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© 2014 Nicolaus Copernicus University. All rights reserved.  
http://www.dem.umk.pl/dem 

D Y N A M I C  E C O N O M E T R I C  M O D E L S  
DOI: http://dx.doi.org/10.12775/DEM.2014.005  Vol. 14 (2014) 93−104 

Submitted October 20, 2014  ISSN 
Accepted December 23, 2014 1234-3862 

Ewa M. Syczewska*  

The EURPLN, DAX and WIG20: The Granger  
Causality Tests Before and During the Crisis 

A b s t r a c t. In this paper the possible interdependence between bilateral exchange rate 
behavior and the corresponding stock indices is checked, with application to the EURPLN 
rate and the DAX and WIG20 stock indices. Methods and results are similar to previous study 
of USDPLN exchange rate, and SP500 and WIG20 indices. The linear (including instantane-
ous) causality test and the Diks-Panchenko test are applied to logarithmic returns and to the  

daily measure of volatility ln ,

,
. Differences between before- and during-crisis 

period results are less vivid than in case of the U.S. and the Polish instruments. But there is 
a substantial difference between linear (and Diks-Panchenko) test results and the instantane-
ous Granger-causality test results, on the other hand – between returns and daily volatility.  

K e y w o r d s: Exchange rates, stock indices, financial crisis, risk, Granger causality, instan-
taneous causality, Diks-Panchenko test.  

J E L Classification: C4, G19. 

Introduction 

 The results presented here are part of the research aimed at detecting 
interdependencies between bilateral exchange rates and stock indices of the 
corresponding two countries, while possible influence of the crisis is taken 
into account. The idea of improvement of the exchange rate model by use of 
the stock indices from the corresponding two countries has been suggested 

                                                 
* Correspondence to: Ewa M. Syczewska, Warsaw School of Economics, Collegium of 

Economic Analysis, Institute of Econometrics, 6/8 Madalinskiego Street, 02-513 Warsaw, 
Poland, e-mail: Ewa.Syczewska@sgh.waw.pl. 



Ewa M. Syczewska 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 93–104 

94

by the Bauwens et al. (2008) model of the Norwegian krona, and used with 
success in the previous research by the author. In Syczewska (2010, 2013, 
2014) this method and the Granger linear causality tests were applied to the 
USD/PLN daily data and two indices – one from the Warsaw Stock Ex-
change, the other representing the U.S. stock indices. It was shown that fore-
cast errors from the ARIMA and GARCH models diminished when the stock 
indices were included in the model as additional explanatory variables (see 
also Matuszewska and Witkowska (2007) for comparison to other methods 
of forecasting). 
 In Syczewska (2013) research it was shown that it is possible to find 
a stationary relationship between the USDPLN exchange rate and the U.S. 
and Polish stock indices. As the U.S. stock exchange opens before the clos-
ing time of the Warsaw Stock Exchange, it was decided to use opening val-
ues of the S&P500 stock index and the closing values both for the USDPLN 
exchange rate and for the WIG stock index. There was a linear combination 
of the three variables, for which hypothesis of nonstationarity had to be re-
jected.  
 In this paper we first perform the Granger causality tests for the 
EURPLN exchange rate and two stock indices: DAX and WIG20. We check 
whether the stock-index returns Granger-cause the relative changes of the 
exchange rate. To this aim we use both the Granger test and the Granger test 
of instantaneous causality1. To take into account possible effects of the cri-
sis, we perform the causality tests and the estimation exercise for two sub-
samples: up to Sept. 15th 2008 (“before crisis”) and since Sept. 16th 2008 
(“during crisis”). Next we apply to the same variables the Diks-Panchenko 
causality test, which is assumed to detect also nonlinear causality.  
 We use daily data provided by stooq.pl, choose the period since the be-
ginning of May 2004 (corresponding to the EU accession) up to beginning of 
October 2013. In Syczewska (2010) behavior of rates and quality of model-
ing was compared for two subperiods: before (up to September 2008) and 
during crisis (up to end of July 2009), showing that2: 

1. Volatility of returns, hence errors of forecasts from the ARMA and 
GARCH models of returns, hugely increased during the crisis.  

2. Introduction of corresponding stock indices returns slightly improved 
performance of the models and forecasts.  

                                                 
1 This was suggested by specification of models for daily returns of Norwegian krona 

(Bauwens et al., 2008). 
2 The paper by Syczewska (2010) was presented at the International Conference 

“Zagadnienia aktuarialne – teoria i praktyka” in Warsaw, 2nd-4th September 2009.  



The EURPLN, DAX and WIG20: the Granger Causality… 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 93–104 

95

The Polish economy performance during the crisis was better than for the 
other European economies. The current condition of the German economy 
(the main trade partner of Poland) and expectations of future development 
give hope for further improvement. The EURPLN exchange rate is important 
for the economic analysis due to the proportion of transactions made in Euro.   

1. Description of the Data 

 We use daily data since 4th May 2004 (the EU accession) until Septem-
ber 2008 and from September 2008 until the September 2013 for the indices 
and exchange rates, and for the sake of comparison we perform the tests to 
the data from the first period (“before the crisis”), and the second period 
(“during the crisis”) starting in mid-September 2008, with the same number 
of observations as the first one3. As a measure of returns we use the standard 
formula: 

)ln(ln*100 1 ttt yyz , (1) 

where ty   – closing values of an instrument, and also logarithm of propor-
tion of daily maximum and minimum: 

)/ln(*100 min,max,
2

ttt yy , (2) 

as a measure of variance/volatility (Brooks, 2008). Figure 1 shows a typical 
behavior of the DAX index returns: there is a marked increase of volatility 
during the 2008-09 crisis, later slight stabilization and again increase of 
volatility due to problems of the Euro zone. Figure 2 illustrates measure of 
volatility of the same stock index defined by equation (2). There is a marked 
increase in volatility during the subprime crisis and subsequent global crisis 
on financial markets. Next, in the year 2009, the situation seems to slightly 
stabilize, but later due to the problems in the Euro area, volatility increases 
again. 
 The summary statistics in the Tables 1 and 2, corresponding to the “pre-
crisis” and “crisis” periods, show that the distribution of the logarithmic 
returns and returns (2) are skewed, which has to be expected. The results of 
the Doornik-Hansen test show that the empirical distribution of all the varia-
bles is non-Gaussian. Note that the empirical distribution of volatility, rDAX 
etc. defined by eqn. (2), is more skewed than the distribution of logarithmic 
returns for the same instrument.  

                                                 
3 http://stooq.pl database, opening, closing, minimum and maximum daily quotes. We use 

only the dates, for which all the quotes of variables of interest were available.  



Ewa M. Syczewska 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 93–104 

96

 
Figure 1. Logarithmic returns of the DAX index 

 
Figure 2. Volatility as in (2)  of the DAX index 

 During the subprime, global and Euro area crisis the volatility substan-
tially increases. The last column of Table 2 gives a measure of this increase, 
computed as a relative change of standard deviations for the second as com-



The EURPLN, DAX and WIG20: the Granger Causality… 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 93–104 

97

pared to the first subsample. The increase is close to 25% for the WIG20 
returns, and around 70% for the EURPLN exchange rate and the DAX in-
dex. The volatility (2) increases are even higher, by 60% for WIG20, almost 
100% for the DAX index and almost 130% for the EURPLN exchange rate.  

Table 1. Summary statistics, 1098 daily observations from 30th Apr. 2004 to 15th 
Sept. 2008 (“before crisis”) 

Variable Mean Median Std. Dev. Skewness Kurtosis 
Doornik-
Hansen 

test 
ld_EURPLN  –0.0323  –0.0361 0.46162 0.1670 1.4535 67.946 

ld_DAX  0.0377 0.1084 1.0459 –0.5392 3.8284 238.571 
ld_WIG20  0.0274 0.0696 1.4138 –0.2944 1.4172 61.228 

rDAX  1.2353 1.0810 0.69478 2.7689 16.812 696.955 
rWIG20  1.7240 1.5224 0.84969 1.9266 6.7395 568.593 

rEURPLN  0.6831 0.6207 0.31109 1.5026 4.3757 329.235 
 

2. The Granger Causality Test 

 The Granger test of the Granger causality, applied to the returns of the 
exchange rate and the corresponding stock indices, can be treated as a tool 
for choice of explanatory variables in the model for exchange rates. Accord-
ing to the well-known definition, a variable  is called  a Granger-cause for 
a variable , if lagged values of  used as additional regressors in a model 
describing  can improve quality of model and/or forecasts4. There are sev-
eral tests of this property. Let  denote observation of the  variable for 
period , , 1,2, … ,  – lagged observations for the same variable, 

	, 0,1,2, … ,  – current and lagged values of , , ,	
1,2, … , , 0,1,2, … ,  – parameters of the model, – error terms.  

 The Granger test of Granger causality is based on VAR – type regres-
sions (regression of Y on its lagged values and the same lags of the X varia-
ble): 

tktkttktktt xbxbxbyayay   12121111111 ...... .  (3) 

The null H0: 0... 11211  kbbb  means that the  does not Granger-cause 
the Y variable. Another variant is so-called instantaneous causality: the re-
gression includes current value of the  variable: 

                                                 
4 But see also the detailed discussion of Granger causality concepts and their interpreta-

tion in Osińska (2008, 2011). 



Ewa M. Syczewska 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 93–104 

98

    tktktttktktt xbxbxbxbyayay   1212111101111 ...... . (4) 

The null H0: 0... 1121110  kbbbb  in (4) means that  is not an 
instantaneous cause for .  

Table 2. Summary statistics, 1098 daily observations from the period 16 Sept. 2008 
to 1rd Feb. 2013 (“during crisis”) 

Va
ria

bl
e 

M
ea

n 

M
ed

ia
n 

St
d.

 D
ev

 

Sk
ew

ne
ss

 

Ku
rto

si
s 

D
oo

rn
ik

-H
an

se
n 

te
st

 

In
cr

ea
se

 o
f 

St
d.

 D
ev

. 
 

ldEURPLN 0.0197 –0.019 0.812 0.040 2.963 216.86 75.97% 
ldDAX 0.0233 0.089 1.754 0.123 5.389 507.16 67.68% 

ldWIG20 0.0051 0.057 1.756 –0.289 3.150 217.24 24.19% 
rDAX 2.0195 1.638 1.384 2.212 7.333 1074.24 99.16% 

rWIG20 1.9622 1.552 1.359 2.544 10.458 1224.63 59.95% 
rEURPLN 1.0716 0.850 0.715 2.283 7.116 1382.02 129.80% 

 
 The results of the Granger causality tests for the EURPLN exchange rate 
returns and the corresponding German and Polish stock indexes returns are 
the following. (We use LS estimates with robust standard errors; p-values 
are given in brackets.) 

2.1. Comparison of Results for Periods Before and During the Crisis  

 First we perform the test for subperiod between 2004–2008, i.e. before 
the crisis (more precisely: since 29 April 2004 until 15th Sept. 2008, 1098 
observations), and compare the results for a similar subsample (with the 
same number of observations) starting on 16th Sept. 2008, and ending at 
2nd Feb. 2013. For each pair of the variables the VAR model was estimated. 
The ∙,∙  test statistic presented in the second and third column of the Ta-
ble 3 corresponds to the null hypothesis that all lags of the explanatory vari-
able are insignificant in the equation for the dependent variable. Next, in 
order to test instantaneous Granger causality, we estimate the regression (4) 
using the OLS with heteroskedasticity and autocorrelation consistent stand-
ard errors, and test the restriction H0: 0... 1121110  kbbbb . The results 
of this test for both periods are given in Table 4.  
 In case of pre-crisis period, the null of no causality was not rejected, for 
data covering the crisis period, only in one case – namely the causality from 
the EURPLN exchange rate returns to the WIG20 stock index returns, the 
null of causality has not been rejected (see Table 3). The results of the linear 



The EURPLN, DAX and WIG20: the Granger Causality… 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 93–104 

99

Granger instantaneous causality test are different. The null hypothesis of 
lack of causality has been rejected in all the cases (see Table 4).  

Table 3. Linear Granger causality before and during the crisis 

Causality The test statistic [p-value] 
Pair of variables Before the crisis During the crisis 

ldDAX to ldEURPLN 0.550 [0.731] 0.217 [0.955] 
ldEURPLN to ldDAX 1.521 [0.180] 1.032 [0.397] 

ldWIG20 to ldEURPLN 0.880 [0.494] 0.771 [0.571] 
ldEURPLN to ldWIG20 1.648 [0.145] 3.660 [0.0027]*** 

ldDAX to ldWIG20 0.984 [0.427] 1.5016 [0.187] 
ldWIG20 to ldDAX 0.469 [0.800] 0.283 [0.923] 

Table 4. Instantaneous Granger causality before and during the crisis 

Instantaneous causality The test F-statistic [p-value] 
Pair of variables Before the crisis During the crisis 

ldDAX to ldEURPLN 10.875 [8.798e-012]*** 46.066 [2.090e-050]*** 
ldEURPLN to ldDAX 9.652 [2.279-010]*** 27.905 [4.170e-031]*** 

ldWIG20 to ldEURPLN 15.021 [1.439e-016]*** 31.744 [2.636e-035]*** 
ldEURPLN to lnWIG20 11.026 [5.888-012]*** 47.805 [3.519e-052]*** 

ldWIG20 to ldDAX 36.004 [6.862-040]*** 75.458 [8.618e-079]*** 
ldDAX to ldWIG20 54.246 [1.215-058]*** 116.092 [3.142e-113]*** 

Linear Causality Tests for the Volatility Measure (2) 

 The similar computations of the linear Granger test have been repeated 
using the volatility measure (2) instead of the log returns. Before the crisis 
the linear test indicates causal relation only from volatility of WIG20 to one 
of the DAX stock index (and we would expect the influence to work the 
other way round). During the crisis the null hypothesis of lack of causality is 
rejected for all pairs of instruments with exception of rDAX to rEURPLN 
and to rWIG20 (see Table 5).  

Table 5. The Granger causality test for volatility measure (2)  

Causality The test statistic [p-value] 
Pair of variables Before the crisis During crisis 

rDAX to rEURPLN 1.1059 [0.3554] 1.7194 [0.1273] 
rEURPLN to rDAX 0.8221 [0.5339] 2.5659 [0.0256]** 

rWIG20 to rEURPLN 1.2961 [0.2631] 3.0783 [0.0091]*** 
rEURPLN to rWIG20 0.1288 [0.9859] 2.4572 [0.0317]** 

rDAX to rWIG20 0.5797 [0.7156] 1.4111 [0.2175] 
rWIG20 to rDAX 2.4223 [0.0340]** 2.4853 [0.0300]** 



Ewa M. Syczewska 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 93–104 

100

Table 6. The instantaneous causality linear test 

Instantaneous causality The test statistic [p-value] 
 Before the crisis During the crisis 

rDAX to rEURPLN 3.934 [0.0006]*** 11.447 [1.92e-12]*** 
rEURPLN to rDAX 2.251 [0.0365]** 9.099 [9.91e-10]*** 

rWIG20 to rEURPLN 1.886 [0.0801]* 8.247 [9.50e-09]*** 
rEURPLN to rWIG20 0.734 [0.6222] 5.999 [3.48e-06]*** 

rDAX to rWIG20 23.263 [6.06e-26]*** 24.122 [6.61e-27]*** 
rWIG20 to rDAX 9.934 [1.08e-10]*** 17.241 [4.07e-19]*** 

 
The results of the instantaneous causality test before the crisis are in better 
agreement with the intuition. There is a strong influence from rDAX to the 
exchange rate, weaker from rWIG20 to rEURPLN, and feedback between 
the two stock indices (see the second column of the Table 6). Last column of 
the same Table shows results indicating strong feedback between all pairs of 
variables.  

3. The Diks-Panchenko Causality Test  

 The improved version of nonlinear Hiemstra-Jones test was introduced 
by Diks and Panchenko (2006). The idea of this nonparametric test is the 
following: The variable X  Granger-causes the Y , if the current and lagged 
values of the kttt xxxX  ,...,,: 1  contain information concerning the future 

values ,..., 21  tt yy , additional to that contained in current and past values of 
this variable. In their paper Diks and Panchenko test conditional independ-
ence of finite number of lags:  

),...,,(|~),...,,,,...,,(| 11111111  XYx lttttltttltttt XXXYYYYXXXY , 

where lX, lY denote numbers of lags of the variables  and , respectively. 
The Diks-Panchenko test is an improved version of the Hiemstra-Jones test, 
based on comparison of the conditional distributions5.  
 Diks and Panchenko use one lag for the variables and the 1tY  forecast 

for the next period. Let ),,(),,( 1 ZYXYYX ttt   and assume that X  and Y  
are strictly stationary variables. The null hypothesis of lack of causality 
means that the conditional distribution of Z  with respect to Y  and X  is the 
same as the conditional distribution of Z  with respect to Y  alone. The joint 
distribution and the marginal distributions are described by the formula 

                                                 
5 More detailed analysis of this test can be found in Osińska (2008), pp. 226–229. 



The EURPLN, DAX and WIG20: the Granger Causality… 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 93–104 

101

)(/),(),(/),,( ,,,, yfzyfyxfzyxf YZYYXZYX  . Diks and Panchenko (2006) 

show some deficiencies of the Hiemstra and Jones approximation of both 
sides of this formula, and propose their own versions: the null hypothesis of 
lack of causality implies that  

    0),,(
)(

),(

)(

),(

)(

),,( ,,,, 



















 ZYXg

Yf

ZYf

Yf

YXf

Yf

ZYXf
Eq

Y

ZY

Y

YX

Y

ZYX
g ,  (5) 

where ),,( ZYXg  denotes a positive weights function, e.g. for 

)(),,( 2 YfZYXg Y  this simplifies to:  

)],(),()(),,([ ,,,, ZYfYXfYfZYXfEq ZYYXYZYXg  . 

Under the null, the expression in parentheses is equal to zero, hence (5) is 
equal to zero. The null of no causality is rejected if the test statistic is high.  
Diks and Panchenko (2006) advocate use for (5) of the following estimator 
based on index function  

   
















 



i ikk jj

YZ
ij

XY
ik

Y
ij

ZYX
ik

ddd

n IIII
nnn

T
ZYX

, 1,

,,

)2)(1(

)2(
)(

 , 

where: 
n  – number of observations, Xd  – number of elements of the X  vector 

etc., 
W

jiI ,  is the index function )(,  ji
W

ji WWII  is equal to 1 if 

 ji WW  and to 0 otherwise, 

  denotes the supremum norm.  

Diks and Panchenko give formula for choice of the   (bandwith) depending 
on number of observations (the default value is 0.5). They show that when 

1 ZYX ddd , the estimator is consistent and has asymptotic Gaussian 
distribution. Their code for application of the test both for Linux and for 
Windows is available at the Panchenko’s webpage: 
http://research.economics.unsw.edu.au/vpanchenko/software/2006_GC_JED
C_c_and_exe_code.zip. 

The Results of the Diks-Panchenko Test  

In our computations we assume 0.5 bandwidth, and we compute the nT  sta-
tistic for one lag. The results are the following (see Table 7). During the 



Ewa M. Syczewska 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 93–104 

102

crisis, the null of lack of causality is strongly rejected for all pairs of varia-
bles. For period 2004–2008, “before the crisis”, the test does not indicate 
causal relationship for logarithmic returns, with only exception of ldDAX  
ldWIG20 influence (the upper part of the Table 7). In case of our volatility 
measure, the nT  test statistic indicates feedback between rDAX and 
rWIG20, and some influence from rWIG20 towards rEURPLN (the lower 
part of the Table 7), all at 10%.  

Table 7. The Diks-Panchenko causality test  

Causality for variables 
The Diks-Panchenko test statistics  

[p-value] 
Logarithmic returns Before the crisis  During the crisis  

¬ ldDAX → ldEURPLN  0.479 [0.3158]  2.697 [0.0035]*** 
¬ ldEURPLN → ldDAX –0.661 [0.7458]  3.506 [0.00023]*** 
¬ ldDAX → ldWIG20  1.541 [0.0617]*  3.589 [0.0017]*** 
¬ ldWIG20 → ldDAX  –0.916 [0.8202]   3.118 [0.0009]*** 

¬ ldEURPLN → ldWIG20  –0.760 [0.7763]  3.625 [0.0014]*** 
¬ ldWIG20 → ldEURPLN –1.648 [0.9503]  2.525 [0.0056]*** 

ln(maxPt/minPt) Before the crisis  During the crisis  
¬ rDAX → rEURPLN –1.104 [0.8652]  2.922 [0.0017]*** 
¬ rEURPLN → rDAX –1.253 [0.8949]  3.612 [0.0002]*** 

¬ rWIG20 → rEURPLN  1.634 [0.0511]*  4.168 [0.0000]*** 
¬ rEURPLN → rWIG20  –1.087 [0.8615]  4.145 [0.0000]*** 

¬ rDAX → rWIG20  1.505 [0.0662]*  2.824 [0.0024]*** 
¬ rWIG20 → rDAX   1.595 [0.0554]*   4.559 [0.0000]*** 

Conclusions 

 The results of the two approaches for testing the Granger causality, pre-
sented here for a daily closing values of the EURPLN exchange rate and the 
two corresponding stock indices – one for Germany as representing the Euro 
zone (DAX), the other for Poland (WIG20) – seem to be influenced by peri-
od and the method of testing. Economic intuition and previous results con-
cerning similar analysis for the USDPLN exchange rate and the two repre-
sentative indices for the U.S. and the Polish stock exchange suggested that 
the global crisis have changed the direction and strength of the causal rela-
tionship for the logarithmic returns, as measured by the linear Granger test of 
the Granger causality. There were differences in lack or presence of  
G-causality between the analysed pairs of variables, and seeming increase of 
the U.S. data influence during the crisis (perhaps a reflection of temporal 
changes in capital flows in the global economy).  
 Here, for the EURPLN exchange rate and the DAX and WIG20 stock 
index, we note much higher homogeneity of results – lack of causality before 



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DYNAMIC ECONOMETRIC MODELS 14 (2014) 93–104 

103

crisis, overall presence of two-side causality during the crisis – when the 
tests are applied to the volatility measure (2). Both the linear Granger test 
and the nonlinear Diks-Panchenko test give similar results (see Table 5 and 
the lower part of the Table 7).  
 Results of the linear Granger test for the logarithmic returns are differ-
ent: this version of the test does not reject lack of linear causal relationship 
neither before the crisis nor during the crisis (see Table 3) with one excep-
tion of Granger-causality from the EURPLN towards WIG20 during the 
crisis. The Diks-Panchenko nonlinear test, on the other hand, does not reject 
lack of causality before the crisis, but strongly rejects it during the crisis (see 
upper part of the Table 7).  
 Additional computations for the instantaneous causality in the linear 
framework show that there is a feedback between all pairs of logarithmic 
returns and indicate Granger causality also for the volatility measure, even 
before the crisis (see Table 4 and 6). The possible explanation of this differ-
ence between (lagged) causality test and instantaneous causality test merits 
further attention – perhaps partial explanation could be based on possible 
analysis of efficiency of the markets, as it seems that changes in returns and 
volatility seem to influence the other instrument at once, on the same day. 
The future research can also take into account indirect influence of other 
variables (e.g., the U.S. indices) on causal relationship between the two Eu-
ropean instruments.  

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Brooks, Ch. (2008), Introductory Econometrics for Finance, 2nd ed., Cambridge University 
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–1669, DOI: http://dx.doi.org/10.1016/j.jedc.2005.08.008.  

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169–180. 

EURPLN, DAX i WIG20: testy przyczynowości Grangera  
przed i podczas kryzysu 

Z a r y s  t r e ś c i. Artykuł dotyczy przyczynowości w sensie Grangera zastosowanej do 
dziennych notowań kursu EURPLN oraz odpowiadających mu dwu indeksów – DAX 
i WIG20. Przedstawia wyniki zastosowania dwu wariantów liniowego testu Grangera – 
w tym wariantu dla tzw. natychmiastowej przyczynowości – oraz nieliniowego testu Diksa-
Panchenki do logarytmicznych zwrotów badanych instrumentów oraz do miary odzwiercie-

dlającej zmienność dzienną ln ,

,
 jako proporcję minimalnych i maksymalnych 

notowań w dniu . Różnice pomiędzy wynikami testu przyczynowości dla par zwrotów po-
między okresem poprzedzającym kryzys a okresem kryzysu nie są tak duże jak w badaniach 
dotyczących kursów i indeksów polskich i amerykańskich. Widoczna jest natomiast różnica 
pomiędzy wynikami dla zwrotów i dla miary zmienności.  

S ł o w a  k l u c z o w e: kurs walutowy, indeksy giełdowe, kryzys finansowy, ryzyko, przy-
czynowość w sensie Grangera, natychmiastowa przyczynowość, test Diksa-Panchenki.  


