European Regional Science Association36th European CongressETH Zurich, Switzerland

26-30 August 1996

Jordi Pons, Ernest Pons and Jordi SuriñachDepartment of Econometrics, Statistics and

Spanish EconomyUniversity of Barcelona

Spainepons@riscd2.eco.ub.es

Stylized Facts of Business Cyclesin the OECD Countries

ABSTRACT : This paper investigates the basic stylized facts of business cyles in the OECDcountries using quarterly data from 1970 to 1994. In the last years the study of businesscycles, on both theoretical and empirical levels, has been again in the forefront of research ineconomics. The purpose of this paper is to determine if the OECD business cycles are indeedin the terminology of Lucas (1977). Lucas concluded that because the coherence and phasecharacteristics of many economic time series appeared to be the same across countries,business cycles are all alike. The methodology used is based on spectral analysis. Thisapproach attempts to identify cycles in the frequency domain. Spectral analysis provides directand relevant information about leads and lags between economic time series and determinesif a substantial degree of coherence at a particular frequency or over a band of frequenciesdoes indeed exist.

Key words. business-cycle, spectral-analysis, frequency-domain.

I. Introduction

The stylized facts of business cycles were in the forefront of research in macroeconomics in

the first half of the twentieth century. Leading article of this literature is the work of Burns

and Mitchell (1946)1. The seminal contribution of Burns and Mitchell was influential because

it provided a comprehensive catalogue of the empirical features of the business cycles of

developed countries, notable, the United States. In recent years, most industrial countries

experienced pronounced cyclical behaviour in an important number of economic indicators.

Since the late sixties and early seventies the study of cycles has experienced a regeneration

of research effort, on both theoretical and empirical levels.

All economies experience recurrent fluctuations in economic activity that persist for periods

of several quarters to several years. Further, there is a definite tendency for the business

cycles of developed countries to move together. The challenge to theory is to develop

consistent explanation for these phenomena. On the theoretical level, renewed interest in

business cycle theory stems from an important article by Lucas (1977). Lucas concluded that

business cycles are all alike, because the coherence and phase characteristics of many

economic time series appeared to be the same across countries. In an attempt to explain this

apparent stylized fact, there has been a proliferation of theoretical business cycle models.

Lucas drew attention to a key business-cycle fact: outputs of broadly-defined sectors move

together. Some important articles in this area are by Kydland and Prescott (1982, 1990 and

1991) and Long and Plosser (1983).

The empirical studies of business cycles have been underpinned by two alternatives

methodologies. The first approach develops the original methodology of Burns and Mitchell

(1946). This method consists of identifying indicators and classifying these indicators as

leading, coincident and lagging by examining the timing and consistency of the turning points

of important economic time series. The second approach attempts to identify cycles in the

frequency domain. This approach consist of characterising business cycles identifying the

presence of peaks in the spectrum and determinying if a substantial degree of coherence at

1Surveys of more recent work on this field are Zarnowitz (1992) and Niemira and Klein (1994).

1

either a particular frequency or over a band of frequencies does indeed exist (see Layton,

1986 and Martin,1987 and 1990).

Perhaps the major limitation of these approaches is that they focus on either time or frequency

domain characteristics, but not on both2. In particular, the purpose of this paper is to

investigate the basic stylized facts of business cycles in the OECD countries using GDP

quarterly data from 1970 to 1994, applying the analysis in time and frequency domain. The

present paper contribute to this literature by applying a methodology based on spectral

analysis. This approach attempts to identify cycles in the frequency domain. Spectral analysis

provides direct and relevant information about leads and lags between countries and

determines if a substantial degree of coherence at a particular frequency or over a band of

frequencies does indeed exist. The series used are the GDP of OECD, Europe, European

Union, Australia, Canada, France, Germany, Italy, Japan, Norway, Spain, Switzerland, United

Kingdom and United States3.

The empirical focus of the paper is on isolating cyclic fluctuations in economic time series,

defined as cycles in the data between specified frequency bands. The scheme of the paper is

as follows. Section II summarises the methodology of the spectral analysis. Section III

presents and discusses the selected stylized facts. Section IV presents the leads and lags

between OECD contries. The main conclusions of the paper are presented in Section V.

II. Methodology

The spectral analysis describes the cycle in terms of a frequency and amplitude. The

frequency is defined as the inverse of the cycle lenght, whereas amplitude is the range

between peak and trough values. Granger and Hatanaka (1964) and Priestley (1981) argue that

the series must be stationary; the mean and variance of the series must remain constant over

2See Bowden and Martin (1992 and 1994).

3Each series is tested for a stochastic trend by using the augmented Dickey-Fuller and Phillips-Perron unit roottests. The results show that the null hypothesis of non-stationarity cannot be rejected.

2

time. If the series are not stationary, as most economic time series tend not to be, a first or

higher difference of the series would be necessary until the differenced series meet the

criterion of a stationary mean and variance. To determine the lead or lag between pairs of

economic indicators, two spectral statistics are used: coherence and phase. Coherence

measures the proportion of variance explained by one of the series at a given frequency of

the second series. This measure can take a value between 0 and 1; the concept is similar to

the square of the correlation coefficient from a regression. Phase measures the time difference

between two series in the frequency domain4.

Using a Fourier transform, one can express a stationary time series as a cyclical components

of different frequencies. The spectrum of the time series which decomposes the series’s total

variance into variance attributed to different frequencies. One can interpret the spectrum as

a density function. The area under the spectrum for an interval between two frequencies

equals the proportion of total variance attributed to components with frequencies within the

interval. We will also consider the coherence and phase between the GDP series of a country

and each of the other country.

It is not meaningful to consider spectra, coherence and phase for series that are not stationary.

We will refer to the statistical procedure used for rendering a time series stationary as

detrending. Given that we do not have a particular theoretical model in mind, and given the

weak power of most tests for stochastic versus deterministic trends, we prefer to take an

agnostic view towards detrending. Therefore, it’s possible to transform the raw economic

series into stationary series in two different ways.

One way to remove a trend from the data is simply to take the rates of growth. Another way

is to use the filter previously used by Hodrick and Prescott (1980) and many others

(application of two-sided moving averages, first-differencing and removal of linear or

quadratic time trends), known as the Whittaker-Henderson type filter. Finally, we apply the

4In the frequency domain, Sargent (1987, p. 282) offers the following update of Burns and Mitchell’s definition:"(...) the business cycle is the phenomenon of a number of important economic aggregates (such as GNP,unemployment, and layoffs) being characterized by high pairwise coherences at the low business cyclefrequencies".

3

rates of growth5. Many recent studies using a battery of such methods to measure business

cycles.

III. Stylized facts

An appropriate starting point in an investigation of business cycles, is to determine if a

substantial degree of coherence at either particular frequency or over a band or frequencies

does indeed exist. We adopt a traditionala priori definition of business cycles,namely

cyclical commovements between important macroeconomic variables with periods of around

five years(Lucas, 1977). Defining the business cycle by frequency of fluctuations, it becomes

natural to exploit spectral analysis.

The spectra for the each series (rates of growth) are shown in figure 1. We have previously

talked about the business cycle as fluctuations withperiods around five years. We make this

more precise by focusing on cycles with periods between six and thirty two quarters6. The

interval between six and thirty two quarters is marked by vertical lines in the spectra (the line

corresponding to thirty two quarters is the left one, since the period (frequency) is decreasing

(increasing) to the right). We specified that business cycles were cyclical components of no

less than six quarters (eighteen months) in duration and fewer that thirty two quarters (eight

years).

Table 1 and figure 1 show that most of the spectral mass for all series is between six and

thirty two quarters. We conclude that there is indeed some empirical support for business

cycles periods between six and thirty two quarters: most of the series have considerable

spectral mass in the corresponding frequency band.

5Because different filters have different transfer functions (that is, they pass through cyclical components atdifferents frequencies to different degrees) choosing a filter is equivalent to choosing which commovements toemphasize. The application of the rates of growth has two effects. A first effect is to reduce the fluctuations inall series and a second effect is to induce a more regular cyclical pattern with larger number of distinguishablecycles.

6This definition of the business cycle was suggested by the procedures and findings of NBER researchers likeBurns and Mitchell (1946). See Baxter and King (1995) for illuminating surveys.

4

Looking at the coherences in table 2 and figure 2, we note that there is relatively high

coherence between OECD and most countries for periods longer that six quarters.

Finally, table 3 shows the commovements of the different countries, as measured by their

correlation with OECD7. This table displays the correlation coefficient between OECD and

each other country lagged from one to five quarters, contemporaneous, and led from one to

five quarters. Most of the correlation coefficients are positive, indicating commovements

between the countries. For most countries, the contemporaneous correlation are the highest.

Of these, the correlation coefficients for Europe and European Union are highest, followed

by those for United States and Canada. The correlation coefficients for Norway are lower.

IV. Leads and lags between OECD countries

The present epigraph benefits from the tools providing with the spectral analysis of time

series in order to obtain an estimation of the lag the economical evolution of some countries

go through in comparison with some others. The estimation of the time lag by using the phase

function presents an important problem since this function is not easy to be interpreted in

practice. It is already known that a null and constant phase function corresponds to a

contemporary relation, whereas a linear phase function with slope being equal to thed lag

corresponds to lag relations of the Xt=aYt-d type. Although, in general, the interpretation of

the estimated phase function seems to be very difficult mainly because of various aspects:

a) When the relation between two variables is more complex, the phase function can

obtain a great deal of different forms depending moreover on the relation parameters.

b) There is a certain indetermination in the phase function. When concerning an angle,

it is not possible to distinguish a value from another being in time different from the

former one in a certain number of entire rounds of a circumference.

The series used for this paper also present those difficulties. Figure 3 shows the phase

function estimated between the OECD variable (the total OECD GNP rates of growth of a

7 The rates of growth of that series are stationary.

5

quarter with respect to the same quarter of the former year) and the EUR variable (referred

to the whole OECD European countries)8.

Figure 3. Phase between OECD and Europe. Figure 4. Phase between Germany and Spain.

The fact that this phase function is so close to the value 0 refers to the almost equality of

both series being then their relation contemporary. A statistical test based on the phase

function as it follows below can confirm that the relation between two variables is

contemporary. By using a spectral window of convenient properties, an estimation of the

individual and cross spectral densities of both variables can be obtained. Noting each variable

for X and Y and the estimated spectral densities for fX,fY and fXY, consistent estimators of the

coherence and the phase function being:

and

(1)κ̂XY(ω)fXY(ω)

fX(ω)fY(ω) 1/2

(2)φ̂XY(ω) tan 1

Im fXY(ω)

Re fXY(ω)

considering that the phase angle must be taken in the [-π,π] interval. Whenever the coherence

is strictly positive, the phase function will asymptotically spread itself as a normal one:

8 The phase function is expressed in sexagesimal degrees to highlight that we are dealing with angles.

6

where am2 depends on the Wk ponderations and the m width of the spectral window used:

(3)φ̂XY(ω) ∼ AN

φXY(ω),a 2

n α̂2XY(ω)

2

1

κ̂XY(ω) 21

andαXY(w) being the width of the cross spectral density between both variables. If the value

a 2m

k <m

W2k

of the coherence is replaced by expression (1), andαXY(w) by a consistent estimator:

the null hypothesis can be contrasted considering that the phase function is null when

(5)α̂XY(ω) fXY(ω)

comparing the following statistical value:

with the table value of a normal distribution. Figure 4 shows when the null hypothesis of a

(6)ZXY(ω) φ̂XY(ω)2 κ̂XY(ω) 2

a 2mα̂2

XY(ω) κ̂XY(ω) 2 1

contemporary relation can be refused by using this test.

When using this contrast in the case of the OECD and Europe, the null hypothesis saying that

the relation is contemporary cannot be rejected. But when comparing other variables, the

interpretation might be less clear9. Figure 4 presents the phase estimated between the quarter

evolution of Germany and Spain. Apparently, in this figure the relation between both

variables can no longer be accepted as contemporary. Precisely, when implementing the

former test both evolutions are refused to be simultaneous. Through the sign of the phase

function, it can also be deduced that the German evolution leads the Spanish one. And then

another problem must be faced. How to know wether this lag consists of one, two or even

more quarters

9 Table 4 shows countries in which the null hypothesis of a contemporary relation can be rejected.

7

Figure 5. Phase between OECD(+1) and Europe.Figure 6. Phase between OECD(-1) and Europe.

When a phase function is linear, the interpretation is then clear. But focusing on our case,

neither the estimated phase functions are linear (both for the case of those countries and for

other variables), nor has it sense to think that the relations between the variables seem so

simple to present such a clear lag. Anyhow, it is worthwhile asking oneself which the

dominant lag is. In most cases, the phase function can give an answer to this question. As far

as the OECD and Europe comparison is concerned, only ask ourselves what effect would

leading or lagging one of both variables a quarter have in the estimated phase function before

considering it. If the relation is mostly contemporary, then the new phase functions should

respectively indicate a lag of 1 and -1. Figures 5 and 6 enclose these new phase functions.

Both estimations cooroborate the already mentioned hypothesis in the sense that the relation

between both variables has neither a lag nor a lead of a quarter. In order to complete the

analysis, it would be also interesting to estimate the phase when a lag or a lead of two

quarters of the OECD variables is previously imposed. Figures 7 and 8 show the new phase

functions.

Figure 7. Phase between OECD(+2) and Europe.Figure 8. Phase between OECD(-2) and Europe.

8

In the case of the OECD and Europe those movements allow the rejection of a likelihood

two-quarter lag. In addition, it is clear that when moving one of both series more than two

quarters, the phase functions will adopt behaviours every time further from a constant value;

consequently the hipothesis is corroborated in the sense that the relation between both

variables is contemporary. On the other hand, in the case of Germany and Spain those

movements provide with some information. As it can be seen in Figure 9 where the variable

enclosing the German evolution leads one quarter, then the phase function reaches the value

0 so that now a contrast of the phase function nullity does not allow the rejection of such

hypothesis. If the DEU variable leads instead of lags a quarter (Figure 10), the phase function

will then confirm that the lag between both evolutions has increased, becoming a realtion with

a lag of two quarters.

Figure 9. Phase between Germany(-1) and Spain.Figure 10. Phase between Germany(+1) and Spain.

Even if all is basically about a graphical analysis, these previous movements of one of both

compared variables can be combined with contrasts over the phase function to determine

roughly the time lag a certain relation among variables dominates. This kind of analysis

implemented in all possible paired variables10 allows the construction of a time lag table as

it is shown in Table 5. The results obtained from the frequency domain are not fully coherent.

For example, it is deduced from the results that no lag exists neither between the OECD and

Spain nor between the OECD and the USA. On the contrary when comparing the USA and

Spain a lag of two quarters is obtained. This fact is influenced by various reasons:

a) Having independently obtained each lag from the others.

10 From the fourteenvariables used in the present research.

9

b) That the null values, more than being something evident of the contemporary relation,

they enclose the impossibility of rejecting that null hypothesis.

c) That the relations among variables are necessarily more complex and the

determination of a whole number as lag supposes a large simplification. Consequently,

the Table 4 results should be understood as simple explanations of a more complex

reality.

If all these factors are gathered as estimation errors it is then senseful trying to obtain a

slightly different table also allowing the whole results to seem reasonable. Through the

average of the results of the initial table of lags the present approach can be then obtained.

This research follows this procedure:

a) The series referred to the OECD total is used as a reference point.

b) All variables related to the OECD are placed in each single row and then a lag related

to OECD is obtained.

c) As in general a different lag can be obtained according to the information of each row,

all these lags are then averaged for each variable. Consequently, a final estimation of

each variable lag related to the OECD is obtained.

Figure 11. Estimated lag at frequency domain. Figure 12. Estimated lag at time domain.

10

d) The value 0 is then assigned to the most leading variable with respect to the OECD

(this case being the USA) and the other lags have their importance diminished in

relation to this variable. Consequently, an ordering of the whole countries is obtained

according to the time lag they go through in relation to the most leading variable

(USA)

Figures 11 and 12 summarize this ordering and the lag in months of each variable. In one

case (Figure 11) the lags obtained in the frequency domain have been used as a reference,

whereas in another one (Figure 12) the lags obtained in the time domain. The following

conclusions are then deduced from this average:

a) Larger lags are obtained when using the time domain results instead of using the

frequency domain ones.

b) The order obtained by using both methodologies is very similar excepting in the case

of Japan. The time domain obtains that Japan finds itself in phase with the USA,

whereas the phase function obtains a significative lag between one and two months.

This paper intends only to be a first approach to the research tackling which lags produce the

different countries economical evolution. That is the reason why, a methodology has been

briefly presented allowing the benefit from the tools of the time series spectral analysis in

order to establish those lags, even if some aspects of this methodology can be criticized:

a) The final result aims to obtain an estimation of the phase function, although this

estimation does not have very clear aspects. Among them, for example, the choice of

the spectral window to be used and its width.

b) The phase function interpretation is not an immediate interpretation despite using the

leading and lagging variables. In some variable combinations, it has been impossible

to determine by using this analysis which is the prevailing lag between two countries.

c) The obtained differences by using the time and frequency domains should catch the

11

researcher’s eye so that in future researches these may allow to find the causes of

those differences.

V. Concluding remarks

In this paper, one examines stylized facts in the frequency domain via the spectral density

function, the Fourier transform of the autocovariance function. The spectral density matrix

decomposes variation and covariation among variables by frequency, permitting one to

concentrate on the periods of interest (business-cycle, for example, correspond to periods of

roughly 6-32 quarters). Transformations of both the real and imaginary parts of the spectral

density matrix have immediate interpretation in business-cycle analysis; the coherence

between any two economics series effectively charts the strenght of their correlation by

frequency, while the phase charts lead/lag relationships by frequency.

We conclude that is indeed some empirical support for business cycles periods between six

and thirty two quarters, because most of the series have considerable spectral mass in the

corresponding frequency band. The commovement of the different countries, as measured by

their correlation with OECD, indicating that the contemporaneous correlation coefficients are

the highest. Of these, the correlation coefficients for Europe and European Union are highest,

followed by those for United States and Canada. The correlation coefficients for Norway are

lower.

And finally, a methodology has been presented allowing to determine the existing lags in the

economical evolution of the analyzed areas. It has been confirmed that the USA is the country

having a more leading evolution with respect to the OECD’s and Switzerland having a larger

lag.

References

-Baxter, M. and King, R.G. (1995):Measuring business cycles: approximate band-pass filtersfor economic time series, National Bureau of Economic Research, Working Paper 5022

-Bowden, R.J. and Martin, V.L. (1992): No, business cycles are not all alike: The UnitedStates and Australia compared,Australian Economic Papers, 31, 385-398.

12

-Bowden, R.J. and Martin, V.L. (1994): International business cycles and financial integration,The Review of Economics and Statistics, 77, 305-320.

-Burns, A.F. and Mitchell, W.C. (1946):Measuring business cycles, National Bureau ofEconomic Research, New York.

-Diebold, F.X. and Rudebusch, G.D. (1996): Measuring business cycles: a modernperspective,The Review of Economics and Statistics, 78, 67-77.

-Granger, C.W.J. and Hatanaka, M. (1964):Spectral analysis of economic time series,Princeton University Press, Princeton, New York.

-Hodrick, R.J. and Prescott, E.C. (1980): Postwar U.S. business cycles: an empiricalinvestigation, Carnegie-Mellon University, Discussion Paper, 451.

-Kydland, F.E. and Prescott, E.C. (1982): Time to build and aggregate fluctuations,Econometrica, 50, 1345-1370.

-Kydland, F.E. and Prescott, E.C. (1990): Business cycles: real facts and a monetary myth,Federal Reserve Bank of Minneapolis Quarterly Review, 14, 1-18.

-Layton, A.P. (1986): A causality analysis of Australia’s growth cycle and the compositeindex of leading indicators,Australian Economic Papers, 25, 57-66.

-Long, J.B. and Plosser, C.I. (1983): Real business cycles,Journal of Political Economy, 91,39-69.

-Lucas, R.E. (1977): Understanding business cycles. In Brunner, K. and Meltzer, A.H. (1977)(eds.): Stabilisation of the domestic and international economy, Carnegie-RochesterConference Series on Public Policy, 5, North Holland, Amsterdam.

-Martin, V.L. (1987): Leads and lags in the Australian business cycle: a canonical approachin the frequency domain,Australian Economic Papers, 26, 188-196.

-Martin, V.L. (1990): Derivation of a leading index for the United States using Kalman filters,The Review of Economics and Statistics, 72, 657-663.

-Niemira, M.P. and Klein, P.A. (1994):Forecasting financial and economic cycles, Wiley,New York.

-Priestley, M.B. (1981):Spectral analysis and time series, Academic Press, New York.

-Sargent, T.J. (1987):Macroeconomic theory, 2nd edition, Academic Press, Boston.

-Zarnowitz, V. (1992):Business cycles: Theory, history, indicators and forecasting, NationalBureau of Economic Research, Ballinger Publishing Company, Cambridge.

13

Table 1. Variance attributed to different frequencies

Country >32 quarters 6-32 quarters <6 quarters

OECD

Europe

European Union

Australia

Canada

France

Germany

Italy

Japan

Norway

Spain

Switzerland

United Kingdom

United States

29.06

29.07

29.06

20.69

29.70

28.50

26.04

19.29

31.43

16.16

38.91

29.53

28.44

27.05

63.91

66.39

66.60

64.26

64.20

66.08

60.88

76.68

62.14

42.36

60.34

67.34

60.77

67.18

7.03

4.54

4.34

15.05

6.10

5.43

13.09

4.04

6.42

41.48

0.75

3.13

10.79

5.77

Table 2. Coherence estimated with OECD at different frequencies

Country >32 quarters 6-32 quarters <6 quarters

Europe

European Union

Australia

Canada

France

Germany

Italy

Japan

Norway

Spain

Switzerland

United Kingdom

United States

0.87

0.86

0.67

0.78

0.72

0.64

0.86

0.80

0.50

0.56

0.79

0.71

0.89

0.79

0.78

0.55

0.66

0,64

0.67

0.73

0.60

0.49

0.49

0.67

0.52

0.82

0.72

0.71

0.29

0.36

0.57

0.37

0.30

0.37

0.41

0.45

0.32

0.56

0.73

14

Tab

le3.

Cro

ss-c

orre

latio

nw

ithO

EC

D

GD

P t-5

GD

P t-4

GD

P t-3

GD

P t-2

GD

P t-1

GD

P tG

DP t

+1

GD

P t+

2G

DP t

+3

GD

P t+

4G

DP t

+5

Eur

ope

-0.0

20.

090.

290.

460.

650.

780.

730.

650.

490.

290.

12

Eur

opea

nU

nion

-0.0

30.

080.

290.

450.

640.

770.

720.

640.

490.

290.

13

Aus

tral

ia0.

020.

110.

220.

320.

450.

540.

510.

430.

310.

09-0

.04

Can

ada

0.14

0.24

0.40

0.55

0.64

0.68

0.62

0.48

0.35

0.19

0.04

Fra

nce

0.03

0.05

0.14

0.29

0.44

0.60

0.60

0.56

0.48

0.34

0.25

Ger

man

y-0

.11

0.01

0.23

0.37

0.52

0.60

0.52

0.42

0.27

0.09

0.05

Italy

-0.2

6-0

.20

-0.0

40.

200.

460.

630.

710.

680.

580.

410.

23

Japa

n0.

080.

280.

450.

550.

620.

630.

550.

460.

380.

270.

19

Nor

way

0.09

0.14

0.29

0.32

0.33

0.29

0.10

0.04

-0.0

2-0

.05

-0.1

1

Spa

in0.

020.

090.

200.

310.

420.

490.

520.

500.

450.

380.

31

Sw

itzer

land

-0.2

3-0

.16

-0.0

30.

160.

360.

500.

580.

610.

560.

450.

29

Uni

ted

Kin

gdom

0.25

0.34

0.45

0.45

0.52

0.52

0.39

0.30

0.14

-0.0

1-0

.11

Uni

ted

Sta

tes

0.17

0.29

0.48

0.65

0.75

0.77

0.59

0.36

0.15

-0.0

8-0

.27

Tab

le4.

Cou

ntrie

sin

whi

cha

cont

empo

rary

rela

tion

can

bere

ject

ed.

OE

CD

Eur

ope

E.

Uni

onA

ustr

alia

Can

ada

Fra

nce

Ger

man

yIta

lyJa

pan

Nor

way

Spa

inS

witz

erla

ndU

.K

ingd

omU

.S

tate

s

OE

CD

**

Eur

ope

**

*

Eur

opea

nU

nion

**

Aus

tral

ia

Can

ada

**

**

**

Fra

nce

**

**

Ger

man

y*

**

**

Italy

**

**

**

*

Japa

n*

**

**

Nor

way

**

**

Spa

in*

**

*

Sw

itzer

land

**

**

*

Uni

ted

Kin

gdom

**

**

**

**

Uni

ted

Sta

tes

**

**

**

**

*

Tab

le5.

Est

imat

edla

gsan

dle

ads

from

GD

Pph

ase

OE

CD

Eur

ope

E.

Uni

onA

ustr

alia

Can

ada

Fra

nce

Ger

man

yIta

lyJa

pan

Nor

way

Spa

inS

witz

erla

ndU

.K

ingd

omU

.S

tate

s

OE

CD

00

00

00

01

0-1

00

00

Eur

ope

00

00

-10

00

00

00

-1-1

Eur

opea

nU

nion

00

00

-10

00

00

00

0-1

Aus

tral

ia0

00

00

22

2-

--

--1

0

Can

ada

01

10

01

11

--

-2

00

Fra

nce

00

0-2

-10

00

-1-1

00

-1-1

Ger

man

y0

00

-2-1

00

10

-11

10

-1

Italy

-10

0-2

-10

-10

-2-1

00

-1-1

Japa

n0

00

--

10

20

-0

2-1

-1

Nor

way

10

0-

-1

11

-0

-2

--

Spa

in0

00

--

0-1

00

-0

2-2

-2

Sw

itzer

land

00

0-

-20

-10

-2-2

-20

-2-2

Uni

ted

Kin

gdom

01

01

01

01

1-

22

0-1

Uni

ted

Sta

tes

01

10

01

11

1-

22

10

Figure 1. Estimated spectrum of quarterly GDP series

Figure 1.1 Spectrum of OECD. Figure 1.2 Espectrum of Europe.

Figure 1.3 Spectrum of European Union. Figure 1.4 Spectrum of Germany.

Figure 1.5 Spectrum of France. Figure 1.6 Spectrum of Italy.

18

Figure 1 (continued)

Figure 1.7 Spectrum of United Kingdom. Figure 1.8 Spectrum of Spain.

Figure 1.9 Spectrum of United States. Figure 1.10 Spectrum of Canda.

Figure 1.11 Spectrum of Japan. Figure 1.12 Spectrum of Australia.

Figure 1.13 Spectrum of Norway. Figure 1.14 Spectrum of Switzerland.

19

Figure 2. Estimated coherences with OECD

Figure 2.1 Coherence of OECD and Europe. Figure 2.2 Coherence of OECD and E. Union.

Figure 2.3 Coherence of OECD and Germany. Figure 2.4 Coherence of OECD and France.

Figure 2.5 Coherence of OECD and Italy. Figure 2.6 Coher. of OECD and Un. Kingdom.

20

Figure 2 (continued)

Figure 2.7 Coherence of OECD and Spain. Figure 2.8 Coherence of OECD and USA.

Figure 2.9 Coherence of OECD and Canada. Figure 2.10 Coherence of OECD and Japan.

Figure 2.11 Coherence of OECD and Australia. Figure 2.12 Coherence of OECD and Norway.

Figure 2.13 Coh. of OECD and Switzerland.

21