Coherent financial cycles for G-7 countries : why extending credit can be an asset.
Date: 2017-05-12
Institutions: European Systemic Risk Board
Subjects: central bank, credit, econometrics, economic cycle, financial market, macroeconomics

Working Paper Series 

No 43 / May 2017 

Coherent financial cycles for 
G-7 countries:  
Why extending credit can be an 
asset 

by 
Yves S. Schüler 
Paul P. Hiebert 
Tuomas A. Peltonen 

 
Abstract

Failing to account for joint dynamics of credit and asset prices can be hazardous for countercycli-
cal macroprudential policy. We show that composite ﬁnancial cycles, emphasising expansions and
contractions common to credit and asset prices, powerfully predict systemic banking crises. Fur-
ther, the joint consideration yields a more robust view on ﬁnancial cycle characteristics, reconciling
an empirical puzzle concerning cycle properties when using two popular alternative methodologies:
frequency decompositions and standard turning point analysis. Using a novel spectral approach, we
establish the following facts for G-7 countries (1970Q1-2013Q4): Relative to business cycles, ﬁnan-
cial cycles differ in amplitude and persistence – albeit with heterogeneity across countries. Average
ﬁnancial cycle length is around 15 years, compared with 9 years (6.7 excluding Japan) for business
cycles. Still, country-level business and ﬁnancial cycles relate occasionally. Across countries, ﬁnan-
cial cycle synchronisation is strong for most countries; but not for all. In contrast, business cycles
relate homogeneously.

Keywords: Financial cycle · Spectral analysis · Macroprudential policy

JEL-Codes: C54 · E32 · E44 · E58 · G01

“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

Financial cycles are central to systemic risk. Experience has shown that imbalances can build up in the

ﬁnancial system that have the propensity to lead to severe recessions, often accompanied by banking

crises (e.g., Minsky (1977), Kindleberger (1978), and Reinhart and Rogoff (2009)). Though the exis-

tence of such boom-bust cycles is widely accepted and already enshrined in macroprudential mandates,

assessment of such cycles remains in its infancy.

Our results suggest that research focusing in isolation on individual variables such as credit aggre-

gates, housing, or equity prices to capture ﬁnancial cycles is incomplete, and possibly misleading. We

propose to combine credit with asset prices, emphasising expansions and contractions common to all

series. The importance of such dynamics has not only been stressed by the theoretical construct of

leverage cycles (see Geanakopolos (2010)) but also empirical studies such as Jordà, Schularick and

Taylor (2015b) concerning the detrimental effects of leveraged asset price bubbles. We go beyond this,

however, showing that combining credit with asset prices leads to marked accuracy of ﬁnancial crisis

prediction, while also reconciling empirical puzzles concerning ﬁnancial cycle characteristics derived

from two popular alternative methodologies: frequency decompositions and standard turning point anal-

ysis.

We offer an integrated approach to empirically identify, characterise, and evaluate ﬁnancial cycles;
exploiting the co-movement of credit and asset prices.1 For identiﬁcation, we select credit and various

asset prices and present similarities in their statistical features that can be justiﬁed by the literature

on leverage cycles (see Geanakopolos and Fostel (2008) and Geanakopolos (2010), as well as work

by Gromb and Vayanos (2002), Brunnermeier and Pedersen (2009), Adrian and Shin (2010)) or in

general by work stressing the importance economics agents’ ability to borrow (see, e.g., Iacoviello

(2005) or Jermann and Quadrini (2012)). Taking this perspective, we highlight the theoretical link

for the interaction of credit and asset prices; through the importance of assets as collateral for loan

creation and existing feedback effects (e.g., changing margin requirements). Based on this idea we

characterise ﬁnancial cycles, i.e., we develop a spectral methodology that exploits the co-movement

of credit and asset prices to capture most important common cycle frequencies – in other words, their

empirical coherence. Further, we emphasise such commonality in aggregating credit and asset prices

into a composite ﬁnancial cycle index focussing on most important common cycle frequencies. We

1Important points of departure for the proposed spectral approach have been studies by A’Hearn and Woitek (2001) and
Croux, Forni and Reichlin (2001) in the context of business cycles. The evaluation exercise builds on the seminal work by
Frankel and Rose (1996), Kaminsky and Reinhart (1999), and Schularick and Taylor (2012).

2

evaluate real time composite ﬁnancial cycle indices via their ability to predict known past episodes of

systemic banking crises.

Three key results emerge when considering ﬁnancial and business cycles of G-7 countries from

1970Q1 until 2013Q4. First, ﬁndings corroborate the rationale of modelling the joint interaction of

credit and asset prices. On the one hand, their statistical features differ from business cycle indicators:

credit and asset prices have higher amplitude and – with the exception of equity prices – higher persis-

tence. Further and across countries, the correlation of credit with house prices and, in most countries,

also bond prices is the strongest contemporaneously; similar to the interaction of business cycle indi-

cators. Equity prices tend to precede credit. On the other hand, our out-of-sample signalling exercise

suggests that composite ﬁnancial cycle indices, exploiting the co-movement of credit and asset prices,

are the best indicators for the prediction of systemic banking crises starts and vulnerability periods for

G-7 economies. Predicting the start of crises, a broad index, considering the interaction of credit, hous-

ing, equity and bond prices, has an area under the receiver operating characteristic (AUROC) curve of

0.78; 19 percentage points higher than the second ranked indicator. A narrow index, mirroring the co-

movement of only credit and house prices, does similarly well as the broad index in our early warning

exercise comparing the area under the curve (AUC). Still, a broad index performs better considering

other criteria, as, e.g., relative usefulness and noise-to-signal ratio.

Second, country ﬁnancial cycles are distinct in many ways from business cycles. Financial cycles

tend to exhibit pronounced booms and busts, with an amplitude of more than twice than that of business

cycles. Financial cycles also tend to be long, lasting on average around 15 years in contrast to business

cycles of only around 9 years (or 6.7 years excluding Japan). There is signiﬁcant variation across

countries. At one extreme, Germany’s ﬁnancial cycle is found to have the lowest amplitude and shortest

length of the G-7 countries, and a close correspondence with business cycles lasting around 9 years. At

the other extreme, Japan’s ﬁnancial cycle is long, and closely corresponds to a protracted business cycle

(lasting over 20 years). Outside these extremes, most other countries differ in ﬁnancial and business

cycle length. In spite of these differences, our results suggest that country-level ﬁnancial and business

cycles coincide occasionally.

Third, we ﬁnd that cross-country synchronisation of ﬁnancial cycles is strong for most of G-7 coun-

tries; but not for all. The ﬁnancial cycles of Germany and Japan seem to be weakly related among

G-7 countries; having shown very distinct movements in credit and house prices (Hume and Sentance

(2009); André (2010); Knoll, Schularick and Steger (forthcoming)). In contrast, business cycles are

homogeneously related across G-7 countries.

These results suggest that macroprudential policies and the surveillance of ﬁnancial stability need to

consider the combined role of indicators for the detection of systemic risk build-up and materialisation.

Notably, the composite ﬁnancial cycle indices perform better in crises prediction than the credit-to-GDP

gap that has received a prominent role for setting countercyclical capital buffer rates in the Basel III reg-

ulations and the EU Capital Requirements Directive (CRD IV). Moreover, the distinct characteristics of

ﬁnancial cycles relative to business cycles within countries, as well as their divergences across countries,

indicate that there is a potential scope for specialised country-level macroprudential policies targeted at

3

the build-up of systemic risk.

This paper relates to an emerging strand of literature analysing the properties of ﬁnancial cycle vari-

ables such as credit, house prices, and equity prices, in contrast to business cycle variables. Studies

so far have stressed their increased length, amplitude, and asymmetry. Claessens, Kose and Terrones

(2011, 2012) ﬁnd that ﬁnancial cycles as separately measured by credit, house prices, and equity prices

are longer, more volatile, and more asymmetric than business cycles identiﬁed through GDP. Focussing

on measures of credit, Aikman, Haldane and Nelson (2015) observe that credit cycles have an important

medium term dimension being distinct from business cycles. Drehmann, Borio and Tsatsaronis (2012)

and Borio (2014) argue, as well, that medium term variance is especially important for credit cycles but

also house price cycles; not so for equity prices. Further, the authors note that the length of ﬁnancial

cycles has increased during the great moderation. Hiebert, Klaus, Peltonen, Schüler and Welz (2014)

stress the heterogeneity of ﬁnancial cycle properties across euro area countries, while also noting dif-

ferences between ﬁnancial cycle properties when using spectral approaches or classical turning points

analysis; both applied by earlier studies. Following these ﬁrst studies, subsequent research supported the

evidence, especially of distinct credit and house price cycles, applying different methodologies as, e.g.,

indirect spectral analysis (see Strohsal, Proaño and Wolters (2015a,b)), multivariate unobserved com-

ponent models (see Rünstler and Vlekke (2016); Galati, Hindrayanto, Koopman and Vlekke (2016)), or

wavelet techniques (see Verona (2016)). In contrast to results of previous literature, Verona (2016) does

not ﬁnd an increase in the length of the US ﬁnancial cycle.

We contribute to this literature on ﬁnancial cycles in ﬁve ways. First, justiﬁed by work on leverage

cycles or in general by research stressing the importance of borrowing constraints, we argue that the

joint ﬂuctuations of credit and asset prices, emphasising expansions and contractions commons to all

series, is vital for understanding ﬁnancial cycles and present an empirical approach for this. Previous
literature has tended to analyse properties of single indicators.2

Second, we are the ﬁrst to systematically evaluate the signiﬁcance of composite ﬁnancial cycle

indices in prediction of systemic banking crises starts and vulnerability periods. This is vital to highlight

their potential usefulness, for instance, for policy makers. While previous studies such as Schularick and

Taylor (2012) predict systemic banking crises with lagged credit growth, we show that the co-movement

of indicators, i.e., a composite ﬁnancial cycle index is an important predictor of crises. This ﬁnding is

consistent with Jordà et al. (2015b) researching on the importance of leverage in fostering bubbles. We

differ from Jordà et al. (2015b) in that our analysis is purely based on common movements of credit and

asset prices both in the frequency and time domain; i.e. we do not identify leveraged asset price bubbles

using selected criteria. Our framework allows for a comparison of regularities of ﬁnancial cycles in

2While Drehmann et al. (2012) base their argument on the univariate properties of indicators, they are actually the ﬁrst to
consider joint ﬂuctuations, however, by averaging ﬁnancial cycle indicators; speciﬁcally, cycles of duration of eight to 30 years
in credit, credit to GDP, and house prices for the US. The authors use this to illustrate increased duration and amplitude by
comparing the latter to short term US GDP cycles. Strohsal et al. (2015b) extract the ﬁrst principal component from the log
levels of credit and house prices for the US and UK. They analyse their interdependence of these two factors in a VAR. Rünstler
and Vlekke (2016) and Galati et al. (2016) test for similar medium term cycles in credit and house prices using a multivariate
unobserved components framework. Theses studies, however, do not identify a composite ﬁnancial cycle modelling the joint
ﬂuctuations of credit and asset prices.

4

relation to business cycles, but also across countries; both crucial for policy making.

Third, we contribute by reconciling differences of ﬁnancial cycle characteristics obtained through

the use of two alternative methodologies: frequency decompositions and standard turning points anal-

ysis. Longer duration ﬁnancial cycles have been found in studies using frequency decompositions (see

Aikman et al. (2015); Drehmann et al. (2012); Strohsal et al. (2015a); Rünstler and Vlekke (2016);

Galati et al. (2016); Verona (2016)), while more similar ﬁnancial and business cycles arise when us-

ing univariate turning point analyses (see, e.g., Claessens et al. (2011, 2012); Drehmann et al. (2012);

Hiebert et al. (2014)). Considering joint ﬂuctuations of indicators in the turning point context, ﬁnancial

cycles turn out to be longer than business cycles.

Fourth, we are the ﬁrst to contrast G-7 ﬁnancial and business cycle synchronisation.

Fifth, we propose new empirical means of endogenously determining country-speciﬁc ﬁnancial and

business cycle frequencies. With this approach, in contrast to seminal work of Drehmann et al. (2012)

and Borio (2014), distinct frequencies in ﬁnancial and business cycles are estimated rather than imposed.

Our study also contributes to research on business cycle measurement and characteristics. Applying

our method to business cycle indicators, we ﬁnd support that longer term business cycles are a phe-

nomenon for the broad set of G-7 countries; thus, supporting results by previous studies, as, e.g., Comin

and Gertler (2006) and A’Hearn and Woitek (2001). Notably, for the US, our methodology consistently

estimates the business cycle length as derived by the NBER dating committee, while also indicating

important ﬂuctuations above 8 years.

The remainder of the paper is organised as follows. Section 2 discusses the indicators that should

feed into ﬁnancial cycle measurement. Section 3 introduces a “power cohesion” methodology to extract

common cyclical movements of a set of cycle indicators and presents the characteristics of ﬁnancial and

business cycles across G-7 countries. Section 4 suggests an approach to ﬁlter common movements of

indicators in the time domain, which are then used to shed light on ﬁnancial cycle synchronisation versus

business cycle synchronisation and the prediction of past systemic banking crises and their preceding

vulnerability periods. Section 5 concludes.

2 FINANCIAL CYCLE INDICATORS, TRANSFORMATIONS, AND

STATISTICAL PROPERTIES

Much the same way as business cycles relate to recessions, ﬁnancial cycle indicators should relate to
ﬁnancial recessions, i.e., recessions that occur in tandem with banking crises.3

In contrast to other

recessions, ﬁnancial recessions occur less frequently, are deeper, and last longer. Further, ﬁnancial

recessions follow credit booms (see Jordà et al. (2013); Boissay, Collard and Smets (2016)).

In this light, credit seems to be a necessary indicator for ﬁnancial cycles. Boissay et al. (2016)

outline several empirical facts about credit, showing that it follows distinct movements, such as higher

variance and persistence around ﬁnancial recessions than other types of recessions. That is, credit

has the potential to encapsulate the build-up of imbalances in the ﬁnancial cycle presaging ﬁnancial

3Financial recessions are deﬁned in this way, for instance, by Jordà, Schularick and Taylor (2013)

5

recessions and its subsequent unwinding. Indeed, Schularick and Taylor (2012) provide evidence that

lagged credit growth predicts ﬁnancial crises well. Studies actually argue that credit can be a source

of instability and not just an ampliﬁer of shocks as described by the ﬁnancial accelerator approach (see

Bernanke (1983), Gertler (1988), Kiyotaki and Moore (1997), Bernanke, Gertler and Gilchrist (1999).

Already Minsky (1977) argued that there may be endogenous ﬁnancial instability through, among other

elements, credit, which pushes investors’ sentiment into either overoptimism or fear. Bhattacharya,

Goodhart, Tsomocos and Vardoulakis (2015) model Minsky’s hypothesis formally with the possibility

of endogenous default, with support for cycles whereby agents update their expectations during good

times and increase their leverage.

While credit may be a necessary element of ﬁnancial cycles, it is less clear whether it is sufﬁcient.

For instance, Mendoza and Terrones (2008) and Gorton and Ordoñez (2016) note that not all credit

booms lead to a ﬁnancial crisis. In this regard, asset prices could complement credit to capture ﬁnancial

cycles arguing via the so-called “balance sheet” channel. That is, one of the implications of credit market

frictions is that the state of balance sheets is an important determinant of agents’ ability to borrow and

lend (e.g., Bernanke and Gertler (1999)). In this view, changes in asset prices alter an agent’s net worth

and, e.g., through the asset’s use as collateral and its associated inﬂuence on leverage, thereby affecting

the scale of borrowing and lending. The importance of this interaction has been the centre of studies on

leverage cycles as, e.g., by Geanakopolos and Fostel (2008) and Geanakopolos (2010), as well as work

by Gromb and Vayanos (2002), Brunnermeier and Pedersen (2009) and Adrian and Shin (2010).

Our suggested set of asset price indicators supplementing credit in a ﬁnancial cycle includes house,

equity, and bond prices. The importance of real estate is, for instance, noted by Iacoviello (2005), who

introduces collateral constraints that are governed by real estate values into a monetary business cycle

model as empirics indicate that a large part of borrowing is secured by real estate (see also Campell and

Hercowitz (2009); Justiano, Primiceri and Tambalotti (2015)). Jordà, Schularick and Taylor (2015a,

2016) note that risks to ﬁnancial stability are strongly linked to real estate lending developments.

Claessens et al. (2012) and Claessens et al. (2011) provide empirical evidence that recessions marked

by equity together with house price busts tend to be deeper and longer. Jordà et al. (2015b) report

that most build-ups of systemic risk involved both equity and house prices past World War 2. Further,

corporate bond prices have been argued to be an important indicator of the soundness of the ﬁnancial

system, e.g., during the Global Financial Crisis (Gilchrist and Zakrajšek (2012). Gilchrist, Yankov and

Zakrajšek (2009) ﬁnd that an unexpected increase in bond spreads, i.e., corporate yield minus risk free

yield, cause large and persistent contractions in economic activity. Further, bond market information is

an integral component of ﬁnancial stress indices. Shocks to these indices have been shown to be highly

detrimental for the economic outlook (e.g., Hubrich and Tetlow (2015); Fink and Schüler (2015)).

Building on these studies suggesting that a joint analysis of credit and asset prices may be needed to

adequately characterise a notional ﬁnancial cycle, we opt for a narrow and broad measure of a ﬁnancial

cycle. The narrow measure bringing in credit and house prices is motivated by the close relation of

credit and real estate as, e.g., argued by Iacoviello (2005) or as evidenced in Jordà et al. (2015a, 2016).

The broad measure also including ﬁnancial asset markets is motivated by evidence that a larger set of

6

asset prices might be vital to identify emerging risks (e.g., Jordà et al. (2015b)), also on a global scale

(see Rey (2015), Miranda-Agrippino and Rey (2015), or Breitung and Eickmeier (2014)). For this we

additionally include equity and bond prices.

A standard set of indicators is selected to encapsulate a reference business cycle based on the same

approach used for identifying ﬁnancial cycles. These are output, consumption, investment, and hours

worked (see, for instance, Burnside (1998)).

Transformations

We analyse cycles in growth rates, rather than classical cycles or growth cycles (Harding and Pagan

(2005)), among others, as the spectral approach taken in this paper requires stationary processes. 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.4 Further, similar to Comin and Gertler (2006),

who research on the importance of medium and long term business cycles, we remove a nonlinear

smooth trend from our indicators, i.e., we ﬁlter growth rates by removing cycles that are longer than
200 quarters using the Christiano and Fitzgerald (2003) band-pass ﬁlter.5 The removed trend, thus,
includes cycles that are larger than 50 years.6 Further, all variables are in real terms. The exact details

on the variables are provided in Appendix A.1.

In sum, total credit, house prices, equity prices, output, consumption, investment, and hours worked

are measured in quarterly ﬁltered growth rates excluding cycles of duration longer than 50 years. Cor-

porate bond yields are transformed to reﬂect ﬁltered growth in bond prices, to be in line with the inter-

pretation of house and equity prices, by exploiting the relation: pb,t = 1/(1 + yb,t), where pb,t denotes
the price and yb,t the current yield of the respective bond at time t. As we analyse bond indices – given
that we require a long history - we do not have all information available for this transformation. Specif-

ically, we assume that all yields have been transformed to zero coupons. Further, given data limitations

for the set of countries considered, we resort to a simplifying assumption that indices are derived from

a portfolio of bonds with constant average yield to maturity.

4Note that cycle characteristics identiﬁed by Drehmann et al. (2012), Strohsal et al. (2015a), and Verona (2016) are recov-
ered from annual growth rates – however, this transformation lacks precision for identifying turning points. Schüler, Hiebert
and Peltonen (2015) contrast the implications of both year on year (yoy) and quarter-on-quarter (qoq) transformations for the
resulting spectral properties. Summarising the results, the authors 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
signiﬁcance of longer term cycles in the case of ﬁnancial indicators; however it does for the business cycle ones, i.e., trans-
formation 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.

5An exception to this is the signalling exercise of Section 4.4, for which we construct real time indices based on unﬁltered
growth rates. This is because the band pass ﬁlter suffers from an endpoint bias, leading to a biased real time estimate of the
nonlinear smooth trend.

6We are aware of the fact such pre-treatment may bias results because of leakage problems and end of sample biases of
ﬁlters. The latter should be small because of restricting only longer term cycles. In general, however, as all indicators (business
versus ﬁnancial and across countries) are treated equally, biases should be systematic and, thus, leave, relative conclusions
valid.

7

Statistical properties

The nascent literature on credit and ﬁnancial cycles indicates that the medium term component is more

relevant relative to the one in output. In this vein, we compare three summary statistics of ﬁnancial

cycle indicators with those of business cycle indicators dividing each variable’s long term cycle (2-200

quarters) into a short (32-2 quarters) and a medium and long (32-200) term frequency component. We

consider standard deviation, autocorrelation, and cross-correlation between indicators; similar to Comin
and Gertler (2006).7 For cross-correlation between indicators we use credit as the base variable because

of its prominent role as a ﬁnancial cycle indicator. Output is chosen for business cycle indicators. Comin

and Gertler (2006) use such an exercise to provide evidence of a medium/long term business cycle. By

simply extending their methodology, we can compare medium and long term components of ﬁnancial

cycle indicators with that of business cycle indicators.

Table 1: US: Descriptive statistics – real growth rates

Standard deviations
High-frequency Medium/long-frequency Medium/long-term
component 2-32

component 32-200

cycle 2-200

First-order autocorrelations

Financial cycle

Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)

Business cycle

Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)

Medium/long-term
cycle 2-200

0.98
1.70
7.96
0.89

0.82
0.66
2.07
0.37

0.67
1.08
7.69
0.72

0.78
0.61
1.92
0.36

0.70
1.23
1.91
0.51

0.26
0.26
0.76
0.06

0.76
0.81
0.05
0.66

0.31
0.33
0.48
-0.12

High-frequency
component 2-32

0.50
0.54
-0.02
0.49

0.23
0.20
0.40
-0.16

Notes: Bold numbers indicate signiﬁcance at least at the 10% level. Statistics are derived using HAC standard errors.

In case the medium and long term components of ﬁnancial cycle indicators were to be more rele-

vant, we would expect three conditions to hold. First, the variance of the medium and long frequency

component (32-200 quarters) relative to the overall variance would be larger for ﬁnancial cycle than for

business cycle indicators. Second, the persistence of ﬁnancial cycle indicators would be located in the

medium and long frequency component more than compared with business cycle indicators. Third, the

highest correlation of other indicators with credit (as an anchor variable of the ﬁnancial cycle) can be

rather attributed to medium and long frequency components when compared to highest correlation of

other indicators with output (as an anchor variable of the business cycle). Results for the US – also the

focus of Comin and Gertler (2006) – are reported in Table 1 and Table 2. The tables for the remaining

countries are in Appendix A.4.

For the narrow ﬁnancial cycle measures (credit and house prices) and with respect to the ﬁrst prop-

erty above (variance), we indeed ﬁnd evidence in case of all G-7 countries that the variance of the

medium/long-frequency component relative to the overall variance is larger for ﬁnancial cycle than for

business cycle indicators. In the case of the US, ﬁgures indicate that while for business cycle indicators

almost all variation is explained by the high-frequency component, the standard deviation of indicators

7Note that Comin and Gertler (2006) analyse growth cycles and not cycles in growth rates.

8

is even higher for the medium- and long-frequency component. The weakest evidence of this difference

is found for Germany, where the overall standard deviation for the medium and long term cycle also

is the lowest across all countries. With respect to the second property above (persistence), the results

indicate that the medium and long term cycle is by far more persistent than considering only a high-

frequency component for narrow ﬁnancial cycle indicators compared to business cycle indicators. In

the case of the US, the ﬁrst order autocorrelation increases from 0.5 to 0.76 in the case of credit and

0.54 to 0.81 for house prices. In contrast, the increase of business cycle indicators is at most from 0.2 to

0.33, for consumption. For house prices in Canada, the increase in persistence is of similar magnitude

as for output. For the third property above (cross correlation), for the narrow ﬁnancial cycle indicators,

the medium and long term cycle is more strongly correlated than the high-frequency component for

both credit and house prices. Again one exception is Germany, where adding the medium- and long-

frequency component does not alter the strength of the correlation. When extending this analysis to

also consider lead and lag of indicators, we ﬁnd that for almost all G7 countries maximum correlation is

contemporaneous; the exception is France where credit is lagging by one quarter. In contrast to ﬁnancial

cycle indicators, business cycle indicators have strong correlations with output that are largely imper-

vious to adding medium and long term cycles. Similarly, all business cycle indicators share highest

co-movement contemporaneously. In the spirit of Comin and Gertler (2006), business cycle indicators,

as well, share some important medium- and long-term cycles – in this case with credit, as their cross

correlation also increases for the medium/long term cycle. However, a lead-lag relation appears to be

present in such a circumstance.

Table 2: US: Maximum absolute correlation with credit and output – leading or
lagging up to 4 quarters

Financial cycle

Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)

Business cycle

Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)

Credit

Output

Medium/long-term
cycle 2-200

High-frequency Medium/long-term
component 2-32

cycle 2-200

High-frequency
component 2-32

-
0.47
0.19
0.40

0.41
0.55
0.43
0.16

(-)
(0)
(-4)
(0)

(-2)
(0)
(-2)
(-4)

-
0.35
0.18
0.48

0.34
0.50
0.44
0.19

(-)
(0)
(-3)
(0)

(-2)
(0)
(0)
(-3)

0.41
0.40
0.34
0.41

-
0.66
0.77
0.43

(2)
(-1)
(-1)
(-2)

(-)
(0)
(0)
(0)

0.34
0.37
0.31
0.41

-
0.62
0.75
0.44

(2)
(-1)
(-1)
(-2)

(-)
(0)
(0)
(0)

Notes: Numbers in brackets denote lead (+) or lag (-) of credit or output to respective variable.

These results for narrow ﬁnancial cycles to some extent carry over when considering a broad ﬁnan-

cial cycle, i.e., also including both equity and bond prices. For equity prices, only a small percentage

of variation located in the medium- and long-frequency component compared with shorter frequencies.

At the same time, this proportion of variance is by far the largest compared to all other indicators – at

1.91 for the US. The characteristics of persistence in equity prices is similar to that of business cycle

indicators. In the case of the US, this is particularly clear, with no signiﬁcant ﬁrst order autocorrelation

9

in either the high-frequency component or the medium- and long-term cycle. The cross-correlation with

credit is mostly located in the high-frequency component. Interestingly, however, equity prices, seem

to be leading credit by several quarters. In that respect, for France and Italy the highest correlation such

a leading property for equity prices appears only relevant for medium- and long-term cycles, not for the

high-frequency component. Bond prices, in contrast share similar features with credit and house prices.

That is, an important share of variance is located at the medium- and long-frequency component while

cycles in the medium- and long-frequency band are highly persistent. Results, however, are rather mixed

about the cross-correlation with credit. Both the medium term cycle and the high frequency component

show highest correlation, which, nonetheless, is in most cases contemporaneous.

In sum, credit and house prices (and also bond prices, to some extent) share characteristics (in their

variance, persistence and correlations) which are distinct from business cycle indicators. For these

indicators, the highest correlation or cohesion is contemporaneous, similar to the analogous ﬁnding

for business cycle indicators. Equity prices represent an exception to these regularities among ﬁnancial

cycle indicators. While equity prices are marked by highest variance in the medium- and long-frequency

component, this is of relatively low importance in capturing overall variance for this volatile series. At

the same time, equity prices appear to lead credit. Business cycle indicators also seem to be related to

credit at medium- and long-term frequencies, however, with no systematic lead-lag relation across our

set of countries.

In light of these observations, there is evidence that especially the narrow set of ﬁnancial cycle

indicators, i.e., credit and house prices, have important ﬂuctuations at cycle lengths between 8 and 50

years. Cohesion of indicators seems to be strongest contemporaneously, but not exclusively. In the

next section, we offer a methodology to arrive at more precise estimates of exact frequencies that are

important to explain their coherence, and contrast these results with business cycle indicators.

3 FINANCIAL CYCLE FREQUENCIES

This section deepens the investigation of whether ﬁnancial cycle indicators share co-movement at dif-

ferent cycle lengths than business cycle indicators. First, a methodology for this purpose is outlined and

second, results are reported. Third, a robustness exercise using turning points is presented.

3.1 Methodology: Power Cohesion – discovering important cycle frequencies across a set

of indicators

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

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 × M ). Further, t = 1, . . . , T and M ≥ 2 reﬂect the time dimension and number of variables

1, . . . , X (cid:48)

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

10

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)

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.

Proposition 1. PCoh discards phase shifts between variables.

Proposition 2. The support of PCoh is normalised and is between 0 and 1 when integrated from −π to

π.

Proposition 3. PCoh indicates the contribution of different cycle lengths to the overall co-variance

between indicators and thus differs importantly to the more common measure of squared coherency.

For the relevant proofs and details on empirical issues please refer Appendix A.2. Note that Propo-

sition 1 takes into account lead and lag relations between indicators, as suggested by the estimates

presented in the preceding section of this paper.

3.2 Cross-spectral densities

Cross-spectral densities, i.e., sxixj (ω), are one of the building blocks of our measure “Power Cohesion”
(PCoh). While the amplitude of PCoh for different sets of indicators cannot be directly related to each

other, for cross-spectral densities this is reasonable. In Figure 1, we show the absolute cross-spectral

densities of the US ﬁnancial and business cycle indicators, i.e., measuring covariances in and out of

phase (see Appendix A.2 for more details). The other country cases are depicted in Appendix A.5. On

the x-axis the graphs indicate the cycle length; from 1.25 years to 50 years. We mark the region of

frequencies that are commonly attributed to the business cycle (2-8 years) and the range of frequencies

from 8 to 20 years that we ﬁnd to be important for ﬁnancial cycles.

In the case of the US, it is evident that ﬁnancial cycle indicators (Figure 1a) share more important

cyclical variance at medium term cycles, indicated by the magnitude of lines, while all most important

common cycle for business cycle indicators (Figure 1b (b)) are within the short term region of cycle

length. Common cycles of house and equity prices (∆ph/∆pe, pink line) are most pronounced just
below 20 and 8 years. Common cycles of credit and equity prices (∆cr/∆pe, green line) are most

pronounced for all medium term cycle frequencies with small spikes at the regions of peaks in house

and equity prices, while credit and house prices (∆cr/∆ph, blue line) share most important frequencies
towards 20 years. Equity and bond prices (∆pe/∆pb, black line), similarly as credit and house prices
have important cycles around 20 years, while, however, marginally more important cyclical variance is

within the short term region. House and bond prices (∆ph/∆pb, turquoise line), have most important
cycle above 8 years and credit with bond prices (∆cr/∆pb, red line) have important both medium as
well short term frequencies, however skewed towards the longer business cycles. For business cycles

indicators the picture is very clear, all pairs of indicators peak around the same frequency region which

is below but close to eight years. Further, business cycle indicators do not have relatively important

11

(a) Financial cycle indicators

(b) Business cycle indicators

Figure 1: US: Absolute cross-spectra
Notes: This panel shows the absolute cross-spectra of the ﬁnancial and business cycle indicators. The x-axis measures the frequencies of
cycles from 1.25 - 50 years. The blue area depicts business cycle frequencies, i.e., cycles with durations of 2-8 years and the purple area
marks frequencies important for ﬁnancial cycles (8-20 years). ∆cr refers to percentage changes in total credit, ∆ph to percentage changes in
house prices, ∆pe to percentage changes in equity prices, ∆pb to percent changes in bond prices, ∆q to percentage changes in GDP, ∆co to
percentage changes in consumption, ∆i to percentage changes in investment, and ∆h percentage changes in hours worked.

cycles located in the medium term region, when compared to ﬁnancial cycle indicators. While these

results seem to hold for most other G-7 countries, there are also exceptional cases. Germany and

the UK, in particular, depart from other G-7 countries in that they exhibit more frequency masses of

important cycles located below but close to 8 years. The agreement of cycle length across indicator

pairs is stronger for Germany, where even common credit and house price cycles are just below 8 years.

Further, business cycles for Germany and Canada appear to be atypically long and located in the medium

term region.

Concerning the amplitude of cycles in the US, it is evident that ﬁnancial cycles are more volatile on

average relative to business cycles. The peaks of the different ﬁnancial cycle cross-spectral densities are

well above the peaks of the cross-spectral densities of business cycle indicators, except for the cases of

house and bond prices as well as credit and bond prices, which are still above most of the cross-spectral

densities of business cycle indicators. Looking beyond the US at other G-7 countries, we ﬁnd that

Germany’s ﬁnancial cycle has the lowest amplitude – contrasting with strong amplitude in both Italy

and the UK.

3.3 Power Cohesion for G7 countries: Financial cycle frequencies

This section presents our measure PCoh, for the narrow (∆cr, ∆ph) and broad (narrow + ∆pe, ∆pb)
ﬁnancial cycle as well as the business cycle. Figure 2 depicts the case of the US. The remaining country

cases are presented in Appendix A.5. Again, graphs indicate on the x-axis the cycle length from 1.25 to

50 years. The region commonly associated with business cycle frequencies is denoted in blue shading,

while in the region in purple represents medium term frequencies.

12

Years2082|ˆsxixj|024681012Δcr/ΔphΔcr/ΔpeΔcr/ΔpbΔph/ΔpeΔph/ΔpbΔpe/ΔpbYears2082|ˆsxixj|00.511.522.5Δq/ΔcoΔq/ΔiΔq/ΔhΔco/ΔiΔco/ΔhΔi/ΔhTo benchmark PCoh as a new approach to measure important cycles pertinent to a set of indicators,

we reference the result for US business cycle indicators to recessions as published by the NBER dating

committee, which implicitly demarcates business cycle frequencies. To this end, the peak of PCoh for

the US business cycle is located at a cycle length of 5.7 years, identical in length to the reference NBER

statistic (average business cycle duration from 1945 to 2009) also at 5.7 years (measuring peak to peak).

Figure 2: US: Power Cohesion
Notes: This graph shows the measure power cohesion of the narrow (black lines) and broad ﬁnancial cycle (blue lines) as well as the business
cycle (red lines). Broad refers to the inclusion of all indicators, i.e., credit, house, equity, and bond prices, whereas narrow is deﬁned by
house prices and credit only. The dashed lines indicate the 68% bootstrapped conﬁdence intervals as discussed in Appendix A.3. The x-axis
measures the frequencies of cycles from 1.25 to 50 years. The blue area depicts business cycle frequencies, i.e., cycles with durations of 2-8
years and the purple area (8-20 years) marks frequencies most important for ﬁnancial cycles.

For the US, both the broad and narrow measure of ﬁnancial cycles, clearly have most mass located at

medium term frequencies, while business cycles just below these cycle lengths – conﬁrming the exercise

conducted in the previous section of this paper. While the broad and narrow deﬁnition of ﬁnancial cycles

share similar important cycle frequencies, the broad measure envelops relatively more frequency mass

amid medium and short term frequencies. That said, most cohesion of ﬁnancial cycle indicators is

located in the frequency range within 20 to 8 years. In this way, ﬁnancial cycle cohesion is above that

of business cycles. While ﬁnancial cycle indicators do not exhibit strong cohesion for cycles between 2

and 8 years, business cycle indicators have higher cohesion in this range.

Highest density regions across G-7 countries

Across G7 countries, these ﬁgures are conveniently summarised by the highest density chart that depicts

25% of most important frequencies between 1.25 and 50 years shown in Figure 3). For the ﬁnancial

cycle, we show the narrow (blue) and broad (black) measure, as well as the narrow plus equity prices

(turquoise) on the one and bond prices (purple) on the other hand for robustness. Coloured bars indicate

at which cycle lengths 25% of most important cohesion between indicators is located and white dashes

indicate the peak of PCoh that is the most important cycle.

Comparing ﬁnancial cycle frequencies across countries, we ﬁnd that for the narrow set of indicators

13

Years2082PCoh00.511.522.533.5USBroad financial cycleNarrow financial cycleBusiness cycleFigure 3: Highest density chart of power cohesion
Notes: This graph depicts the 25% highest density region (see Hyndman (1996)). Broad refers to the inclusion of all indicators, i.e., credit,
house, equity, and bond prices, whereas narrow is deﬁned by house prices and credit only. The x-axis measures the frequencies of cycles from
1.25 to 50 years. The blue area depicts business cycle frequencies, i.e., cycles with durations of 2-8 years and the purple area (8-20 years)
marks frequencies most important for ﬁnancial cycles.

almost all G-7 countries have most important cycles close to 20 years. Germany remains a notable

exception, while both the UK and Canada exhibit important broad cycles at business cycle frequencies.

Further robustness checks suggest that equity and bond prices lower cycle length for these countries in

contrast to other G-7 counterparts.

Comparing ﬁnancial and business cycle within countries the following can be noticed: First, all

G-7 countries ﬁnancial cycles are considerably longer than business cycles with the only exception

of Germany. That said, business cycles tend to embed multiple peaks – with a meaningful medium-

term component to business cycles for Canada, Germany, and Japan. For Canada and Germany, this

may relate to a relative lack of systemic banking crises, while for Japan, a distinct history including a

substantial cycle build-up followed by so-called “lost decades” during a lengthy correction phase.

Peak of power cohesion and frequency window across G-7 countries

Table 3 shows the peak of PCoh for the narrow and broad measure of the ﬁnancial cycle, as well as the

business cycle indicators. In addition, we report a frequency window spanned around that peak deﬁned

by a maximum and minimum cycle length in years. This frequency window is deﬁned to capture 67%

of the densest area around the frequency peak of the function.

Concerning business cycles, the US business cycle length as measured by the peak of PCoh coincides

with the one of the NBER committee. Moving to a 67% window, frequencies from 2.6 to 14.5 years

are captured for the US, which implies that some more longer cycles should be considered relative to

standard ﬁndings, i.e., cutting of frequencies above 8 years. The average peak across other G-7 countries

is a business cycle of length 8.9 years, which is heavily skewed by the atypical results of Japan – with a

14

Broad financial cycleNarrow financial cycleNarrow plus equity pricesNarrow plus bond pricesBusiness cycleCA DE FR IT JP UK US 20 8 2 Years Table 3: Financial and business cycle frequencies

Narrow
ﬁnancial cycle

Broad
ﬁnancial cycle

Business cycle

Country

max.

peak min. max.

peak min. max.

peak min.

Canada
Germany
France
Italy
Japan
UK
US

Avg.
CV

50.0
15.4
36.0
45.6
50.0
25.3
29.7

36.0
0.37

14.1
7.4
15.0
15.9
23.0
16.4
17.5

15.6
0.30

4.0
2.3
6.5
3.9
5.2
5.0
7.0

4.8
0.33

50.0
45.6
50.0
50.0
50.0
50.0
29.7

46.5
0.16

7.3
8.5
15.4
16.9
18.8
16.4
15.0

14.0
0.31

2.7
3.0
4.0
3.3
4.0
4.4
4.8

3.7
0.20

13.7
18.8
50.0
38.7
50.0
26.6
14.5

30.3
0.52

9.8
9.1
6.7
3.7
22.0
5.4
5.7

8.9
0.69

2.1
2.7
2.5
2.8
2.3
3.1
2.6

2.6
0.12

Notes: The table shows the peak, maximum (max.), and minimum (min.) cycle length in
years. The frequency range, deﬁned by the maximum and minimum, capture 67% of the
densest area around the peak. Broad refers to the inclusion of all indicators, i.e., credit,
house, equity, and bond prices, whereas narrow is deﬁned by house prices and credit only.
Avg. denotes the average and CV the coefﬁcient of variation that relates the standard
deviation to the mean.

minimum window of 2.6 years, and 30.3 as a maximum.

Turning to the narrow ﬁnancial cycle, it is about 17.5 years long for the US and the actual frequency

window is close the one described by Drehmann et al. (2012), i.e., 29.7 to 7 relative to 30 to 8 years.

However, across other G-7 countries, the shortest cycles included range around 4.8 years and maximum

36 years. Outliers with respect to cycle length include Germany, which has a very short narrow ﬁnancial

cycle (even shorter than the business cycle), and Japan, which has a very long cycle, exceeding the 20

year range.

With respect to the broad ﬁnancial cycle, the area around the peak is generally less dense, so that

on average the frequency window covers longer as well as shorter cycles on average of 3.7 years.

The average cycle length is 14 years, and thus slightly shorter than the narrow ﬁnancial cycle. While

the peaks for the narrow and ﬁnancial cycle can be argued to be similar for most countries, Canada

represents an exception, with the average cycle length reducing from 14.1 (narrow) to 7.3 years.

The coefﬁcient of variation indicates relative variation, so we can compare the spread of the peaks

of the different cycles. Results indicate that differences in business cycle length are actually stronger

than in ﬁnancial cycle length; at 0.69 versus 0.3 and 0.31.

3.4 Robustness: Reference cycles through turning points

This robustness exercise aims at using another methodology to validate a comovement in ﬁnancial indi-

cators yielding longer cycles than that of business cycle indicators. To this end, we apply the methods

of turning points as suggested by Harding and Pagan (2002), that extends the methodology Bry and

Boschan (1971) to quarterly data and has seen many applications in the business cycle literature. On

the one hand, an advantage of the turning points algorithm over the spectral approach is its robustness

with respect to non-linearities and structural breaks in the data. On the other hand, a disadvantage lies

in its limited mathematical or economic grounding – including notably that censoring rules are chosen

arbitrarily. Further, the method is skewed towards shorter term frequencies as it does not decompose

15

time series into individual cyclical components but considers cycles of all lengths jointly.

One means of overcoming the problem of bias toward shorter frequencies is to consider the joint

information inherent across a set of indicators. With this aim in mind, we construct reference cycles
using the distribution of turning points of individual indicators.8 We rely on the approaches by Harding
and Pagan (2006) and Canova and Schlaepfer (2015).9

In more detail, the methodology adds a small additional number of censoring rules to all turning
points.10 It contains the following steps:11 First, turning points of individual indicators are located via
the standard methods established in the literature.12 Second, from each series of turning points, for every

indicator we construct the distance in quarters to the nearest peak and the distance to the nearest trough.

Third, the series for distance to peak is aggregated for each period t across every indicator. The series

for distance to trough is aggregated similarly. As aggregation method, we choose the median value as

recommended by Harding and Pagan (2006). Fourth, local minima are considered in the aggregated

series as candidate peaks and troughs for a reference cycle.

Results

The exercise supports the general notion that ﬁnancial cycles, i.e. common ﬂuctuations in credit and

house prices or credit, house, equity, and bond prices, are longer thank business cycles on average across

countries, while some country cycles differ in length from the one identiﬁed by power cohesion (see

Table 4).

Reference cycles as identiﬁed with this modiﬁed turning points methodology for the narrow set of in-

dicators (credit and house prices) are on average 13 years, not dissimilar to the cycle lasting around 15.6

years on the basis of power cohesion. Highest deviations between the two methodological approaches

are found for Italy (reference cycle about 8 years shorter), Canada (6 years shorter), and Germany (4.5

years longer), while the turning points approach constructing reference cycles does not yield results for

France as there are ties in the location of the turning points of the reference cycle, i.e., house and credit
cycles indicate opposite phases.13 US, UK, and Japan are all found to be slightly shorter, however still

quite close to the length reported in the main exercise.

The broad ﬁnancial cycle indicators lead to a reference cycle that is on average 9.23 years compared

8This is, in many ways, the conceptual analogue of our approach of PCoh based on the frequency comovement of indicators,
and in particular also has the potential to allow for phase shifts between variables a local minima are considered and not global.
9Next to constructing a reference cycle from indicators, another option is to aggregate information ﬁrst and then locate
turning points, which is more similar to what is done by the NBER and the CEPR Business Cycle Dating Committees as
indicated by Canova and Schlaepfer (2015).

10The transformation of variables follows the usual one in the literature, i.e., we use indicators in log levels, thereby not

taking a stance of trend.

a

be

brieﬂy:

Let xi,t

11We use the code as kindly provided by Canova and Schlaepfer (2015). For more details, please refer to the indicated paper.
12Summarising
∈
max{xi,t−2; xi,t−1; xi,t; xi,t+1; xi,t+2} and a candidate trough if xi,t ∈ min{xi,t−2; xi,t−1; xi,t; xi,t+1; xi,t+2}. A
candidate is conﬁrmed in case the following conditions are met:
In case of two
subsequent peaks, for instance, the lower one is eliminated. (ii) A peak must be higher than the previous trough and a trough
must be lower than the previous peak. (iii) 5 quarters is the minimum length of a cycle, i.e., peak to peak or trough to trough.
(iv) 2 quarters is the minimum phases of a cycle. A phase is peak to trough or trough to peak. (v) Turning points at the ﬁrst or
last two quarters are excluded. (vi) Peaks at the beginning or the end are excluded in case of being lower than the initial or last
values. Similarly, troughs at the beginning or the end are excluded in case of being higher than the initial or last values.

(i) Peaks and troughs must alternate.

process xi

stochastic

candidate

if xi,t

peak

the

of

13This is a problem that is more likely to occur using only two indicators and the likelihood of course decreasing the more

indicators in use.

16

Table 4: Reference cycles length through turning points

Narrow
ﬁnancial cycle

Broad
ﬁnancial cycle

Business cycle

Canada
Germany
France
Italy
Japan
UK
US

Avg.

8.00
11.90
n.a.
7.60
20.00
13.83
16.88

13.03

10.00
4.93
8.66
9.00
9.19
10.56
12.25

9.23

11.92
7.55
4.73
6.46
3.17
6.29
8.64

6.96

Notes: Table depict length of reference cycles in years for nar-
row (credit and house prices) and broad (narrow + equity and bond
prices) set of ﬁnancial cycle indicators as well as for the business cy-
cle indicators (output, consumption, investment, and hours worked).
Avg. denotes the mean of column and n.a. denotes not available, due
to missing coincident turning points in the sample.

to 14 years when applying power cohesion. For all countries but CA reference cycles are found to be

shorter than the ones found with PCoh, but Canada, for which the reference cycle length is 10 years as

opposed to 7.3. Differences are most prominent for Japan (9.19 from 18.8) and Italy (9.19 from 16.9).

They are weakest for the US (12.25 from 15) and Canada.

Reference cycle from business cycle indicators are very similar to the one measured by PCoh. Only

in the case of Japan the reference cycle indicates an average cycle length of 3.17 years (from 22.0

years), which however is also a highest density region of PCoh but not the most important one. For the

US the length is 8.64. The identiﬁed set of turning points for the US misses interestingly the recession

subsequent to the bursting of the dot-com bubble explaining the longer duration.

In sum, the construction of reference cycle based on a set of turning points of individual indicators

leads to a similar picture than our introduced approach. Whereas previous results based only on turning

points of individual indicators, e.g. Claessens et al. (2011, 2012) and Hiebert et al. (2014), cannot

reconcile evidence on medium term ﬁnancial cycles, the results suggests that this is possible when

considering credit and asset prices jointly.

4 COHERENT FINANCIAL CYCLES ACROSS TIME

In this section, we transfer the concept of co-movement of indicators from the frequency domain to

the time domain. In this respect we present a methodology for combining indicators into a composite

ﬁnancial cycle index. Further, we discuss both the use of the identiﬁed frequency windows of the

previous section as well as a weighted moving average to ﬁlter the composite indices. Based on the

latter, we analyse ﬁnancial cycle synchronisation across countries and research whether the common

movement can be used both as a coincident as well as an early warning indicator of systemic banking

crises.

17

4.1 Methodology: Time-varying aggregation of standardised indicators and ﬁltering

Time-varying aggregation of standardised indicators

The collation of the ﬁltered growth rates of indicators into a composite ﬁnancial cycle index requires

two steps. First, we standardise variables given different measurement units, but also in light of dis-

similar variances and equilibrium growth rates. Second, we aggregate these standardised indicators into

composite ﬁnancial and business cycle series. In keeping with the nomenclature of the previous section,

we distinguish between a narrow composite ﬁnancial cycle (consisting of credit and house prices) and a

broad measure (combining credit, house, equity, and bond prices). For these representations, as well as

analogous measures for the business cycle, we construct time-varying aggregation weights that exploit

changing correlation structures between variables. Our approach is closely related to the methodol-

ogy followed by Holló, Kremer and Lo Duca (2012) for constructing an indicator of systemic ﬁnancial
stress.14 Our approach is speciﬁcally suited for modelling cyclical ﬂuctuations, while Holló et al. (2012)

capture spikes in systemic risk.

More speciﬁcally, we transform respective underlying cycle indicators using their empirical distri-

bution function, i.e., each value of a single indicator is mapped into a unit free ordinal scale in (0,1].

Let (xi,[1], xi,[2], . . . , xi,[T ]) denote the ordered sample of variable xi,t. The transformed indicators are
derived by

yi,t = Fi,T (xi,t) =




r
T


1

for xi,[r] ≤ xi,t < xi,[r+1],

r = 1, 2, . . . , T − 1

(3)

for xi,t ≥ xi,[T ],

where Fi,T denotes the empirical cdf.

These standardised indicators are then taken to construct synthetic cycles by linearly combining

these using time-varying weights that exploit positive time-varying correlations between indicator pairs.

Speciﬁcally, let Yt = (y1,t, . . . , yM,t) and ι be a vector of ones of dimension M × 1. 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 a matrix of time-varying cross-correlations that is based on exponentially-weighted
moving average processes, i.e., σij,t = λσij,t−1 + (1 − λ)(yi,t − 0.5)(yj,t − 0.5), where yi,t is centered
using the median and λ represents the decay factor.15 Due to the aggregation method ζt ∈ (0, 1] as
well.16 ζt is then called the unﬁltered composite indicator.17

14One alternative approach for aggregating common information contained in several variables is through principal compo-
nent 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. Second,
real-time updating is an issue in that new data points might alter the selection of indicators most relevant for common ﬂuctu-
ations. Indeed, a principal component analysis is static by deﬁnition and thus does not allow for capturing changing trends in
the interdependence between ﬁnancial indicators.

15Time-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 negligible at a faster rate. Further, covariances are initialised using the ﬁrst 8 quarters
of observations for each variable.

16For expositional purposes, we re-map ζt into (0,1] using equation 3. As the case of all four indicators being close to their

historical max- or minima is unlikely, the amplitude of the not yet re-mapped indicator ζt is dampened towards the median.

17Real time updating of ζt (as, e.g., done in Section 4.4.1) is done by applying Equation (3) recursively over expanding

18

While the diagonal elements of Ct are one, the off-diagonal elements, cij,t with i (cid:54)= j, are restricted

by

cij,t =

ρij,t = σij,t/(

√





0

σii,tσjj,t)

if σij,t ≥ 0

.

if σij,t < 0

(4)

That is, our aggregation scheme emphasises positively related or alike movements. While all series

enter the ﬁnal index by construction, it implies that movements of positively related series are empha-
sised.18 In capturing cyclical swings to construct a macroprudential notion of the cycle, we emphasise

directional developments of a systemic nature, or put differently, movements of a set of indicators that

are in a similar direction, i.e., indicators that are positively correlated. This is in line with our aim to

capture the build-up of imbalances across different variables.

Filtering

As the signal obtained from the combination of quarterly standardised growth rates is volatile, we ﬁlter

this composite ﬁnancial index, in a ﬁnal step, using our country-speciﬁc frequency bands that are based

on PCoh (see Table 3). The country-speciﬁc frequency bands are employed as an input into the band

pass ﬁlter proposed by Christiano and Fitzgerald (2003) that allows to specify the exact frequency band

of interest.

4.2 Composite cycles

Figure 4 depicts composite ﬁnancial and business cycle indices for the US in deviations from historical

median growth. It is particularly noteworthy that mere aggregation produces a strong cyclical impetus,

from which inherent movements can be further emphasised by means of ﬁltering (see Figure 4 (a)).

This, in turn, suggests that high frequency noise surrounding certain ﬁnancial asset prices, such as equity

prices, are effectively dampened as part of the aggregation process. The right panel complements this

information, showing both the narrow and broad composite ﬁnancial cycle as well the business cycle.

It is important to keep in mind that we construct cycles in growth rates. However, there is a close

correspondence to growth cycles or gap measures given our quarter-on-quarter differencing. That is, a

peak is reached when the composite indices pass from above 0.5 to below; a through when from below

0.5 to above.

A divergence of US ﬁnancial and business cycles during upswing phases (growth rates above 0.5),

seems to precede systemic banking cries. Speciﬁcally, Laeven and Valencia (2012) deﬁne two US

systemic banking crises for our sample period, i.e., the savings and loans crises in 1988 (borderline

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

18To 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.

19

case) and the global ﬁnancial crises in 2007. Before both crises a divergence of ﬁnancial (both broad

and narrow) and business cycle is visible. Or put differently, the upswing phases of the ﬁnancial cycles

preceding crises are especially long.

Further, recovery periods are longer for both ﬁnancial cycles than for the business cycle.

Nonetheless, there is an apparent co-movement between the two cycles, which is both in line with

our analysis of statistical properties as well with the literature emphasising a medium term link between

ﬁnancial and business cycles (see Rünstler and Vlekke (2016)) or the importance of ﬁnancial cycle

indicators’ downturns in shaping recessionary phases (see Claessens et al. (2012)). These results are

broadly consistent with the ﬁndings for the remaining country composite cycles (see Appendix A.6).

Interestingly the composite ﬁnancial cycles of Germany and Japan follow very distinct movements

around the last global ﬁnancial crises. Further, for UK is seems that ﬁnancial and business cycles have

been very similar until a peak located around 1990.

(a) Filtered and unﬁltered ﬁnancial cycle, broad

(b) Filtered composite cycle indices

Figure 4: US’ composite cycles
Notes: This panel shows the US composite ﬁnancial and business cycles in standardised growth rates, where 0.5 denotes the historical median
after removing a nonlinear trend; 0 is the smallest and 1 the largest growth rate observed in a country’s history. A crossing of 0.5 from above
can be interpreted as locating the peak of a hypothetical gap measure, while from below as reﬂecting the trough. Left graph depicts the broad
composite ﬁnancial cycle (ﬁltered and unﬁltered) combining information from credit, house prices, equity prices and bond prices. Right graph
shows the ﬁltered ﬁnancial (narrow and broad) and business cycles. Filtering is done using the Christiano and Fitzgerald (2003) band-pass
ﬁlter employing country speciﬁc frequency windows as described in Table 3. Aggregation of standardised indicators is done using linear
averaging in case of the narrow ﬁnancial cycle and using time-varying weights that emphasise directional movements between indicators for
the broad ﬁnancial cycle. See Section 4.1 for further details. Grey area indicates NBER recession dates.

4.3

Synchronisation of ﬁnancial and business cycles

Next we consider how G-7 ﬁnancial (broad and narrow) and business cycles relate to the respective

country cycles. We construct G-7 cycles as the ﬁrst principal component of the respective country cycles

(see Figure 5 (a)). In case of the ﬁnancial cycles (broad) a ﬁrst principal component summarises 54.2%

of the common contemporaneous variation; in case of the ﬁnancial cycle (narrow) 46.3% and in case of
the business cycle 52.6%.19 The broad and narrow G-7 ﬁnancial cycle seem to be strongly correlated,

while the G-7 business cycle less. The broad and the narrow measure are correlated with a coefﬁcient of

0.74. The business cycle is correlated with a coefﬁcient of 0.68 with the broad and 0.47 with the narrow

ﬁnancial cycle. In this context, Breitung and Eickmeier (2014) ﬁnd evidence of a global factor affecting

19The second principal components only capture 18.4%, 16.8%, and 16.47% respectively.

20

0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (broad), unfiltered Financial cycle (broad)YearDeviation from historical median growth0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleDeviation from historical median growthYearboth business and ﬁnancial cycles, while there is still an important ﬁnancial factor independent from

the macro factors affecting ﬁnancial variables. Note that similar to the US ﬁnancial cycle, we observe

phases of coupling and de-coupling of ﬁnancial and business cycles. Speciﬁcally, there is one phase

during which ﬁnancial cycles in their upswing phase (above 0.5) decouple from business cycles. This

is the period that leads into the global ﬁnancial crisis that had severe effects on all G-7 countries, but

Canada.

In the right panel of Figure 5 we relate the G-7 cycles to their respective country cycles, that is for

instance, G-7 ﬁnancial cycle (broad) with the ﬁnancial cycle (broad) of France. At least three results are

worth emphasising. First, while ﬁnancial cycles (broad and narrow) seem to strongly relate to a group

of countries and not so strongly to another, business cycles are rather homogeneously related across

G-7 countries. Speciﬁcally, the broad measure of ﬁnancial cycles is closely related to France (0.85),

UK (0.84), and the US (0.80), but also Canada (0.73) and Italy (0.72). It is less related to Germany

and Japan (0.62 and 0.53). Results are even more heterogeneous when considering the narrow measure.

Related are France (0.91), UK (0.80), Canada (0.77), and Italy (0.74). Less related are US (0.61),

Germany (0.43), and Japan (0.27). The weak relation of Germany and Japan to a common component

might be partly related to their distinct development both in the housing and credit market in recent

years. These are the only countries where house prices have been declining alongside stagnated or

declining residential investment at least until 2009 (see André (2010); Knoll et al. (forthcoming)). In

light with our argument that joint movements in credit in asset prices matter, it is also Germany and

Japan that do not undergo a credit boom (see Hume and Sentance (2009)). In contrast to heterogeneous

ﬁnancial cycles linkages, business cycles relate homogeneously between a correlation of 0.81 and 0.66.

The strongest link to the common component shares Germany while the weakest Canada and the US

(both 0.66), which however is still elevated compared to the results of ﬁnancial cycles. Second, ﬁnancial

assets (equity and bond prices) are an important link for ﬁnancial cycles across countries. In general,

total interlinkage is stronger among the G-7 countries when considering a broader class of assets in line

with the studies of Rey (2015) and Breitung and Eickmeier (2014). Explanations entail for example

that credit and house prices are rather a domestic component. For instance, houses are not tradable and

underly strong country-speciﬁc regulations, also with respect to ﬁnancing. Third, while Germany and

Japan have the weakest links with the G-7 ﬁnancial cycles, i.e., broad and narrow, their business cycles

rank among the most linked.

In sum, we ﬁnd that business cycle relations are strong and homogeneous across G-7 countries, while

ﬁnancial cycle synchronisation is rather heterogeneous. Germany and Japan are the least linked. In line

with previous studies, we ﬁnd that ﬁnancial asset prices account for strong international linkages.

4.4 Coincident and early warning indicator of systemic banking crises

To validate the coherent ﬁnancial cycles, we conduct a signalling exercise testing their performance

both as coincident as well as early warning indicators of systemic banking crises. We compare their

performance to the indicators and the credit-to-GDP gap. In the following we lay out the methodology

for conducting our signalling exercise and present the results subsequently.

21

(a) G-7 ﬁnancial (narrow and broad) and business
cycles

(b) Correlation of respective G-7 with respective
country cycles

Figure 5: G-7 cycles and correlation with country cycles
Notes: The left panel depicts the ﬁrst principal component of the countries’ ﬁnancial and business cycles. The right panel shows the correlation
of country ﬁnancial (narrow and broad) and business cycles with the respective ﬁrst principal components. Countries are ordered by highest
correlation of ﬁnancial cycles (broad) with the G-7 ﬁnancial cycle (broad) principal component.

4.4.1 Methodology: Pooled logit and real time composite cycles

The signalling approach is based on the predicted probabilities of a logit model estimated on a pooled

data set to explain the start as well as a one to four quarters ahead vulnerability horizon prior to systemic

banking crises as deﬁned by Laeven and Valencia (2012). Speciﬁcally, we use the quarterly starting

dates of systemic banking. To this end we code two dummy variables (˜ylt for l ∈ {1, 2}), each taking a
value of one at the pre-speciﬁed event and zero otherwise.20

We assess the signalling properties of indicator(s) ( ˜Xt) using both a pseudo-out-of- and an in-sample
setup, whereas we put more emphasis on the former analysis as it mirrors more closely the decisions

faced by policy makers in real time.

The pseudo-out-of-sample exercise predicts the one quarter ahead probabilities using the lagged

relation

˜ylt = φ0 +

5
(cid:88)

k=1

φk ˜X (cid:48)

t−k + εt,

(5)

where φ0 is the intercept, φk a vector of coefﬁcients, and εt the error term. We use ﬁve lags in
accordance with the study by Schularick and Taylor (2012). Such setup accounts on the one hand

for a publication lag of one quarter of economic aggregates and on the other hand for the persistence

of indicators. We estimate the model on data from 1980Q1 until 1999Q4 – using the period prior

1980Q1 to initialise the standardisation of indicators (see Equation (3)) – and conduct the pseudo-out-

of-sample exercise on an expanding sample for the period thereafter. For each sample (1,. . . , t) we

determine the optimal signalling threshold using the predicted probabilities up to period t. Following,

we evaluate whether the one quarter ahead out-of-sample prediction, i.e., for t + 1, breaches the optimal

threshold that has been derived for information up to time period t. The threshold value is optimally

determined by minimising a loss function that gives equal importance to avoiding Type I (missing

20We include the US 1988 crisis which is described as a borderline case by Laeven and Valencia (2012) and use Q1 as its

starting date.

22

19751980198519901995200020052010G-7 financial cycle (narrow)G-7 financial cycle (broad)G-7 business cycleDeviation from historical trend growthYear00.10.20.30.40.50.60.70.80.91FRUKUSCAITDEJPFinancial cycle (narrow)Financial cycle (broad)Business cyclecrisis or vulnerability period) and II (false alarms) errors, i.e., L = Quarters no signal

Quarters crisis + Quarters signal
Quarters no crisis .
In this manner, we collect the true positive (TP), false positive (FP), true negative (TN), and false

negative (FN) rates for the entire out-of-sample period. Using these we derive the Type I (TI) and II
(TII) errors, the relative usefulness (U r), the noise-to-signal ratio (NtS), and the area under the curve

(AUC). Relative usefulness is deﬁned as (0.5 − L)/0.5 and measures the relative gain to discarding

the indicator(s) (see Alessi and Detken (2011)). The noise-to-signal ratio is captured by TII/(1−TI),

relating two ratios: the ratio of bad signals to all quarters without crisis (noise) to the ratio of good

signals to all quarters with crisis (signal) (see Kaminsky, Lizondo and Reinhart (1998)). Finally, the

AUC is reported for the collection of all out-of-sample predicted probabilities. Note an indicator based

on a coin toss would lead in large samples to an AUC of 0.5. A perfect indicator, on the other hand,

would completely discriminate between crisis and non-crisis, leading to an AUC of 1.

Still we use the lagged values of indicators, i.e., ˜X (cid:48)

For the in-sample exercise we discard the publication lag as all data is assumed to be available.
t−k for k ∈ {0, 1, 2, 3, 4}. The in-sample predicted
probabilities are then evaluated against the crisis starting dates (and the vulnerability periods) using all

thresholds values; summarised by the AUC.

For both exercises we employ real time estimates of our ﬁltered ﬁnancial cycles.21 To construct such

measures we smooth our unﬁltered ﬁnancial cycle estimates using a weighted moving average of six

quarters instead of applying the Christiano and Fitzgerald (2003)’ band pass ﬁlter, as the latter is known

to suffer from endpoint biases. We employ declining weights that are based on an one sided Bartlett

window that gives highest weight to the last observation at time t. Weights are 1 (ζt), 5/6 (ζt−1), 4/6
(ζt−2), 3/6 (ζt−3), 2/6 (ζt−4), and 1/6 (ζt−5) scaled by their sum to keep the scale (0,1]. The real time

cycles of the US are depicted in Figure 6. The one of the remaining countries are shown in Appendix

A.7. Note that while these are more volatile than the Christiano and Fitzgerald (2003)’s band pass

ﬁltered cycles, the changes in cyclical phases are still clearly visible.

We compare the signalling performance of our real time composite cycles 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 Capital Requirements Directive (CRD IV).22 Further, studies

have suggested that the latter variable ranks among the ones with the best early warning properties for

banking crises (see, e.g., Behn, Detken, Peltonen and Schudel (forthcoming)). Note that the credit-to-

GDP gap is a level concept, but our composite indices are built from growth rates. This means that

the credit-to-GDP gap indicates a build up of imbalances explicitly, i.e. through the deviation from an

assumed trend. Our measure emphasises expansions and contractions common to credit and asset prices

and is, thus, related to the build-up and corrective phases of leverage cycles. Three advantages of our

measure compared to the credit-to-GDP gap are worth stressing: First, the application of the HP ﬁlter

on the credit-to-GDP ratio for extracting medium term ﬂuctuations has been shown to induce spurious

medium term cycles by amplifying speciﬁc medium term movements and dampening shorter term ones

21As indicated in Section 2, for the real time estimates we use the unﬁltered, i.e., standard, growth rates of indicators.
22The credit-to-GDP gap is derived on an expanding window and using the HP-ﬁlter with a smoothing parameter of λ =
400, 000. This reﬂects the exact speciﬁcation as laid down in the Ofﬁcial Journal of the European Union (2014/C 293)
“Recommendation of the European Systemic Risk Board of 18 June 2014 on guidance for setting countercyclical buffer rates”.

23

(see Schüler (forthcoming)). Besides possibly not reﬂecting the country-speciﬁc cycle of interest, the

so-called credit gap is necessarily a bad coincident indicator of crises, as abrupt changes (short term

cycles) are dampened. Our measure allows for abrupt changes. Second and in a similar vein, a decline

in growth rates always precedes peaks of a gap measure. Thus, considering growth rates can possibly

signal vulnerability periods better than a gap measure. Third, the credit gap mixes two indicators for

which we ﬁnd very different cyclical patterns. These different patterns can be argued to originate from

differing propagation mechanisms of ﬁnancial and technology shocks (see Jaccard (forthcoming)). This

implies that movements in the overall credit gap measure can be caused by either of the shocks, which,

however, have different implications for systemic banking crises. On the contrary, our measures com-

bine indicators with similar statistical properties that are also linked through the concept of leverage

cycles.

Figure 6: US real time composite ﬁnancial and business cycles
Notes: The real time US composite ﬁnancial and business cycles are measured in standardised growth rates, where 0.5 denotes the historical
median; 0 is the smallest and 1 the largest growth rate observed in a country’s history. A crossing of 0.5 from above can be interpreted as
locating the peak of a hypothetical gap measure, while from below as reﬂecting the trough. Smoothing is done using a 6 quarter one-sided
moving average based on the weights of a Bartlett window. See Section 4.1 and 4.4.1 for further details. Grey area indicates NBER recession
dates.

4.4.2 Results

The signalling results reinforce the case for aggregation, suggesting that combining information helps to

improve the capacity of ﬁnancial variables to predict the start and vulnerability periods prior to systemic

banking crises.

Panel A of Table 5 offers the results for the signalling of start of crisis. The left part of the table, “One

quarter out-of-sample”, suggests that – by far – the broad ﬁnancial cycle index is the best coincident

indicator, while the narrow ﬁnancial cycle ranks second. The broad measure allows to detect 3 (TP)

out of 5 (TP+FN) crisis starting dates correctly. Its relative usefulness is highest (0.47) and noise to

signal ratio lowest (0.22). The AUC is found to be 0.78, while it is 0.59 for the narrow ﬁnancial

cycle, the second ranked speciﬁcation. On the contrary, the credit-to-GDP gap does not indicate any

start of crisis correctly. In-sample, the broad ﬁnancial cycle measure receives the highest AUC (0.90),

however the differences are marginal when compared to the speciﬁcation employing the entire set of

indicators (0.87). The narrow ﬁnancial cycle does not rank second for the in-sample exercise. Overall,

24

0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleYearDeviation from historical median growthTable 5: Signalling exercise: Coincident and early warning

Observ.

TP

FP

One quarter out-of-sample
TII
TN

FN

TI

U r

NtS

AUC

Observ.

AUC

In-sample

Panel A: At start of crisis
Financial cycle (narrow)
Financial cycle (broad)
Business cycle
∆cr
∆cr & ∆ph
∆cr, ∆ph, ∆pe, & ∆pb
Credit-to-GDP gap

392
392
392
392
392
392
392

Panel B: 1-4 quarters before crisis
392
Financial cycle (narrow)
392
Financial cycle (broad)
392
Business cycle
∆cr
392
∆cr & ∆ph
392
∆cr, ∆ph, ∆pe, & ∆pb
392
392
Credit-to-GDP gap

2
3
1
2
2
0
0

14
15
9
10
9
8
11

77
50
142
121
116
51
131

170
136
174
88
99
83
98

310
337
245
266
271
336
256

202
236
198
284
273
289
274

3
2
4
3
3
5
5

6
5
11
10
11
12
9

0.60
0.40
0.80
0.60
0.60
1.00
1.00

0.30
0.25
0.55
0.50
0.55
0.60
0.45

0.20
0.13
0.37
0.31
0.30
0.13
0.34

0.46
0.37
0.47
0.24
0.27
0.22
0.26

0.20
0.47
-0.17
0.09
0.10
-0.13
-0.34

0.24
0.38
-0.02
0.26
0.18
0.18
0.29

0.50
0.22
1.83
0.78
0.75
-
-

0.65
0.49
1.04
0.47
0.59
0.56
0.48

0.59
0.78
0.40
0.47
0.41
0.26
0.37

0.70
0.72
0.57
0.64
0.56
0.58
0.50

924
924
924
924
924
924
924

924
924
924
924
924
924
924

0.76
0.90
0.82
0.65
0.75
0.87
0.74

0.73
0.85
0.65
0.70
0.71
0.80
0.59

Notes: Table shows results of the out-of- and in-sample exercise as described in Section 4.4.1. “Observ.” refers to observations,
“TP” to true positive, “FP” to false positive, “TN” to true negative, “FN” to false negative, “TI” to Type I error, “TII” to Type II
error, “U r” to relative usefulness, “NtS” to noise-to-signal ratio, and “AUC” to area under the curve. “-“ indicates that the statistic is
not deﬁned.

this points to the beneﬁts of combining information for a real time exercise. Idiosyncratic movements

in individual indicators are damped and, thus, the signalling performance increases over considering

individual indicators.

Panel B of the same table shows the results of the early warning exercise. In the context of the out-

of-sample exercise, similarly to before, the broad ﬁnancial cycle indicator ranks ﬁrst when considering

the AUC (0.72). On this dimension the narrow ﬁnancial cycle measure does, however, equivalently well

(0.70). Thus, additionally considering a larger fraction of asset markets does not necessarily increase
the early warning performance of the composite indicator.23 Nonetheless, the broad measure performs

better considering relative usefulness or noise-to-signal ratio. Within the early warning exercise, credit

and the credit-to-GDP gap do not perform as bad as in the previous analysis. Their noise-to-signal ra-

tios are even marginally below the one of the broad ﬁnancial cycle (0.47 and 0.48 compared to 0.49).

In-sample, the broad ﬁnancial cycle measure does again slightly better than considering the single in-

dicators (0.85 to 0.8). The narrow ﬁnancial cycle ranks third with an AUC of 0.73. The credit-to-GDP

gap reaches only to 0.59 and ranks last. Again the relatively stronger performance of our indicators in

the out-of- but not in-sample exercise stresses the beneﬁts of combining information.

5 CONCLUSIONS

Attenuating ﬁnancial cycles, i.e., preventing the build-up of systemic risk, is one of the main goals of

macroprudential policy. Indeed, recent experience of the global ﬁnancial crisis and its aftermath has

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

cycles. Despite the prominence of this goal in macroprudential policy our knowledge with respect to

23Of course, the negative shock of the global ﬁnancial crises, which is the only crisis contained in the out-of-sample sig-

nalling exercise, was related to imbalances in the housing markets.

25

ﬁnancial cycles is still limited.

Our results suggest that the joint ﬂuctuations of credit and asset prices, i.e., emphasising expan-

sions and contractions common to all series, are important for the early detection of a systemic risk

build-up. This joint modelling is both in line with theoretical research on leverage cycles as well as

empirical studies on the detrimental effects of leveraged asset price bubbles. Additionally, it reconciles

differences of ﬁnancial cycle characteristics obtained through two alternative methodologies: frequency

decompositions and classical turning point analysis.

Empirical regularities of indicators suggest that credit and asset prices exhibit ﬂuctuations distinct

from indicators commonly associated with business cycles – notably higher amplitude and persistence;

especially at medium and long term frequencies. Employing a novel spectral methodology, we show

that ﬁnancial cycle frequencies tend to differ from those of business cycles; around 15 years on average

in contrast to only 9 years or 6.7 years when excluding Japan. In the time domain, we ﬁnd that domestic

ﬁnancial cycles are heterogeneously synchronised across countries. Most ﬁnancial cycles of G-7 coun-

tries are closely related while the ones of Germany and Japan are not. In comparison, business cycles

are closely linked within this set of countries.

Two main policy conclusions can be drawn. First, differences between ﬁnancial and business cycles

such as increased length and amplitude, but also the high predictive power of ﬁnancial cycles, support a

case for macroprudential policy addressing the build-up of systemic risk at the national level that might

differ both from policies aimed at business cycle stabilisation, as well as policies across countries. This

case is especially strong for the subset of euro area countries considered: while we ﬁnd that business

cycles are closely linked across our selected euro area countries, there are differences in ﬁnancial cy-

cle synchronisation. Even abstracting from different properties of ﬁnancial and business cycles, still it

seems unlikely that one instrument can sufﬁce to curb heterogeneously related ﬁnancial cycles. Second,

macroprudential policy and ﬁnancial stability surveillance may gain considering the common move-

ment of indicators jointly describing the health of balance sheets as we ﬁnd that the combined role of

indicators is important for the detection of systemic risk build-up; also when compared to the Basel III

credit-to-GDP gap. While macroprudential tools, such as loan-to-value ratio or countercyclical capital

buffer are speciﬁc instruments, one may gain from a coordination of policies. But of course, the under-

lying drivers of the ﬁnancial cycle need to be understood in order to efﬁciently address the building up

of vulnerabilities with macroprudential instruments.

Paths for future research are ample. Possibilities for extensions range from deepening the under-

standing of ﬁnancial cycles across countries – such as the exact lead-lag relation – and their interaction

with macroeconomic policies. Just as important, theoretical work is clearly needed to complement these

empirical estimates, and explain diverging ﬁnancial and business cycle phases also to inform the best

use of policies.

Adrian, T. and Shin, H.: 2010, Liquidity and leverage, Journal of Financial Intermediation 19, 418–437.

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A.1 Data

A APPENDIX

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

Financial Data (GFD), Haver Analytics (HA), or the OECD. The business cycle data set is taken from
Ohanian and Raffo (2012).24 All series are measured in real terms and deﬂated with the respective

country consumer price index (CPI). Seasonal adjustment is carried out using X-12.

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 households)

adjusted for breaks.

House prices: This measure reﬂects real residential property prices from the BIS. Italy’s house price

series starts in 1970Q3.

Equity prices: We employ the index from OECD main economic indicators, except in the case of

the US. In the case of the US we choose for the S&P500 index instead of the OECD main indicator, as

this one is more standard in academic research. Datastream code is S&PCOMP.

Corporate bond yields: Corporate bond yields are downloaded from GFD. For Canada, the long

term corporate bond yields are employed until Q1 2006 (Source: Bank of Canada), whereas for periods

24An updated dataset can be found on Andrea Raffo’s homepage (http://www.andrearaffo.net/araffo/

Research.html, last accessed 19/07/16)

31

after Q1 2006 we use the Bank of America Merril Lynch Canada Corporate Effective Yield from HA.

For Germany, we use yields on debt securities outstanding issued by residents from the Bundesbank.

For France, we take the ﬁrst class private bonds average yields provided by the Banque de France. For

Italy, the average corporate bond yield is provided by Banca d’Italia. For Japan, data are from The

Economist. From November 2011, the yield on Nomura Securities bonds is used. For the UK, data are

taken from an index of corporate bond yields as calculated by the Financial Times. From November

2011, the EIB 2028 bond is used. For the US, we use Moody’s Corporate BAA yield. Moody’s tries to

include bonds with remaining maturities as close as possible to 30 years. Moody’s drops bonds if the

remaining life falls below 20 years, if the bond is susceptible to redemption, or if the rating changes.

Inﬂation: CPI is taken from the OECD main economic indicators database.

Business cycle indicators: The data by Ohanian and Raffo (2012) provides real GDP, real private

consumption, real gross ﬁxed capital formation from the OECD Economic Outlook database. The study

derives their own dataset on hours worked which is consistently measured across countries.

A.2 Power Cohesion

Proof of Proposition 1. 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.25 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

.

(6)

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

preserved.

Proof of Proposition 2. Further, we use the normalised cross-spectral densities to construct our measure

of power cohesion 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.

(7)

(8)

25Out 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.

32

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.

(9)

The upper bound of 1 in Equation (9) holds as the covariance in phase and out of phase cannot

exceed the product of the standard deviations of both variables.

Proof of Proposition 3. To better understand our proposed measure, we contrast power cohesion to co-

hesion derived from a comparable traditional measure of squared coherency. More speciﬁcally, we

show that power cohesion 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 similarities

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 correlation similarly

relates the co-spectrum to the autospectra at different frequencies and, thus, suffers from a similar
disadvantage.26 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)

.

(10)

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):

which is characterised by a cyclical component

xi,t = ψi,t + εi,t,

ψi,t = αi,t cos(λt).

(11)

(12)

αi,t denotes a random amplitude, which may follow a stationary autoregressive process of order one,
λ is the cycle frequency.27 The idiosyncratic component, εi,t, is white noise with possible contempora-
neous covariance.

26Dynamic 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.

27A 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.

33

A common cycle is present if αi,t = γiαt, where γi is assumed to be some nonzero constant. Then,

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

t = (ε1,t, . . . , εM,t), and stacking equations yields

Xt = γψt + εt.

(13)

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))

(14)

(15)

(16)

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

(17)

The last equality holds as, due to the random amplitude αt, sψ(ω) has nonzero power for all fre-
quencies. 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

(18)

(19)

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

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.

34

A.3 Empirical issues

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

bandwidth of

T ·8 is used, which compared to the bandwidth used in Aikman et al. (2015) is larger and

√

emphasises our aim to have rather unbiased spectral density estimates; at the cost of a higher variance.

As is common, we only regard 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, e.g., Figure 2). 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 resample from a χ2
each periodogram.28

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. We restrict the possible cycles to be within 5 and 200 quarters. Five quarters as

a minimum is standard in the literature on turning points. 50 years as the maximum length of cycles

can be derived from the phenomenon of Kondratiev waves. Further, we require to capture 67% of total

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

the minimum cycle length is around 2.5 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 ∈ [2π/200, 2π/5] ∧ ω2 ≥ ω1) through

min
ω2−ω1

(cid:82) ω2
ω1
(cid:82) 2π/200
2π/5

PCohX (ω)dω

PCohX (ω)dω

≥ p.

(20)

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 and above 50 years.29 In our setup we assume

p = 0.67. 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; i.e., densest

area of PCoh around the peak.

28This 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.

29An unrestricted range would select ultra-high frequencies, which can be related to the high ampliﬁcation that occurs using

the quarter-on-quarter ﬁlter.

35

A.4 Statistical properties of ﬁnancial and business cycle indicators

Table 6: Descriptive statistics – real growth rates

Standard deviations
High-frequency Med./long-frequency Med./long-term
component 32-200
component 2-32

cycle 2-200

First-order autocorrelations

Country

Variables

Med./long-term
cycle 2-200

Canada

Germany

France

Italy

Japan

UK

Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)
Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)
Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)
Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)
Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)
Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)
Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)
Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)
Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)
Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)
Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)
Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)

1.02
2.49
7.46
0.84

0.82
0.79
2.26
0.41

0.75
0.81
8.26
0.66

0.56
0.61
1.20
0.36

0.98
1.30
9.03
0.90

0.99
0.95
2.67
0.64

1.45
1.93
10.69
1.32

0.82
0.72
1.70
0.57

1.22
1.62
8.58
1.06

1.07
1.11
2.04
0.80

2.04
2.75
8.17
1.21

0.96
1.07
2.94
0.39

0.81
2.29
7.28
0.64

0.76
0.71
2.14
0.40

0.64
0.69
7.92
0.53

0.49
0.56
0.97
0.33

0.80
0.80
8.67
0.63

0.96
0.92
2.58
0.63

1.11
1.53
10.06
0.99

0.78
0.65
1.55
0.56

0.93
1.16
8.01
0.82

1.03
1.08
1.86
0.79

1.68
2.23
7.90
0.95

0.89
0.97
2.82
0.37

0.61
0.95
1.55
0.50

0.31
0.33
0.66
0.08

0.37
0.34
2.15
0.36

0.24
0.24
0.66
0.13

0.53
1.02
2.39
0.62

0.21
0.23
0.60
0.06

0.90
1.12
3.43
0.83

0.24
0.30
0.68
0.10

0.73
0.99
2.77
0.62

0.28
0.23
0.75
0.14

1.13
1.48
2.03
0.72

0.32
0.44
0.72
0.10

0.54
0.39
0.27
0.64

0.38
0.08
0.34
-0.08

0.35
0.43
0.36
0.49

0.51
0.05
0.63
0.79

0.50
0.81
0.33
0.71

0.12
-0.23
-0.14
-0.27

0.45
0.82
0.39
0.70

0.48
0.34
0.28
-0.29

0.58
0.78
0.37
0.59

0.12
-0.21
0.15
-0.28

0.40
0.78
0.27
0.59

0.20
0.13
0.03
-0.17

High-frequency
component 2-32

0.27
0.28
0.23
0.40

0.27
-0.12
0.26
-0.14

0.12
0.22
0.31
0.23

0.38
-0.14
0.44
0.76

0.25
0.51
0.28
0.42

0.07
-0.33
-0.21
-0.28

0.08
0.71
0.31
0.46

0.42
0.19
0.13
-0.34

0.28
0.60
0.28
0.32

0.04
-0.28
-0.02
-0.33

0.12
0.67
0.22
0.34

0.08
-0.07
-0.04
-0.25

Notes: Bold numbers indicate signiﬁcance at the 10% level. Statistics are derived using HAC standard errors. Med. refers to medium.

36

Table 7: Maximum absolute correlation with domestic credit and output – leading or lagging up to 4
quarters

Country

Variable

Domestic credit

Domestic output

Med./long-term
cycle 2-200

High-frequency Med./long-term
component 2-32

cycle 2-200

High-frequency
component 2-32

Canada

Germany

France

Italy

Japan

UK

Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)
Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)
Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)
Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)
Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)

Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)
Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)
Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)
Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)
Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)
Financial cycle:
Credit (∆cr)
House price (∆ph)
Equity price (∆pe)
Bond price (∆pb)
Business cycle:
Output (∆q)
Consumption (∆co)
Investment (∆i)
Hours worked (∆h)

-
0.31
0.21
-0.31

0.35
0.40
0.32
0.19

-
0.24
-0.13
-0.28

0.18
0.18
0.17
-0.11

-
0.27
0.15
0.35

0.25
0.26
0.24
-0.13

-
0.27
-0.09
0.37

0.17
0.23
0.29
-0.10

-
0.67
0.27
0.52

0.35
0.44
0.40
0.16

-
0.47
0.34
0.40

0.28
0.35
0.25
0.17

(-)
(0)
(-4)
(4)

(-2)
(-3)
(-3)
(-3)

(-)
(0)
(4)
(4)

(0)
(-4)
(1)
(-3)

(-)
(-1)
(-4)
(0)

(-2)
(-2)
(-2)
(1)

(-)
(0)
(3)
(0)

(-2)
(-3)
(-2)
(1)

(-)
(0)
(0)
(0)

(0)
(0)
(0)
(-1)

(-)
(0)
(-3)
(0)

(0)
(0)
(-4)
(-3)

-
0.22
0.24
-0.26

0.29
0.26
0.25
0.20

-
0.24
-0.11
-0.23

0.05
0.14
0.07
-0.12

-
0.11
0.17
0.44

0.19
0.22
0.20
0.13

-
0.07
0.15
0.30

0.13
0.12
0.17
0.07

-
0.55
0.23
0.72

0.28
0.43
0.28
0.20

-
0.31
0.34
0.39

0.23
0.24
0.16
0.16

(-)
(0)
(-4)
(4)

(-2)
(-3)
(-3)
(-3)

(-)
(0)
(4)
(4)

(3 )
(-4)
(1)
(-3)

(-)
(0)
(1)
(0)

(-2)
(-2)
(-2)
(-3)

(-)
(0)
(2)
(0)

(-2)
(-3)
(-2)
(4)

(-)
(0)
(0)
(0)

(0)
(0)
(0)
(-1)

(-)
(0)
(-3)
(0)

(0)
(0)
(-4)
(-3)

0.35
0.29
0.38
0.33

-
0.53
0.50
0.26

0.18
0.23
0.21
0.27

-
0.55
0.77
-0.23

0.25
0.25
0.27
0.24

-
0.49
0.73
0.35

0.17
0.28
0.29
0.28

-
0.50
0.59
0.21

0.35
0.38
0.28
0.24

-
0.72
0.65
0.22

0.28
0.50
0.35
0.38

-
0.68
0.39
0.23

(2)
(-1)
(-1)
(-3)

(-)
(0)
(0)
(0)

(0)
(2)
(-1)
(-4)

(-)
(0)
(0)
(4)

(2)
(0)
(-1)
(-3)

(-)
(0)
(0)
(0)

(2)
(2)
(-1)
(-3)

(-)
(0)
(0)
(0)

(0)
(0)
(-1)
(0)

(-)
(0)
(0)
(-1)

(0)
(0)
(-3)
(0)

(-)
(0)
(0)
(0)

0.29
0.26
0.40
0.31

-
0.46
0.46
0.25

0.05
0.20
0.25
0.27

-
0.46
0.72
-0.24

0.19
0.29
0.27
0.26

-
0.46
0.72
0.38

0.13
0.25
0.29
0.35

-
0.44
0.56
0.23

0.28
0.37
0.23
0.32

-
0.71
0.62
0.21

0.23
0.43
0.35
0.35

-
0.63
0.34
0.19

(2)
(-1)
(-1)
(-3)

(-)
(0)
(0)
(0)

(-3)
(2)
(-1)
(-4)

(-)
(0)
(0)
(4)

(2)
(0)
(-1)
(-3)

(-)
(0)
(0)
(0)

(2)
(2)
(-1)
(-3)

(-)
(0)
(0)
(0)

(0)
(0)
(-1)
(0)

(-)
(0)
(0)
(-1)

(0)
(0)
(-3)
(0)

(-)
(0)
(0)
(0)

Notes: Number in brackets denotes lead (+) or lag (-) of credit or output to respective variable. Med. refers to medium.

37

A.5 Cross spectral densities and Power Cohesion

(a) Canada

(b) Germany

(c) France

(d) Italy

(e) Japan

(f) UK

Figure 7: Absolute cross-spectra for ﬁnancial cycle indicators
Notes: This panel shows the absolute cross-spectra of the ﬁnancial indicators. The x-axis measures the frequencies of cycles from 1.25 - 60
years. 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). ∆cr refers to percentage changes in total credit, ∆ph to percentage changes in house prices, ∆pe to percentage changes
in equity prices, ∆pb to percent changes in bond prices.

38

Years2082|ˆsxixj|0246810Δcr/ΔphΔcr/ΔpeΔcr/ΔpbΔph/ΔpeΔph/ΔpbΔpe/ΔpbYears2082|ˆsxixj|012345Δcr/ΔphΔcr/ΔpeΔcr/ΔpbΔph/ΔpeΔph/ΔpbΔpe/ΔpbYears2082|ˆsxixj|0246810Δcr/ΔphΔcr/ΔpeΔcr/ΔpbΔph/ΔpeΔph/ΔpbΔpe/ΔpbYears2082|ˆsxixj|02468101214161820Δcr/ΔphΔcr/ΔpeΔcr/ΔpbΔph/ΔpeΔph/ΔpbΔpe/ΔpbYears2082|ˆsxixj|0246810Δcr/ΔphΔcr/ΔpeΔcr/ΔpbΔph/ΔpeΔph/ΔpbΔpe/ΔpbYears2082|ˆsxixj|02468101214161820Δcr/ΔphΔcr/ΔpeΔcr/ΔpbΔph/ΔpeΔph/ΔpbΔpe/Δpb(a) Canada

(b) Germany

(c) France

(d) Italy

(e) Japan

(f) UK

Figure 8: Absolute cross-spectra of business cycle indicators
Notes: This panel shows the absolute cross-spectra of the business cycle indicators. The x-axis measures the frequencies of cycles from 1.25
- 50 years. 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). ∆q refers to percentage changes in GDP, ∆co to percentage changes in consumption, ∆i to percentage changes in
investment, and ∆h percentage changes in hours worked.

39

Years2082|ˆsxixj|00.20.40.60.811.21.41.6Δq/ΔcoΔq/ΔiΔq/ΔhΔco/ΔiΔco/ΔhΔi/ΔhYears2082|ˆsxixj|00.10.20.30.40.50.60.70.80.91Δq/ΔcoΔq/ΔiΔq/ΔhΔco/ΔiΔco/ΔhΔi/ΔhYears2082|ˆsxixj|00.20.40.60.811.21.41.6Δq/ΔcoΔq/ΔiΔq/ΔhΔco/ΔiΔco/ΔhΔi/ΔhYears2082|ˆsxixj|00.20.40.60.811.2Δq/ΔcoΔq/ΔiΔq/ΔhΔco/ΔiΔco/ΔhΔi/ΔhYears2082|ˆsxixj|00.511.5Δq/ΔcoΔq/ΔiΔq/ΔhΔco/ΔiΔco/ΔhΔi/ΔhYears2082|ˆsxixj|00.511.522.53Δq/ΔcoΔq/ΔiΔq/ΔhΔco/ΔiΔco/ΔhΔi/Δh(a) Canada

(b) Germany

(c) France

(d) Italy

(e) Japan

(f) UK

Figure 9: Power cohesion of G7 countries
Notes: This graph shows the measure power cohesion of the narrow (black lines) and broad ﬁnancial cycle (blue lines) as well as the business
cycle (red lines). Broad refers to the inclusion of all indicators, i.e., credit, house, equity, and bond prices, whereas narrow is deﬁned by
house prices and credit only. The dashed lines indicate the 68% bootstrapped conﬁdence intervals as discussed in Appendix A.3. The x-axis
measures the frequencies of cycles from 1.25 to 50 years. The blue area depicts business cycle frequencies, i.e., cycles with durations of 2-8
years and the purple area (8-20 years) marks frequencies most important for ﬁnancial cycles.

40

Years2082PCoh00.511.52CABroad financial cycleNarrow financial cycleBusiness cycleYears2082PCoh00.20.40.60.811.21.41.61.82DEBroad financial cycleNarrow financial cycleBusiness cycleYears2082PCoh00.511.522.53FRBroad financial cycleNarrow financial cycleBusiness cycleYears2082PCoh00.511.522.53ITBroad financial cycleNarrow financial cycleBusiness cycleYears2082PCoh00.511.522.53JPBroad financial cycleNarrow financial cycleBusiness cycleYears2082PCoh00.511.522.53UKBroad financial cycleNarrow financial cycleBusiness cycleA.6 Composite ﬁnancial and business cycles

(a) Canada

(b) Germany

(c) France

(d) Italy

(e) Japan

(f) UK

Figure 10: Composite cycles
Notes: This panel shows composite ﬁnancial and business cycles in standardised growth rates, where 0.5 denotes the historical median after
removing a nonlinear trend; 0 is the smallest and 1 the largest growth rate observed in a country’s history. A crossing of 0.5 from above can
be interpreted as locating the peak of a hypothetical gap measure, while from below as reﬂecting the trough. Speciﬁcally, it depicts the ﬁltered
ﬁnancial (narrow and broad) and business cycles. Filtering is done using the Christiano and Fitzgerald (2003) band-pass ﬁlter employing
country speciﬁc frequency windows as described in Table 3. Aggregation of standardised indicators is done using linear averaging in case of
the narrow ﬁnancial cycle and using time-varying weights that emphasise directional movements between indicators for the broad ﬁnancial
cycle. See Section 4.1 for further details.

41

0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleDeviation from historical median growthYear0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleDeviation from historical median growthYear0.00.20.40.60.81.019751980198519901995200020052010Financiall cycle (narrow)Financial cycle (broad)Business cycleDeviation from historical median growthYear0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleDeviation from historical median growthYear0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleDeviation from historical median growthYear0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleDeviation from historical median growthYearA.7 Real time composite ﬁnancial and business cycles

(a) Canada

(b) Germany

(c) France

(d) Italy

(e) Japan

(f) UK

Figure 11: Real time composite cycles
Notes: The real time composite ﬁnancial and business cycles are measured in standardised growth rates, where 0.5 denotes the historical
median; 0 is the smallest and 1 the largest growth rate observed in a country’s history. A crossing of 0.5 from above can be interpreted as
locating the peak of a hypothetical gap measure, while from below as reﬂecting the trough. Smoothing is done using a 6 quarter one-sided
moving average based on the weights of a Bartlett window. See Section 4.1 and 4.4.1 for further details.

42

0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleYearDeviation from historical median growth.0.1.2.3.4.5.6.7.8.919751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleYearDeviation from historical median growth0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleYearDeviation from historical median growth0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleYearDeviation from historical median growth0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleYearDeviation from historical median growth0.00.20.40.60.81.019751980198519901995200020052010Financial cycle (narrow)Financial cycle (broad)Business cycleDeviation from historical median growthYearImprint and acknowlegements 

The authors would like to thank Jörg Breitung, Fabio Canova, Matteo Ciccarelli, Mathias Drehmann, Sandra 
Eickmeier, Stephan Fahr, Wouter den Haan, Philipp Hartmann, Skander van den Heuvel, Stefanie Huber, 
Kirstin Hubrich, Ivan Jaccard, Peter Karadi, Benjamin Klaus, Manfred Kremer, Alexander Kriwoluzky, Siem Jan 
Koopman, Luc Laeven, Simone Manganelli, Massimiliano Marcellino, Emanuel Mönch, Giulio Nicoletti, Ana 
Regina Nunes Pereira, Giorgio Primiceri, Ju H. Pyun, Gerhard Rünstler, Moritz Schularick, Harald Uhlig, Shang-
Jin Wei, an anonymous referee, the audiences of the EABCN conference on “Econometric methods for 
business cycle analysis, forecasting and policy simulations”, the workshop on “Financial and Business Cycles” 
at the European Central Bank, the “First annual ECB macroprudential policy and research conference”, the 
“International Conference on Financial Cycles, Systemic Risk, Interconnectedness, and Policy Options for 
Resilience”, the “31st Annual Congress of the European Economic Association”, the “CEQURA Conference 
2016” and participants of the research seminars at the Halle Institute of Economic Research, University of 
Cologne, Freie University of Berlin, as well as the Research Centre of the Deutsche Bundesbank for helpful 
discussions and comments. Further, we would especially like to thank Jan Hannes Lang and Peter Welz for 
their invaluable contribution to the validation exercise, as well as their 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 Deutsche Bundesbank, the European Systemic Risk Board, or the International Monetary Fund. This paper 
reflects a revised version of the ECB Working Paper 1846 entitled “Characterising the financial cycle: A 
multivariate and time-varying approach”. 

Yves S. Schüler 
Deutsche Bundesbank; email: yves.schueler@bundesbank.de 

Paul P. Hiebert 
International Monetary Fund; email: phiebert@imf.org 

Tuomas A. Peltonen 
European Systemic Risk Board; email: tuomas.peltonen@esrb.europa.eu 

© European Systemic Risk Board, 2017 

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Note: 
The views expressed in ESRB Working Papers are those of the authors and do not necessarily reflect 
the official stance of the ESRB, its member institutions, or the institutions to which the authors are 
affiliated. 

ISSN 
ISBN 
DOI 
EU catalogue No 

2467-0677 (online) 
978-92-95210-05-9 (online) 
10.2849/872841 (online) 
DT-AD-17-010-EN-N (online)