation weightECB Working Paper 1846, September 201549Figure 19: For each country:
1. Unﬁltered (blue) and ﬁltered (black) composite ﬁnancial cycle,
2. Filtered indicator series: ∆c (blue), ∆ph (green), ∆pe (red), and −∆r (purple),
3. Time-varying aggregation weights: ∆c (blue), ∆ph (green), ∆pe (red), and −∆r (purple)
Notes: The x-axis measures the date. For each country the y-axis of the upper two graphs shows the relative historical position, where
0/1 represents the min/max and 0.5 is the historical median. The y-axis of the lower graph depicts the time-varying aggregation weights
exploiting time-varying correlations between indicators, where the 0.25 line indicates equal weighting. Filtered indices use the respecti
frequency window as depicted in Table 2. The grey shaded areas indicate systemic banking crises as identiﬁed by Laeven and Valencia
ve
(2012).

758085909500051000.51YearHistorical positionNL9092949698000204060810121400.51YearHistorical positionPT758085909500051000.51YearHistorical position9092949698000204060810121400.51YearHistorical position75808590950005100.150.20.250.3YearAggregation weight909294969800020406081012140.20.250.3YearAggregation weight758085909500051000.51YearHistorical positionSE758085909500051000.51YearHistorical positionUK758085909500051000.51YearHistorical position758085909500051000.51YearHistorical position75808590950005100.150.20.250.3YearAggregation weight75808590950005100.150.20.250.3YearAggregation weightECB Working Paper 1846, September 201550Table 9: Concordance of ﬁltered and unﬁltered ﬁnancial cycles

AT

AT
0.69
BE
DE
0.59
DK 0.71
0.75
ES
0.70
FI
FR 0.70
0.58
IE
0.72
IT
0.59
NL
0.59
PT
SE
0.76
UK 0.66
0.67

Mean

AT
0.65
BE
DE
0.63
DK 0.71
0.65
ES
FI
0.68
FR 0.72
0.63
IE
0.64
IT
0.64
NL
0.62
PT
SE
0.63
UK 0.58
0.65

Mean

BE
0.69

0.57
0.77
0.81
0.84
0.72
0.81
0.78
0.76
0.68
0.78
0.80
0.75

0.65

0.60
0.83
0.75
0.80
0.68
0.78
0.66
0.78
0.74
0.75
0.75
0.73

DE
0.59
0.57

0.53
0.47
0.56
0.42
0.55
0.48
0.63
0.58
0.54
0.42
0.53

0.63
0.60

0.52
0.49
0.55
0.60
0.57
0.55
0.72
0.58
0.42
0.49
0.56

DK
0.71
0.77
0.53

0.71
0.80
0.63
0.77
0.59
0.68
0.76
0.74
0.74
0.70

0.71
0.83
0.52

0.77
0.82
0.74
0.80
0.66
0.78
0.71
0.77
0.74
0.74

ES
0.75
0.81
0.47
0.71

0.72
0.86
0.73
0.82
0.63
0.64
0.76
0.91
0.73

0.65
0.75
0.49
0.77

0.74
0.84
0.84
0.84
0.76
0.77
0.88
0.85
0.77

Filtered
FR
0.70
0.72
0.42
0.63
0.86
0.75

0.64
0.71
0.54
0.56
0.79
0.83
0.68

Unﬁltered
0.72
0.68
0.60
0.74
0.84
0.74

0.74
0.79
0.67
0.66
0.76
0.78
0.73

IE
0.58
0.81
0.55
0.77
0.73
0.74
0.64

0.63
0.80
0.72
0.74
0.76
0.71

0.63
0.78
0.57
0.80
0.84
0.71
0.74

0.71
0.87
0.74
0.72
0.78
0.74

FI
0.70
0.84
0.56
0.80
0.72

0.75
0.74
0.63
0.65
0.71
0.79
0.75
0.72

0.68
0.80
0.55
0.82
0.74

0.74
0.71
0.62
0.74
0.72
0.80
0.68
0.72

IT
0.72
0.78
0.48
0.59
0.82
0.63
0.71
0.63

0.62
0.52
0.67
0.73
0.66

0.64
0.66
0.55
0.66
0.84
0.62
0.79
0.71

0.67
0.64
0.72
0.72
0.69

NL
0.59
0.76
0.63
0.68
0.63
0.65
0.54
0.80
0.62

0.62
0.62
0.67
0.65

0.64
0.78
0.72
0.78
0.76
0.74
0.67
0.87
0.67

0.80
0.66
0.72
0.73

PT
0.59
0.68
0.58
0.76
0.64
0.71
0.56
0.72
0.52
0.62

0.73
0.67
0.65

0.62
0.74
0.58
0.71
0.77
0.72
0.66
0.74
0.64
0.80

0.75
0.65
0.70

SE
0.76
0.78
0.54
0.74
0.76
0.79
0.79
0.74
0.67
0.62
0.73

0.75
0.72

0.63
0.75
0.42
0.77
0.88
0.80
0.76
0.72
0.72
0.66
0.75

0.79
0.72

UK Mean
0.67
0.66
0.75
0.80
0.53
0.42
0.70
0.74
0.73
0.91
0.72
0.75
0.68
0.83
0.71
0.76
0.66
0.73
0.65
0.67
0.65
0.67
0.72
0.75
0.73
0.68

0.73

0.58
0.75
0.49
0.74
0.85
0.68
0.78
0.78
0.72
0.72
0.65
0.79

0.71

0.65
0.73
0.56
0.74
0.77
0.72
0.73
0.74
0.69
0.73
0.70
0.72
0.71
0.71

Notes: This table shows the bilateral concordance between indicated countries. Statistics are produced using the turning point algorithm as
indicated in Section 3.3.

ECB Working Paper 1846, September 201551A.4.2 A comparison to business cycles

Figure 20: Financial (black) and business (red) cycles
Notes: This panel shows the ﬁltered ﬁnancial and business cycles using the frequency bands presented in Table 2. The x-axis measures
the date and the y-axis the relative historical position, where 0/1 represents the min/max and 0.5 is the historical median. The grey shaded
areas indicate systemic banking crises as identiﬁed by Laeven and Valencia (2012).

889092949698000204060810121400.51YearHistorical positionAT758085909500051000.51YearHistorical positionBE758085909500051000.51YearHistorical positionDE758085909500051000.51YearHistorical positionDK77808285879092959700020507101200.51YearHistorical positionES758085909500051000.51YearHistorical positionFI758085909500051000.51YearHistorical positionFR828486889092949698000204060810121400.51YearHistorical positionIE758085909500051000.51YearHistorical positionIT758085909500051000.51YearHistorical positionNL9092949698000204060810121400.51YearHistorical positionPT758085909500051000.51YearHistorical positionSE758085909500051000.51YearHistorical positionUKECB Working Paper 1846, September 201552Figure 21: Unﬁltered (blue) and ﬁltered (red) business cycle composite index
Notes: This panel shows the unﬁltered and ﬁltered business cycle composite index using the frequency bands presented in Table 2. The
x-axis measures the date and the y-axis the relative historical position, where 0/1 represents the min/max and 0.5 is the historical median.
The grey shaded areas indicate systemic banking crises as identiﬁed by Laeven and Valencia (2012).

99000102030405060708091011121300.51YearHistorical positionEA758085909500051000.51YearHistorical positionAT758085909500051000.51YearHistorical positionBE758085909500051000.51YearHistorical positionDE758085909500051000.51YearHistorical positionDK77808285879092959700020507101200.51YearHistorical positionES758085909500051000.51YearHistorical positionFI758085909500051000.51YearHistorical positionFR828486889092949698000204060810121400.51YearHistorical positionIE758085909500051000.51YearHistorical positionIT758085909500051000.51YearHistorical positionNL758085909500051000.51YearHistorical positionPT758085909500051000.51YearHistorical positionSE758085909500051000.51YearHistorical positionUKECB Working Paper 1846, September 201553Table 10: Correlation of unﬁltered indicators with unﬁltered composite business cycle

Country
AT
BE
DE
DK
ES
FI
FR
IE
IT
NL
PT
SE
UK
Mean

∆q
0.43
0.47
0.44
0.59
0.57
0.50
0.58
0.51
0.50
0.38
0.50
0.55
0.42
0.50

∆u ∆πp
0.59
0.67
0.50
0.52
0.57
0.59
0.58
0.58
0.52
0.60
0.43
0.60
0.43
0.55

-0.55
-0.53
-0.61
-0.60
-0.59
-0.63
-0.61
-0.53
-0.49
-0.60
-0.28
-0.27
-0.68
-0.54

∆r
-0.63
-0.57
-0.50
-0.49
-0.62
-0.65
-0.48
-0.64
-0.50
-0.49
-0.55
-0.59
-0.38
-0.55

Notes: Table shows the correlation between each unﬁltered indicator and the unﬁltered composite business cycle across the longest available
sample in each country case. ∆q to percentage changes in GDP, ∆u to percentage point changes of the unemployment rate, ∆πp to
percentage point changes in inﬂation, and ∆r to percentage point changes in bond yields.

ECB Working Paper 1846, September 201554Acknowledgements 
The authors would like to thank Fabio Canova, Matteo Ciccarelli, Stephan Fahr, Kirstin Hubrich, Benjamin Klaus, Manfred Kremer, Siem 
Jan Koopman, Jan Hannes Lang, Simone Manganelli, Massimiliano Marcellino, Giulio Nicoletti, Ana Regina Nunes Pereira, Giorgio 
Primiceri, Gerhard Rünstler, Harald Uhlig, an anonymous referee, and the audience of the EABCN conference on “Econometric 
methods for business cycle analysis, forecasting and policy simulations” as well as of the workshop on “Financial and Business Cycles” 
at the European Central Bank for helpful discussions and comments. Codruta-Olivia Boar read the last draft carefully and pointed out a 
number of typos. Further, we would especially like to thank Peter Welz for his invaluable contribution to the validation exercise, as well 
as his insightful comments. All errors are our own. The opinions expressed in this paper are those of the authors and do not necessarily 
reflect the views of the European Central Bank, the Eurosystem, or the European Systemic Risk Board. A previous version of this paper 
was circulated under the title “Characterising financial cycles across Europe: One size does not fit all”. 

Yves S. Schüler 
European Central Bank, Frankfurt am Main, Germany;  
e-mail: yves.schueler@protonmail.com 

Paul P. Hiebert 
European Central Bank, Frankfurt am Main, Germany;  
e-mail: paul.hiebert@ecb.europa.eu  

Tuomas A. Peltonen 
European Systemic Risk Board, Frankfurt am Main, Germany;  
e-mail: tuomas.peltonen@esrb.europa.eu 

© European Central Bank, 2015 

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ISSN 
ISBN 
DOI 
EU catalogue No 

1725-2806 (online) 
978-92-899-1659-2 
10.2866/22606 
QB-AR-15-086-EN-N