Is there an empirical link between the dollar price of the
euro and the monetary fundamentals?
by
Costas Karfakis1
ABSTRACT
This paper examines the empirical link between the dollar exchange rate of the
euro and the monetary fundamentals. The exchange rate is found to be
cointegrated with money and income differentials, while the homogeneity
restrictions are supported by the data. The weak form restrictions of the presentvalue model of the foreign exchange market are not rejected by the data, but the
most stringent restrictions are strongly rejected. An estimated error-correction
model explains a substantial part of the short-run exchange rate volatility and
outperforms the random walk forecasts.
Keywords: dollar price of euro, monetary fundamentals, present-value model,
cointegration, VAR, error-correction model
JEL classification: F31
1
University of Macedonia, 256 Egnatias Street, Thessaloniki 540 06, GREECE, email:
Ph.: 2310-891 466, Fax: 2310-891 421
ckarf@uom.gr,
1
Is there an empirical link between the dollar price of the
euro and the monetary fundamentals?
1. Introduction
Since euro began its life in January 1999, it was trading at 1,167 dollars. By
September 2000 the euro had fallen below 0,90 dollars and by early November
2000 had reached its nadir of 0,83 dollars. Thereafter, the euro fluctuated
significantly with an upward trend. By the end of 2002, the euro was trading at
par with the dollar. The appreciation of the euro continued and in the beginning
of the first week of 2004 it hit a lifetime high, rising to 1,27 dollars. In turn, it
slipped back to 1,20 dollars per euro, and then started to rise again.
Market commentators and currency analysts have attributed the swings of the
dollar price of the euro to the combination of a number of factors, such as
differences in the rates of growth and productivity between the euro area and the
USA, differences in the interest rates between the two areas, the alarming
increase in the US current account deficit and the cross border capital
movements.
The empirical literature has investigated the determinants of the “synthetic”
nominal and real exchange rates of the euro against the dollar. Sartore et al (2002)
constructed an econometric model of the euro-dollar real exchange rate, which
estimated from January 1990 to December 1999. The real exchange rate equation
depended on the real long-term interest rate differential, the ratio of traded to
2
non-traded goods prices, a measure of fiscal policy, the real price of oil and the
terms of trade. The cointegration analysis showed a well-established real
exchange rate equation, while the forecasting performance of the short-run
model was satisfactory compared with random walk forecasts. Jamaleh (2002),
on the other hand, constructed an econometric model of the euro-dollar nominal
exchange rate, which estimated from January 1992 to August 2000. The exchange
rate equation depended on short-term interest rate differential, income
differential and inflation differential. The empirical analysis showed that the
model performed well, while the introduction of nonlinear effects improved the
forecasting performance of the model. Ehrmann and Fratzscher (2004) examined
whether the real-time news of fundamentals in USA and in the euro area affected
the euro-dollar exchange rate using daily data from 1 January 1993 to 14
February 2003. The empirical findings confirmed that the new component of
macroeconomic announcements had a significant impact on the exchange rate.
Brooks et al (2004) examined the role of capital flows in determining the dollar
price of the euro, using quarterly data from 1988 to 2000. The analysis showed
that net portfolio flows tracked movements in the exchange rate of the euro
against the dollar.2
The purpose of this paper is to contribute to the existing literature by analyzing
the behaviour of the dollar price of the euro since its inception in the context of
Neely and Sarno (2002) review the ability of the monetary fundamentals to forecast exchange
rates.
2
3
the analytically attractive present-value monetary model.3 The following issues
are addressed:
1. Is there an empirical link between the dollar price of the euro and the
monetary fundamentals?
2. Does the difference between the current exchange rate and the current
monetary fundamentals determine the future changes in the monetary
fundamentals, as implied by the present-value monetary model?
3. To what extent the changes in the dollar price of the euro are
predictable and how they are related to random walk forecasts?
2. The Present-Value Monetary Model
The present-value monetary model of the exchange rate determination is given
by the following equation:
et 
1   j
) E t (f t  j  t )
(
1   j 0 1  
(1)
where et, ft denote is the logarithms of the exchange rate, defined as dollars per
euro, and the monetary fundamentals, defined as (y-y*)-(mt-mt*), where y, y* are
the logarithms of the domestic and foreign income, and mt, mt* are the
logarithms of the domestic and foreign money stocks, σ is the interest rate
elasticity of money demand and Ht is the information set.
Subtracting ft from both sides yields, after a little manipulation:
3
MacDonald and Taylor (1993) applied the present-value model of the foreign exchange market
4

Dt   (
j1
 j
) Et (ft j  t )
1 
(2)
where Dt=et-ft.
Bringing (2) one period backward and taking expectations at t-1, yields:

D t 1   (
j1
 j
) E t 1 (ft  t )
1 
(3)
Multiplying (3) by 1+σ/σ and subtracting the resultant expression from (2),
yields, after little manipulation:
1 
)D t 1  ft 


 j
(
) [E t ( ft  j  t )  E t 1 ( ft  j  t )]

j1 1  
Dt  (
(4)
The left-hand side of expression (4) is the unforecastable revision from t-1 to t
in the expected change in the monetary fundamentals.
3. Methodological Issues
Assuming that the monetary fundamentals are I(1) processes, the right-hand
side of (2) is stationary, implying that the left-hand side must also be stationary.
Alternatively, et and ft are cointegrated with a cointegrating vector [1 –1]. Thus,
we can model the data generation process for Δft and Dt as a bivariate VAR
system, in the context of which the restrictions of the present-value monetary
model can be examined.
to the mark price of the dollar over the period January 1979 to December 1990.
5
Consider the following bivariate VAR model
z t    A(L)z t 1  v t
(5)
where z=[Δf D]’ is a 2x1 vector of endogenous variables; Ψ=[Ψ1 Ψ2]’ is a fixed
intercept vector; A(L)=[AΔf(L)
AD(L)] is a 2x2 polynomial matrix in the lag
operator, with AΔf(L)=[a(L) c(L)]’ and AD(L)=[b(L) d(L)]’; Σt=[v1t, v2t]’ is a 2x1
vector of white noise errors with properties: E(vt)=0, E(vt, vt-s)=Σ when t=s and
zero otherwise, with Σ denoting the variance-covariance matrix of residuals. The
polynomials in the lag operators a(L), b(L), c(L) and d(L) are all of order p.
An implication of the present-value model of exchange rate determination for
the VAR system (5) is that Dt will Granger-cause the future path of Δft if agents
have information beyond the history of Δft. This constitutes the weak form
restrictions of the present-value model. If we assume that a second-order VAR
captures the time-series properties, the VAR model (5) can be written as:
  f t  a 1
 f   1
 t 1  = 
D t  c1

 
D t 1   0
a2
b1
0
c2
0
d1
0
1
b 2  ft 1   v 1 
0  ft 2  0 

 
d 2  D t 1   v 2 
 
  
0  D t  2  0 
(6)
or, in compact notation, as Xt=ΓXt-1+wt, where E(Xt+jΩt)=ΓjXt for all j, where Ωt is
the information set containing current and lagged values of Δft and Dt. Using (6),
the restrictions on Dt in (2) can be expressed as:

g'   (
j1
 j
) h'  j
1 
(7)
6
0 
1 
0 
0 


and h    .
g
1 
0 
 
 
0 
0 
where
These restrictions insure that for any Xt, Dt equals the expected present value of
Δft. Post-multiplying both sides of (7) by (I-(σ/1+σ))Γ yields the following set of
restrictions:
g'[I  (


)]  h' (
)
1 
1 
(8)
By writing out the restrictions on the individual coefficients of matrix Γ, we get
–c1=a1, -c2=a2, d1+b1=1+σ/σ, -d2=b2. To interpret these restrictions, add the Δft
equation of the VAR to the Dt equation to get:
or,
D t  ft  (c1  a 2 )ft 1  (c 2  a 2 )ft 2 
(d1  b1 )D t 1  (d 2  b 2 )D t 2  v 1t  v 2 t
(9)
 t  v 1t  v 2 t
(10)
where  t  D t  (
1
)D t 1  ft

The left-hand side of (10) is unpredictable given lagged values of Δf and D,
which follows from equation (4). Hence a test of this set of restrictions can be
obtained using a Wald test of the orthogonality of ξt on the information set
consisting of lagged values of Δf and D. This constitutes the strong form
restrictions of the present-value model.
7
4. Empirical Analysis
Data. We use monthly US and euro area observations on the exchange rate,
defined as dollars per euro, money supplies and industrial production indices
from the International Statistical Yearbook CD-ROM from January 1999 to March
2004. All the data were transformed in logarithms.
Unit roots. Estimation of the VAR system (5) requires investigation of the timeseries properties of the variables involved. Chart 1 plots the variable D t, which is
the difference between the current exchange rate and the current monetary
fundamentals - called the error correction (EC) term. A feature of this graph is
the marked decrease for Dt up to the end of 2001 and a substantial increase
thereafter, implying that the series exhibits a change in the slope around the end
of 2001. Thus, the unit root test proposed by Perron (1988), and Zivot and
Andrews (1992) is used to test the univariate time-series properties of Dt. This
test is more robust than the traditional ADF test, when the time series has a
structural break.
Consider the null hypothesis that the series Dt is integrated without an
exogenous structural break, that is:
D t    D t1  t
(11)
where  is the constant and ωt is a stationary error term. The alternative
hypothesis stipulates that the EC term Dt can be represented by a trend-
8
stationary process with a one-time break in the slope of the trend function,
occurring at an unknown point in time, that is
k
D t    t  DT()  D t 1    j D t  j  u t
(12)
j1
where DTt ()=t-T if t>T and 0 otherwise, =TB/T and TB is the breakpoint.4
The goal is to estimate the breakpoint that gives the most weight to the trendstationary alternative. Equation (12) was estimated with the breakpoint TB,
ranging from t=2 to t=T-1, and the breakpoint is the month corresponding to the
minimum t-statistic over all regressions.
Table 1 reports the results for those months where the breakpoint gives most
weight to the trend-stationary alternative. The estimated break date occurs at
December 2001 and the unit root hypothesis is rejected at the 1 percent
significance level. This result states that the EC term Dt can be characterized as a
trend-stationary process with on-time shift in the slope of the trend function.
ARDL Cointegration. The hypothesis that the EC term Dt is stationary can
also be investigated in a multivariate context by testing whether or not e t, (yt-y*t)
and (mt-m*t) are cointegrated with a cointegrating vector [1 1 –1]. The
proportionality postulate between exchange rate, income differential and money
The k extra regressors added to the estimating equations to eliminate possible nuisanceparameter dependencies in the limit distributions of the test statistics caused by temporal
dependence in the disturbances. The number of these regressors is determined by a test on the
significance of the estimated coefficients j. Setting k equal to a maximum lag, we choose the first
value of k such that the t statistic on k was greater than 1.6 in absolute value and the t statistic on
J for j>k was less than 1.6. The inclusion of too many extra regressors of lagged first-differences
does not affect the size of the test but only decreases its power. Including too few lags may have a
substantial effect on the size of the test.
4
9
differential is explained by means of the Autoregressive Distributed Lag (ARDL)
procedure advanced by Pesaran, Shin and Smith (2001). The main advantage of
this strategy is that it can be applied irrespective of whether the series are I(0) or
I(1) processes. The maximum lag length is set at 6 and the optimum lag structure
is selected by using the Schwarz Bayesian Criterion (SBC). The underlying
ARDL(2,1,0) exchange rate equation, which is reported in the first panel of Table
2, satisfies all econometric criteria namely absence of serial correlation, absence
of functional misspecification, existence of normality and homoscedasticity.
CUSUM stability tests showed that the equation remained stable over the sample
period. The estimated long-run monetary model using the ARDL approach is
presented in the second panel of Table 2. The Wald test statistics of the
homogeneity restrictions do not reject the hull hypothesis in all cases.
We have also tested for the proportionality postulate between et and ft by
means of the ARDL approach. The underlying ARDL(2,0) exchange rate
equation, which is also reported in the first panel of Table 2, is well specified. The
Wald test statistic of the unit restriction does not reject the hull hypothesis. This
evidence, which is consistent with the stationarity of Dt, suggests that the
monetary model is validated as a long-run equilibrium relationship, in the sense
that a cointegrating relationship exists among the exchange rate and the
monetary fundamentals, which appears to satisfy the homogeneity restrictions.
VAR model. The data generation mechanism of Δft and Dt is modeled as a
bivariate VAR system in the context of which the present-value monetary model
10
can be examined. The strategy adopted in specifying the optimum lag length of
the VAR model was based on the SBC along with LM tests for serial correlation,
functional form, normality and heteroscedasticity. In applying these criteria, the
maximum lag length of the model was set at 6. The system also included three
exogenous regressors: an intercept, a time trend and the dummy variable DT
with the breakpoint set at December 2001. The results showed that the SBC
selected a VAR(2), while the diagnostic tests, which are reported in the first panel
of Table 3, rejected any kind of misspecification.
The results of Granger causality F-tests, which are shown in the second panel of
Table 3, suggest that the past history of Dt does not have information content to
predict future movements in Δft. Since this finding is sensitive to the presence of
the exogenous regressors in the equation of Δft,5 and given that the past history
of Δft does not Granger cause Dt, a restricted VAR system was estimated by
SURE. The Δft equation included two lagged values of both variables, while the
Dt equation included two lagged values of itself together with the three
exogenous regressors. The result of the Wald statistic indicates that the past
history of Dt has information content to predict future movements in Δft, as
suggested by the present-value approach to exchange rate determination.
The most stringent restrictions of the present-value model were examined by
regressing the variable ξt, which was calculated for different values of the interest
The F-statistic of the hypothesis that the exogenous regressors are jointly zero is equal to
F(3,53)=1,27 with a p-value of 0,29. The F-statistic of the hypothesis that the exogenous regressors
and the two lagged values of Dt are jointly zero is equal to F(5,53)=2,87 with a p-value of 0,02.
5
11
rate elasticity of money demand, on lagged values of Δf and D and tested the
hypothesis that the coefficients are jointly zero. The evidence reported in the
third panel of Table 3 rejected the restrictions imposed on the data. Despite the
rejection of the strong form restrictions, the monetary model is validated as a
long-run equilibrium relationship, in the sense that we have found a
cointegrating
relationship
between
exchange
rate
and
the
monetary
fundamentals which appears to satisfy the homogeneity restrictions.
EC model. Estimated exchange rate models, by and large, perform poorly
when predicting out-of sample, compared to random walk forecasts. Given the
strong link between the dollar exchange rate of the euro and the monetary
fundamentals, it is interesting to see how an estimated EC model predicts postsample. The results of the EC model, which is estimated by the method of
Instrumental Variables (IV) in order to correct for the possibility of simultaneous
equations bias, is presented in Table 4. All diagnostics show that the model is
well specified. The Wald test statistic, which is equal to 0,096 (with a p-value of
0,76), shows that the growth rate of the monetary fundamentals has a
proportional impact on the growth rate of the exchange rate. The EC term is
negative and statistically significant. The size of the EC term, which is equal to –
0,53, suggests a high speed of adjustment of the exchange rate to equilibrium. In
Chart 2, we have plotted the actual and fitted values of the EC model. The value
of R2 suggests that 40 percent of the short-run variation in the dollar exchange
rate of the euro is explained by the monetary fundamentals.
12
In Table 4, summary statistics for forecasts from the EC model for the period
March 2003 to March 2004 are set out and compared to those from a random
walk. The statistics indicate reasonable out-of-sample forecasting ability. In
general, the model outperforms a random walk with lower mean absolute
prediction errors and lower root-mean-square prediction errors. Furthermore, it
should be noted that the estimated equation accurately predicts the signs of the
change in the exchange rate in 9 of the 12 predictions with a p-value of 0,9807.6
5. Conclusions
This paper has examined the empirical link between the dollar price of the euro
and the monetary fundamentals. The unit root test with structural breaks
showed that the deviations of the current exchange rate from the current
monetary fundamentals can be characterized as a trend-stationary process. The
ARDL approach to cointegration showed that the exchange rate was cointegrated
with the monetary fundamentals and the homogeneity restrictions were
supported by the data. This evidence suggests that the monetary model is
validated as a long-run equilibrium relationship. An interesting aspect of the
VAR analysis is the evidence that the deviations of the current exchange rate
from the current monetary fundamentals have predictive power for future
movements in the monetary fundamentals, which is consistent with the
Let the probability of predicting the sign correctly equal π, so that if the predictions were
random, π=1/2. As long as the predictions are independent, the number of correct predictions of
6
13
predictions of the present-value model of the foreign exchange market. An
estimated EC model of the dollar price of the euro explains a substantial part of
the short-run exchange rate volatility and outperforms the random walk
forecasts.
the sign under the null of π=1/2 is ~B(12,1/2).
14
REFERENCES
Brooks, R., H. Edison, M.S. Kumar and T. Slok (2004). Exchange Rates and
Capital Flows. European Financial Management 10( 3): 511-533.
Ehrmann, M., and M. Fratzscher (2004). Exchange Rates and Fundamentals.
Working Paper Series 365, ECB.
Jamaleh, A. (2002). Explaining and Forecasting the Euro/dollar Exchange
Rate Through a Non-linear Threshold Model. The European Journal of
Finance 8: 422-448.
MacDonald, R., and M.P. Taylor (1993). The Monetary Approach to the
Exchange Rate: Rational Expectations, Long-Run Equilibrium, and
Forecasting. International Monetary Fund Staff Papers 40: 89-107.
Neely, C.J., amd L. Sarno (2002). How Well Do Monetary Fundamentals
Forecast Exchange Rates. Federal Reserve Bank of St. Louis Review, September/
October: 51-74.
Perron, P. (1988). The Great Crash, the Oil Price Shock, and the Unit Root
Hypothesis. Econometrica 57: 1361-1401.
Pesaran, M.H., Y. Shin, and R.J. Smith (2001). Bounds Testing Approaches
to the Analysis of Level Relationships. Journal of Applied Econometrics 16:
289-326.
Saerore, D., L. Trevisan, M. Trova and F. Volo (2002). US dollar/Euro Exchange
Rate: A Monthly Econometric Model for Forecasting. The European Journal
of Finance 8: 480-501.
Zivot, E., and D.W.K. Andrews (1992). Further Evidence on the Great Crash, the
Oil-Price Shock, and the Unit-Root Hypothesis. Journal of Business &
Economic Statistics 10(3): 251-270.
15
Table 1: Unit root test with structural breaks for the EC term Dt.
TB
j
μ
ρ
2001/9
1
2001/10
1
2001/11
1
2001/12
3
2002/1
3
2002/2
3
2002/3
3
0,29
(4,47)*
0,32
(4,63)*
0,35
(4,91)*
0,50
(5,25)*
0,54
(5,21)*
0,52
(4,66)*
0,42
(3,62)*
-0,003
(-3,51)*
-0,003
(-3,64)*
-0,003
(-3,88)*
-0,004
(-4,43)*
-0,004
(-4,39)*
-0,004
(-3,83)*
-0,003
(-2,78)*
γ
0,01
(4,52)*
0,01
(4,67)*
0,01
(4,94)*
0,02
(5,36)*
0,02
(5,31)*
0,02
(4,74)*
0,02
(3,69)*
α
x2(12)
-0,46
(-4,67)*
-0,50
(-4,82)*
-0,56
(-5,10)*
-0,78
(-5,40)*
-0,85
(-5,36)*
-0,82
(-4,80)*
-0,68
(-3,76)*
12,74
[0,39]
12,24
[0,43]
10,26
[0,59]
10,57
[0,57]
10,27
[0,59]
9,68
[0,64]
14,16
[0,29]
Notes: λ=time break relative to total sample size. t-statistics are in parentheses.
The critical values obtained from Zivot and Andrews (1992) are –4,904 (λ=0,5)
and –4,88(λ=0,6) at 1 percent significance level. Numbers in squared brackets are
p-values. The x2-statistic tests for serial correlation of the residuals.
16
Table 2: Estimates of the ARDL model of the dollar price of the euro
Dependent variable: et
A. Estimates of the selected ARDL Models.
ARDL(2,1,0)
Regressor
Coefficient(t-ratio)
Constant
0,31779(2,6999)*
time
-0,00339(-2,5935)*
DT
0,012793(4,8581)*
et-1
0,95566(7,5346)*
et-2
-0,4790(-3,8121)*
*
yt-y t
-0,31467(-0,7283)
*
yt-1-y t-1
1,0661(2,4763)*
mt-m*t
-0,47350(-2,2631)*
ft
ARDL(2,0)
Coefficient(t-ratio)
0,31060(2,7104)*
-0,0025(-3,1646)*
0,01136(4,4494)*
0,93425(7,0946)*
-0,41697(-3,2734)*
0,48791(2,5392)*
R2=0,97, SEE=0,02
SC: x2(12)=5,8589[0,923]
FF: x2(1)=2,5212[0,112]
NO: x2(2)=1,5124[0,469]
HE: x2(1)=1,4943[0,222]
B. Estimated long-run coefficients.
Constant
time
DT
yt-y*t
R2=0,97, SEE=0,02
SC: x2(12)=5,7130[0,93]
FF: x2(1)=2,5428[0,111]
NO: x2(2)=1,8186[0,403]
HE: x2(1)=0,0536[0,817]
0,60723
(3,0134)*
0,64344
(3,0135)*
-0,90476
(-2,4279)
---------
-0,0065
(-2,9175)*
-0,0051
(-5,7018)*
0,02445
(9,8031)*
0,0235
(13,0815)*
1,4358
(1,8878)***
-------
mt-m*t
ft
1,0108
(2,7154)*
Wald tests
Homogeneity restriction on relative income: x2(1)=0,32834[0,567]
Homogeneity restriction on relative money: x2(1)=0,065317[0,798]
Homogeneity restrictions on relative income & money: x2(2)=0,38269[0,826]
Homogeneity restriction on monetary fundamentals: x2(1)=0,0008[0,98]
Notes: Numbers in parentheses (square brackets) are t-ratios (p-values). SC, FF,
NO, HE denote serial correlation, functional form, normality, heteroscedasticity.
* indicates significance at 1 percent
** indicates significance at 5 percent
*** indicates significance at 10 percent
17
Table 3: Empirical analysis of the VAR model
A. Misspecification tests
Dep. V/ble
R2
SEE
Δf
0,18
0,01
D
0,97
0,02
SC:x2(12)
14,21[0,29]
4,44[0,97]
FF:x2(1)
3,43[0,06]
1,57[0,21]
NO:x2(2)
2,53[0,28]
1,30[0,52]
HE:x2(1)
1,43[0,23]
0,02[0,91]
B. Granger causality tests
Unrestricted VAR (OLS) Restricted VAR (SURE)
Dep. V/ble
Lags F-test (p-value)
Lags Wald test (p-value)
Δf
2
0,64(0,53)
(2,2)
9,55(0,00)*
D
2
2,07(0,14)
(0,2)
C. Orthogonality tests of the rational expectations restrictions
Regression: ξt on constant, Δft-1, Δft-2, Dt-2
σ
1+σ/σ
Wald test
p-value
2
0,02
51
x (3)=944,08
0.00*
2
0,10
11
x (3)=90,03
0.00*
0,16
7,25
x2(3)=43,21
0.00*
2
0,25
5
x (3)=24,14
0.00*
System
Δf, D
Note: In section B, the F and Wald statistics test the joint hypothesis that the
coefficients of the lagged values of the independent variable are zero. In section
C, the Wald statistic tests the hypothesis that the coefficients of the lagged values
of Δf and D are jointly zero.
18
Table 4: IV estimates of the EC model of the dollar price of the euro
Dependent variable: Δet
Regressors
Coefficients
Standard Error
t-ratio
Constant
0,32259
0,092822
3.4754*
time
-0,002157
0,001005
-2,1451**
DT
0,011826
0,003416
3,4612*
Δet-1
0,44736
0,14312
3,1257*
Δft
0,85902
0,45468
1,8893***
Dt-1
-0,53297
0,13891
-3,8367*
Diagnostics tests:
R2=0,39, SEE=0,02
SC:x2(12)=9,24[0,68], FF:x2(1)=0,22[0,65], NO:x2(2)=3,25[0,20], HE:x2(1)=1,02[0,31]
Sargan’s test for the adequacy of the selected instruments: x2(14)=7,90[0,90]
Sargan’s test statistic for serial correlation: x2(12)=9,24[0,68]
Wald test x2(1)=0,096[0,76]
Summary statistics for forecasts of Δet (2003:3-2004:3)
EC Model
Random walk
MSAPE
0,0262
0,0322
RMSPE
0,032
0,0365
Notes: The selected instruments included the three exogenous regressors, five
lagged values of Δe and two lagged values of Δf. Number in square brackets are
p-values. The Wald statistic tests the hypothesis that the coefficient of Δf is equal
to unity. MSAPE=mean sum absolute prediction error, and RMSPE=root-meansquare prediction error.
19
Chart 1. Deviations of the current exchange rate from
the current monetary fundamentals - EC term D
1,2
1
0,8
0,6
0,4
0,2
2004M1
2003M9
2003M5
2003M1
2002M9
2002M5
2002M1
2001M9
2001M5
2001M1
2000M9
2000M5
2000M1
1999M9
1999M5
1999M1
0
Chart 2. Actual and fitted values of the EC model of
the dollar price of the euro
ACTUAL
FITTED
0,08
0,06
0,04
0,02
-0,06
20
2004M2
2003M11
2003M8
2003M5
2003M2
2002M11
2002M8
2002M5
2002M2
2001M11
2001M8
2001M5
2001M2
2000M11
2000M8
-0,04
2000M5
-0,02
2000M2
0
19
99
M
19 1
99
M
19 5
99
M
20 9
00
M
20 1
00
M
20 5
00
M
20 9
01
M
20 1
01
M
20 5
01
M
20 9
02
M
20 1
02
M
20 5
02
M
20 9
03
M
20 1
03
M
20 5
03
M
20 9
04
M
20 1
04
M
5
The dollar price of the euro
1,4
1,2
1
0,8
0,6
0,4
0,2
0
21