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© 2013 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.2013.001  Vol. 13 ( 2013) 5−31 

Submitted June 16, 2013  ISSN 
Accepted December 5, 2013 1234-3862 

Małgorzata Doman, Ryszard Doman*  

The Dynamics and Strength of Linkages between  
the Stock Markets in the Czech Republic, Hungary  

and Poland after their EU Accession∗∗  

A b s t r a c t. We analyze the dynamics and strength of linkages between the Czech, Hungari-
an and Polish stock markets after the EU accession of the corresponding countries. In addi-
tion, we examine linkages between each of the markets and developed markets (European and 
US). The analysis is based on the daily quotations of the main representative stock indices 
(PX, BUX, WIG20, DAX, S&P 500) and includes the period from May 5, 2004 to July 20, 
2012. The dynamics of dependencies is modeled by means of Markov-switching copula mod-
els, and the applied measures of the strength of the linkages are dynamic Spearman’s rho and 
tail dependence coefficients. The results show that dependencies between the considered 
emerging markets are very sensitive on market situation, but the linkages of these markets 
with the developed ones are stable. 

K e y w o r d s: Central European stock market, conditional dependence, Markov-switching 
copula model, Spearman’s rho, tail dependence, model confidence set, stock index.  

J E L Classification: G15; G01; C32; C58. 

                                                 
* Correspondence to: Małgorzata Doman, Poznań University of Economics, Department 

of Applied Mathematics, Al. Niepodległości 10, 61-875 Poznań, Poland, e-mail: malgorza-
ta.doman@ue.poznan.pl; Ryszard Doman, Adam Mickiewicz University  in Poznań, Faculty 
of Mathematics and Computer Science, Umultowska 87, 61-614 Poznań, Poland, e-mail: 
rydoman@amu.edu.pl. 

∗∗ This work was financed from the Polish science budget resources in the years 2010-
2013 as the research project N N111 035139. 



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

6

Introduction  
 In the paper, we analyze the dynamics and strength of linkages between 
the Czech (Prague Stock Exchange, PSE), Hungarian (Budapest Stock Ex-
change, BSE) and Polish (Warsaw Stock Exchange, WSE) stock markets 
after the EU accession of the corresponding countries. In addition, we exam-
ine the linkages between each of the markets and developed markets (Euro-
pean and US). The analysis is based on the daily quotations of the main rep-
resentative stock indices (PX, BUX,WIG20, DAX, S&P 500). The dynamics 
of dependencies is modeled by means of Markov-switching copula models 
and the applied measures of the strength of the linkages are dynamic Spear-
man’s rho and tail dependence coefficients. We investigate the period from 
May 5, 2004 to July 20, 2012. It begins shortly after the three considered 
Central European countries joined the European Union and includes 
subperiods of two recent financial crises (the US subprime and European 
debt crises). 

The Czech Republic, Hungary and Poland are often perceived by inves-
tors as one block of very similar markets. In particular, bad news concerning 
one of these countries strongly impacts all the markets. The history of the 
three economies looks similar. In 1989 all they started the transformation 
process, in May 2004 joined the European Union, and now all they are get-
ting ready to adopt the euro. Nevertheless, their specific paths of develop-
ment differ from each other. The impact of the recent crisis on the econo-
mies, measured with the evolution of the GDP annual growth rate, was dis-
similar to that exerted on the stock markets (see Federation of European 
Securities Exchange, 2013; Trading Economics, 2013). The stock mar-kets 
themselves are unlike each other as well. The Warsaw Stock Exchange plays 
the special role in the region as the largest stock exchange market (see Fed-
eration of European Securities Exchange, 2013). A comparison of the quota-
tions of the representing stock indices with the evolution of GDP annual 
growth rate in the considered countries (see Federation of European Securi-
ties Exchange, 2013; Trading Economics, 2013) shows that during the sub-
prime crisis of 2007–2009 all the markets experienced significant decline, 
and the same applies to their GDP growth rate, though the Polish GDP 
growth rate remained positive.  

There exists a quite extensive literature on linkages between the three 
Central European stock markets. Many investigations were performed for 
the period before the recent crises (see for instance Scheicher, 2001; Gilmore 
et al., 2008; Caporale, Spagnolo, 2011). Some newer papers on the subject, 
mostly concerning the impact of the recent crises, can also be found. For 



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DYNAMIC ECONOMETRIC MODELS 3 (2013) 5–31 

7 

instance, Ülkü and Demirci (2012) present a thorough analysis of the joint 
dynamics of foreign exchange and stock markets in emerging European 
countries for the period 2003–2010 and document the key role of global 
developed market returns in driving the stock market–exchange rate interac-
tion in emerging economies. Their study uses impulse response functions 
from a cointegrating structural vector autoregressive model as the research 
tool. Another methodology, involving a dynamical conditional correlation 
model, has been applied by Kiss (2011) who examines the transmission 
mechanism of interbank, stock and currency market crashes for the Czech 
Republic, Hungary and Poland as well as for the US and Euro area, using 
daily data from January 2002 to October 2010.  

The main novelty in our analysis is a detailed description of the dynam-
ics of two types of dependence between the considered markets: an average 
dependence measured by Spear-man’s rho, and tail dependence estimated by 
means of upper and lower tail dependence coefficients. Unlike Pearson’s 
correlation, which is invariant only under increasing affine trans-formations 
of the margins of a bivariate random vector, the dependence measures ap-
plied by us are invariant with respect to strictly increasing transformations of 
the margins. Hence, the measures are more suitable in detecting dependen-
cies of non-linear type between analyzed stock returns. In fact, we use 
a copula regime-switching approach to model the conditional bivariate dis-
tributions of the returns. So, the aforementioned properties of the applied 
depend-ence measures can be drawn from the fact that the measures are cop-
ula-based. What is more, using copulas models allows to leave behind the 
class of elliptical distributions. This is because, in this approach, description 
of the behavior of the marginals is separated from model-ing their depend-
ence structure. The advantages of our approach stem also from the fact that 
the tail dependence coefficients reflect the dependence in extreme values, 
which is very fruitful in describing the market linkages during crisis periods. 
Additionally, a Markov regime switching mechanism we use provides 
a possibility to model the temporal fluctuation of the strength and character-
istics of the modeled dependencies. We also compare the estimates of the 
measures of the dependencies between the Czech, Polish and Hungarian 
stock markets with the corresponding quantities obtained for the dependen-
cies between these markets and Western European and American stock mar-
kets represented by the stock indices DAX and S&P 500. Our results show 
that the dynamics of dependencies in the two cases are completely different, 
and that the dependencies between the emerging markets are more sensitive 
to new information flow. However, the linkages of these markets with the 
main world markets are rather stable.  



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

8

1. Markov-Switching Copula Models 
 Modeling the dynamics of dependencies between financial returns is not 
an easy task because of interaction between the volatility of the individual 
returns and the dependence structure. The interaction is especially apparent 
during the periods of financial crises and turbulence in financial markets 
(Ang, Bekaert, 2002; Forbes, Rigobon, 2002). In such circumstances, the 
investigation of the dynamics of the linkages becomes more difficult due to 
different types of asymmetries and structural breaks which are likely to arise 
(Ang, Bekaert, 2002; Ang, Chen, 2002; Patton, 2004). From the point of 
view of the choice of a suitable multivariate statistical model for the condi-
tional distribution of the returns, this means that elliptical distributions 
should hardly be assumed. As a consequence, multivariate GARCH models 
(see a survey by Bauwens et al., 2006) can be an inappropriate tool for mod-
eling the dynamics of linkages. In such a situation, a concept of copula can 
provide an alternative solution.  

A bivariate copula is a mapping :[0,1] [01] [0,1]C × →  from the unit square 
into the unit interval, which is a distribution function with standard uniform 
marginal distributions.  

Assume that ),( YX  is a 2-dimensional random vector with joint distribu-
tion H and marginal distributions F and G. Then, by a theorem by Sklar 
(1959), H can be written as: 

)).(),((),( yGxFCyxH =   (1) 

If F and G are continuous then the function C is uniquely given by the for-
mula: 

)),(),((),( 11 vGuFHvuC −−=   (2) 

for ]1 ,0[, ∈vu , where 1( ) inf{ :   ( ) }F u x F x u− = ≥  (Nelsen, 2006). In this case, 
C is called the copula of H or of ( , )X Y . Since the marginal distributions in 
the decomposition (1) are separated, it makes sense to interpret C as the de-
pendence structure of the vector ( , )X Y . We refer to Patton (2009) and refer-
ences therein for an overview of applications of copulas in analysis of finan-
cial time series.  

The simplest copula is defined by uvvuC =Π ),(  and it corresponds to 
independence of marginal distributions. In the empirical part of this paper 
we will also use the Gaussian, Clayton, and Joe-Clayton copulas. They are 
defined as follows: 



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DYNAMIC ECONOMETRIC MODELS 3 (2013) 5–31 

9 

( ), )(),(),( 11 vuvuCGauss −− ΦΦΦ= ρρ  (3)  

,)1(),( 1 γγγ
γ

−−− −+= vuvuC Clayton  (4) 

( ) ,)1])1(1[])1(1([11 

),(
/1/1

,

κγγκγκ

γκ

−−−

−

−−−+−−−−=

=

vu

vuC ClaytonJoe

   (5) 

where ρΦ  denotes the distribution of a 2-dimensional standardized normal 
vector with the linear correlation coefficient ρ , Φ  stands for the standard 
normal distribution function, and 1≥κ , 0>γ . The Clayton copula ClaytonC γ is 

a special case of the Joe-Clayton copula ClaytonJoeC −
γκ ,  for 1=κ . In the limit 

case 0=γ , the Clayton copula approaches the independent copula ΠC  (Nel-
sen, 2006).  

The density associated to an absolutely continuous copula C is a function 
c defined by: 

.),(),(
2

vu
vuCvuc

∂∂
∂

=  (6) 

For an absolutely continuous random vector, the copula density c is related 
to its joint density function h by the following canonical representation: 

),()())(),((),( ygxfyGxFcyxh =  (7) 

where F and G are the marginal distributions, and f and g are the marginal 
density functions.  

In the case of nonelliptical distributions, the most well-known copula-
based dependence measures, which are more appropriate than the linear cor-
relation coefficient, are Kendall’s tau and Spearman’s rho (Embrechts et al., 
2002). Since the dynamics of Spearman’s rho is exploited in this paper, we 
recall a suitable definition. If ( , )X Y  is a random vector with marginal distri-
bution functions F and G, then Spearman’s rho for ( , )X Y  can be defined as: 

)),(),((),( YGXFYXS ρρ =  (8)  

whereρ denotes the usual Pearson correlation. For continuous marginal dis-
tributions, Spearman’s rho, ( , )S X Yρ , depends only on the copula C linking 
X and Y, and, in particular, is given by the formula: 

3),(12),( 2]1,0[ 
−== ∫∫ dudvvuCYX CS ρρ  (9) 



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

10

 (Nelsen, 2006). It follows from (9) that if a copula C is a mixture of copulas 
1C  and 2C : 21 )1( CCC αα −+= , 10 ≤≤α , then:  

.)1(
21 CCC ρααρρ −+=  (10) 

For the Gaussian copula, GaussCρ , Spearman’s rho equals ρπ 2
16 arcsin . For the 

Clayton and Joe-Clayton copulas it can be computed numerically using (9).  
Another concept of dependence, which depends only on the copula of 

a random vector ),( YX , is tail dependence. It measures the dependence be-
tween extreme values of the variables. If F and G are the cumulative distri-
bution functions of X and Y, then the coefficient of upper tail dependence is 
defined as follows: 

)),(|)((lim 11
1 qFXqGYPqU

−−
→

>>= −λ  (11) 

provided a limit ]1,0[∈Uλ  exists. Analogously, the coefficient of lower tail 
dependence is defined as: 

)),(|)((lim 11
0 qFXqGYPqL

−−
→

≤≤= +λ   (12) 

provided that a limit [0,1]Lλ ∈   exists. If (0,1]Uλ ∈  ( (0,1]Lλ ∈ ), then X and 
Y are said to exhibit upper (lower) tail dependence. Upper (lower) tail de-
pendence quantifies the likelihood to observe a large (low) value of Y given 
a large (low) value of X. The coefficients of tail dependence can be ex-
pressed in terms of the copula C of X and Y in the following way: 

,),(lim 0 q
qqC

qL +→
=λ   (13) 

,),(ˆ
lim 0 q

qqC
qU +→

=λ  (14) 

where )1,1(1),(ˆ vuCvuvuC −−+−+= . For the Gaussian copula it holds 
0== LU λλ  (see Embrechts et al., 2002), meaning asymptotic independence 

in the tails. The Clayton copula ClaytonCγ has lower tail dependence: 1/2 .L
γλ −=  

In the Joe-Clayton copula case, κλ /122 −=U  and γλ /12−=L  for 0γ >  (Pat-
ton, 2006). Thus both upper and lower tail dependence can be nonzero, and, 
moreover, they can change independently of each other.  

In applications of copulas to financial time series the notion of condi-
tional copula introduced by Patton (2004) is usually employed. It allows to 



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DYNAMIC ECONOMETRIC MODELS 3 (2013) 5–31 

11

model the joint conditional distribution 1| −Ω ttr , where ),(  ,2 ,1 ttt rr=r  is 

a bivariate vector of financial returns, and 1−Ωt is the information set availa-
ble up to time 1−t . In this paper we consider the following general condi-
tional copula model:  

),(  ~| 1,1 ⋅Ω − ttt Fr    ),(  ~| 1,2 ⋅Ω − ttt Gr  (15)                                      

),|)(),((~| 11 −− Ω⋅⋅Ω tttttt GFCr   (16) 

where tC  is the conditional copula linking the marginal conditional distribu-
tions, and the information set 1−Ωt remains the same for the copula and 
marginals. Further, we assume that:   

,ttt yμr +=     ),|( 1−Ω= ttt E rμ   (17) 

,,,, tititiy εσ=    ),|var( 1,
2
, −Ω= ttiti rσ   (18) 

),,,1 ,0(_ iid~, iiti tSkew ηξε   (19) 

where ),,1 ,0(_ ηξtSkew  denotes the standardized skewed Student t distribu-
tion with 2>η  degrees of freedom, and skewness coefficient 0>ξ  (Lambert, 
Laurent, 2001). Moreover, the marginal return series tir , , 2 ,1=i , are mod-
eled as ARMA-GARCH processes. 

When the conditional copula tC  is allowed to fluctuate over time, some 
model for its evolution has to be specified. Commonly, the functional form 
of the conditional copula is fixed but its parameters evolve through time 
(Patton, 2004, 2006). In this paper, however, we apply an alternative ap-
proach (Okimoto, 2008; Garcia, Tsafack, 2011) assuming the existence of 
regimes where a fixed copula prevails, which are switched according to 
some homogeneous Markov chain. Thus, in the applied Markov-switching 
copula model (MSC model) the joint conditional distribution has the follow-
ing form: 

),|)(),((~| 11 −− Ω⋅⋅Ω tttStt GFC
t

r  (20) 

where tS  is a homogeneous Markov chain with state space }2 ,1{ . The pa-
rameters of the model are the parameters of the univariate models for the 
marginal distributions, the parameters of the copulas 1C  and 2C , and the 
transition probabilities: 



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

12

11 1( 1| 1),t tp P S S −= = =  22 1( 2| 2)t tp P S S −= = =   (21) 

of the Markov chain.  
We estimate the MSC models by the maximum likelihood method. 

 The main by-product of the estimation are the probabilities ),|( 1−Ω= tt jSP  
)|( tt jSP Ω= , 2 ,1=j , which are calculated by means of Hamilton’s filter 

(Hamilton, 1994):  

,)|()|(
2

1
111 ∑

=
−−− Ω==Ω=

i
ttijtt iSPpjSP  (22) 

,
)|(),|(

)|(),|(
)|( 2

1
11

11

∑
=

−−

−−

Ω=Ω=

Ω=Ω=
=Ω=

i
ttttti

tttttj
tt

iSPiSc

jSPjSc
jSP

u

u
 (23) 

where:          
12 1 11( 2 | 1) 1t tp P S S p−= = = = − , 21 1 22( 1| 2) 1t tp P S S p−= = = = − ,  

),,( ,2,1 ttt uu=u  )( ,1,1 ttt rFu = , )( ,2,2 ttt rGu = ,   (24) 

and ),|( 1−Ω=⋅ ttj jSc  is the density of the conditional copula coupling the 
conditional marginal distributions in regime j. By the arguments of Hamilton 
(1994), the maximized log-likelihood function has the form: 

( ) ( )∑∑

∑ ∑

=
−

=
−

=
−

=
−

Ω+Ω+

⎟
⎟
⎠

⎞
⎜
⎜
⎝

⎛
Ω=Ω==

T

t
ttt

T

t
ttt

T

t
tt

j
tttj

rgrf

jSPjScL

1
21,2

1
11,1

1
1

2

1
1

);|(ln);|(ln   

);|();,|(ln

θθ

θθu

, (25)   

where tf  and tg  are the density functions corresponding to tF  and tG , 
fitted using ARMA-GARCH models. 

In the empirical results presented in this paper we apply the so-called 
smoothed probabilities which can be obtained from the probabilities (23) and 
(24) by using the backward recursion: 

, 
)|(

)|(
)|()|(

2

1 1

1∑
= +

+

Ω=

Ω=
Ω==Ω=

i tt

Ttji
ttTt iSP

iSPp
jSPjSP  

 .1,,1…−=Tt   (26) 



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DYNAMIC ECONOMETRIC MODELS 3 (2013) 5–31 

13

The series )|( Tt jSP Ω=  indicates which regime prevails at each date, using 
all the information in the sample. 

2. The Model Confidence Set Methodology 
 The Model Confidence Set (MCS) methodology, introduced by Hansen 
et al. (2003), is usually applied to select in a set of forecasting models a sub-
set of models which are better than the others in terms of forecasting ability, 
with a given level of confidence. More precisely, for some collection 0  of 
models for which the subset of superior models, * , is defined, the MCS 
procedure produces a subset ˆ  of 0 that contains the set *  with a giv-
en confidence level α−1 . The collection 0  can be any finite set of ob-
jects indexed by 01, ,i m= …  and evaluated in terms of a loss function that 
assigns to the object i  in period t the loss ,i tL , 1, ,t n= … . If the relative 

performance is defined as , , ,ij t i t j td L L≡ −  for 0,i j∈  and the mean

,( )ij ij tE dμ ≡  is finite and does not depend on t, then the set of superior ob-
jects is defined by: 

{ }* 0 0: 0 for all  iji jμ≡ ∈ ≤ ∈ . 

The MCS procedure is based on an equivalence test δ that tests the hy-
pothesis:  

0, : 0ijH μ =  for all ,i j∈ ,  

 at levelα for any 0⊂ . When 0,H  is rejected, an elimination rule e  
is applied to identify the object of  that is to be removed from . The 
MCS algorithm proposed by Hansen et al. (2003) is as follows: 
− Step 0: Set 0 . 
− Step 1: Test 0,H  using δ  at significance level α . 

− Step 2: If 0,H  is not rejected define, *
  1
ˆ

α− = , otherwise use e  to 
eliminate an object from and repeat the procedure from Step 1. 

It is proved in Hansen et al. (2011) that under some standard requirements 
for the equivalence test and the elimination rule it holds that: 

* *
  1
ˆliminf ( ) 1 ,n P α α→∞ −⊂ ≥ −   (27) 



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

14

*
  1
ˆlim ( ) 0n P i α→∞ −∈ = for all *,i∉  (28) 

* *
  1
ˆlim ( ) 1n P α→∞ −= =  if *  is a singleton. (29) 

If 
0  , iHP denotes the p-value associated with the null hypothesis 

 0, i
H  (with 

convention that 
0  0, 1

mHP = ) , then the MCS p-value for model 
  

0
j

e ∈M  is 

defined as 
0    ,ˆ max .

j ie i j Hp P≤≡  

It is shown in Hansen et al. (2011) that 0,H  can be tested using tradi-
tional quadratic-form statistics or multiple t-statistics. In this paper we apply 
the t-statistic ,RT  defined as: 

, ,
max | |,R iji j

T t
∈

=  (30) 

where: 

( )ˆvar
ij

ij

ij

d
t

d
=  for ,i j∈ ,  (31) 

and 1
,1

n
ij ij ttd n d−

=
= ∑ . The asymptotic distribution of the statistic ,RT  is 

nonstandard. The bootstrap implementation of the MCS procedure involving 
this statistic is described in Appendix B in the paper by Hansen et al. (2003). 
The estimated bootstrap distribution of ,RT , under the null hypothesis, is 
given by the empirical distribution of:  

( )
*
,*

, ,

| |
max

ˆvar
b ij ij

b R i j
ij

d d
T

d∈

−
= , (32) 

where * 1
, ,1 bt

n
b ij ijn t

d d τ=
= ∑  is the bootstrap resample average, and 

( ) ( )2*1
,1

ˆvar B
ij b ij ijB b

d d d
=

= −∑ . For generating B resamples, the block boot-

strap is used. The p-value of 0,H  is given by: 

0,

*
, ,

1

1 1{ }
B

H b R R
b

P T T
B =

= >∑ . (33) 

Even though the MCS methodology was originally designed in Hansen 
et al. (2003) to select the best volatility forecasting models, its applications 
are not limited to comparisons of models. It can be used as well to compare 



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DYNAMIC ECONOMETRIC MODELS 3 (2013) 5–31 

15

the means of two or more populations. In this paper, we apply the MCS pro-
cedure to establish rankings of strength of conditional dependencies between 
the investigated stock markets, calculated by means of the discussed copula-
based measures of dependence. 

3. The Data 
 The dataset used in the analysis includes closing quotations of the fol-
lowing stock indices: the Hungarian BUX, the Czech PX, the Polish WIG20, 
the DAX, and the S&P 500, from the period May 5, 2004 to July 20, 2012. 
The period under scrutiny begins after the Czech Republic, Hungary and 
Poland joining the European Union. This allows us to avoid a possible struc-
tural break in the data caused by that event. The quotations of the PX index 
were obtained from the website of the Prague Stock Exchange, and those of 
the other indices come from the website Stooq.pl.  
 

 

Figure 1. Time plots of daily quotations of BUX/10, PX, WIG20, DAX/5 and 
S&P500 from May 5, 2004 to July 20, 2012. Scaling in the case of BUX 
and DAX is performed for easier comparison  

Since the patterns of non-trading days in the national stock markets dif-
fer, for the purposes of modeling the dependencies, the dates of observations 
for all the indices were checked and observations not corresponding to ones 
in the other index quotation series were removed. The plots of the adjusted 
series of quotations are presented in Figure 1. The modeled time series are 
percentage logarithmic daily returns calculated by the formula: 

0

500

1000

1500

2000

2500

3000

3500

4000

4500

05/04/2004 02/24/2005 12/27/2005 10/19/2006 08/23/2007 06/23/2008 04/20/2009 02/16/2010 12/13/2010 10/07/2011

BUX/10 PX WIG20 DAX/5 S&P500



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

16

1100  (ln ln )t t tr P P−= − , (34) 
where tP  denotes the closing index value on day t. 

 
Figure 2.  Evolution of GDP annual growth rate in the Czech Republic, Hungry, 

Poland, the UE, and the USA, 2004–2012. Data source: Trading Econom-
ics (2013)  

 

Figure 3.  Market capitalization of the stock exchanges WSE, BSE, and PSE in mil-
lions euro, 2004–2012  

Data source: Federation of European Securities Exchanges (2013). 

‐10

‐8

‐6

‐4

‐2

0

2

4

6

8

10

Czech Republic Hungary Poland  EU USA

0

20 000

40 000

60 000

80 000

100 000

120 000

140 000

160 000

2004 2005 2006 2007 2008 2009 2010 2011

WSE BSE PSE



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In Figure 2, we show time plots displaying the evolution of GDP annual 
growth rate in the Czech Republic, Hungry, Poland, the UE, and the USA 
during the period under scrutiny. The market capitalization of the analyzed 
stock exchanges is presented in Figure 3 and shows the leading position of 
the Warsaw Stock Exchange in the region. From the plots in Figures 1–3, it 
is evident that during the subprime crisis of 2007–2009 all the markets expe-
rienced significant decline, and that the same applies to their GDP growth 
rate, though the Polish GDP growth rate remained positive.  

As in many papers dealing with dynamic copula models, we separate the 
estimation of models for marginal distributions from the estimation of the 
model for the dependence structure. The resulting multi-stage maximum 
likelihood estimation method, known as „inference functions for margins” 
(Joe, Xu 1996; Joe, 1997), is not fully efficient but there are simulation re-
sults that motivate this approach (Patton, 2009). To describe marginal distri-
butions, we use ARMA-GARCH models. The estimation of the parameters 
of the marginal distributions (ARMA-GARCH) was performed using 
G@RCH6.2 package (Laurent, 2009; Doornik, 2006).  

 
Figure 4.  Volatility estimates for the indices DAX, S&P 500, BUX, WIG20, and PX 

for the period May 5, 2004 – July 20, 2012 

In Table 1, the parameter estimates of best fitted models are presented. 
In the case of the WIG20, the best fitted model is GARCH(3,1) with the 
innovation term following a standardized Student t distribution. The result 
indicates lack of asymmetry in volatility dynamics. For all the other indices, 
the chosen volatility models are ARMA-GJR-GARCH models specified as: 

0

10

20

30

40

50

60

70

80

05/05/2004 12/15/2004 07/29/2005 03/08/2006 10/20/2006 06/11/2007 01/25/2008 09/04/2008 04/21/2009 12/03/2009 07/19/2010 02/25/2011 10/10/2011 05/25/2012

DAX S&P500 BUX WIG20 PX



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

18

,)(
11

t

q

i
iti

p

i
itit yybrar ++−=− ∑∑

=
−

=
− μμ  (35) 

,ttty εσ=  (36) 

( )( )2 2 2 2

1 1
0 ,

q p

t i t i i t i t i j t j
i j

y I y yσ ω α γ β σ− − − −
= =

= + + < +∑ ∑  (37) 

where I is the indicator function. 

Table 1.  Parameter estimates for fitted GJR-GARCH models 
Parameters BUX PX WIG20 DAX S&P500 

μ  0.0542 
(0.0294) 

0.0586 
(0.0239) 

0.0563 
(0.0278)  0.0313 

(0.157) 

1a  0 0.0257 
(0.0249)   0.6577 

(0.1084) 

2a   –0.0550 
(0.0226) 

 –0.005 
(0.0236)    

1b       –0.7240 
(0.0987) 

ω  0.0743 
(0.0221) 

0.0622 
(0.0166)  0.0309 

(0.0099) 
0.0146 

(0.0053) 

1α  0.0581 
(0.0206) 

0.0919 
(0.0193) 0  –0.0214 

(0.0095) 
 –0.0860 
(0.0097) 

2α    0  0 

3α    0.1040 
(0.0202)  0.0828 

(0.0153) 

1γ  0.0859 
(0.0255) 

0.0898 
(0.0332)  0.1784 

(0.0376) 
0.0952 

(0.0317) 

2γ      0.1876 
(0.0568) 

3γ       –0.1644 
(0.0283) 

1β  0.8741 
(0.0255) 

0.8351 
(0.0227) 

0.8833 
(0.0212) 

0.9177 
(0.0182) 

0.9106 
(0.0204) 

ξln    –0.0842 
(0.0289)   –0.1475 

(0.0263) 
 –0.1644 
(0.0283) 

DF 10.2987 
(2.0213) 

6.9791 
(1.0306) 

8,8613 
(1.5857) 

8.7099 
(1.7851) 

7.0120 
(1.1411) 

Figure 4 presents the plots of volatility (conditional variance) estimates 
from fitted models for the period from May 5, 2004 to July 20, 2012. The 
plots allow to easy identify periods of turmoil in financial markets. In the 
considered period, usually the PX index exhibits the highest volatility level. 
An explosion of volatility visible in Figure 4 is the result of a panic after 



The Dynamics and Strength of Linkages between the Stock Markets…                                                  

DYNAMIC ECONOMETRIC MODELS 3 (2013) 5–31 

19

bankruptcy of Lehman Brothers. The peaks in the volatility of the BUX and 
PX indices appearing just after October 22, 2008 are likely to be a reaction 
to Hungary’s request for financial support directed to the International Mon-
etary Fund.  

4. The Analysis of Dependencies 
 Modeling the dependencies between the European and the US market 
one meets the problem of non-synchronic observations due to different trad-
ing hours. There is no a really good solution to this difficulty. The most fre-
quently applied approaches include using weekly data (thus losing much of 
the available information), interpolating the quotations beyond the trading 
hours to get simultaneous observations (thus introducing additional noise), 
or analyzing the observations that are coincident but locally come from dif-
ferent phases of a trading day (thus approving of noise caused by microstruc-
ture effects). In our research, we decided to use the close to close returns, but 
in the cases involving the S&P 500 index we investigate two types of de-
pendencies. In the first case the analysis is performed for the returns corre-
sponding to the same date, and in the second – for the returns of the S&P 
500 one-day lagged with respect to the returns on the European indices, de-
noted as S&P 500(–1). A part of the results concerning the WIG20 index 
was first published in Polish (Doman, Doman, 2013). We quote them here 
for the reader’s convenience. 

Tables 2–4 show parameter estimates of the MSC models fitted to the re-
turns of each of the considered pairs of the indices. A large set of copula 
specifications was considered during the fitting procedure. Taking into ac-
count the results by Doman and Doman (2012), we considered MSC models 
with 3 and 2 regimes, and static copula models. The best models are selected 
on the basis of information criteria and the results of likelihood ratio tests. 
Apart from the pair (WIG20, S&P 500), in all cases we apply 2-regime MSC 
models with the first regime described by the Gaussian copula and the se-
cond characterized by the Clayton or the Joe-Clayton copula. So, in the first 
regime there is no dependence in tails, and in the second at least dependence 
in lower tail is observed. 

The plots of estimated dynamic dependence measures are presented in 
Figures 5–8. The first impression from the pictures is that the dependencies 
within the group of the Central European markets are stronger and exhibit 
stronger dynamics, in comparison with their linkages with the considered 
developed markets. It means that the linkages within the group of the Central 
European markets are more sensitive on new information.  



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

20

Table 2.  Linkages of the BUX: parameter estimates for the MSC models. Standard 
errors in parentheses 

BUX   and PX WIG20 DAX S&P 500 S&P 500(–1) 

11p  0.9960 0.9895 0.9994 0.9982 0.9991 

22p  0.8957 0.9702 0.9987 0.9964 0.9991 
Copula 

in regime 1 
Gauss
ρC  Gauss

ρC  Gauss
ρC  Gauss

ρC  Gauss
ρC  

ρ  0.6658 
(0.0183) 

0.6799 
(0.0216) 

0.5937 
(0.0157) 

0.4260 
(0.0275) 

0.3089 
(0.0343) 

Spearman’s rho 0.6482 0.6624 0.5756 0.4100 0.2962 
Copula 

in regime 2 
Clayton
γC  ClaytonJoe

,
−

γκC  Clayton
γC  Clayton

γC  Clayton
γC  

κ   1.3925 
(0.1281)    

γ  0.4769 
(0.1179) 

0.4144 
(0.1872) 

0.3533 
(0.0811) 

0.1680 
(0.0854) 

0.1382 
(0.0401) 

Lλ  0.2338 0.1878 0.1406 0.0162 0.0066 

Uλ   0.3549    
Spearman’s rho 0.2843 0.4265 0.2230 0.1159 0.0968 
 

 

Figure 5.  Dependencies between the BUX and the other indices. Estimates of 
Spearman’s rho  

 

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

05/05/2004 12/15/2004 07/29/2005 03/08/2006 10/20/2006 06/11/2007 01/25/2008 09/04/2008 04/21/2009 12/03/2009 07/19/2010 02/25/2011 10/10/2011 05/25/2012

PX WIG20 DAX S&P500 S&P LAG



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DYNAMIC ECONOMETRIC MODELS 3 (2013) 5–31 

21

 
Figure 6.  Dependencies between the BUX and the other indices. Estimates of lower 

tail dependence coefficient 

The first observation concerning models describing the linkages of the 
BUX with the other indices (Table 2) is that in each case the value of 
Spearman’s rho is higher in the regime with the Gaussian copula. Figure 5 
indicates an increase in the strength of connection between the BUX and 
DAX, which can be interpreted as an effect of the EU joining. During the 
period of the subprime crisis we observe a drop in the strength of dependen-
cies between the returns on the BUX and lagged returns on the S&P 500. At 
the same time, however, there is an increase in the strength of dependencies 
between the returns with the same date. Taking into account different impact 
of the Hungarian and the US market on the global economy, we can formu-
late a conjecture that during the crisis period the dependencies between the 
markets were affected by a common factor driving the prices’ dynamics. 

In Figure 6, the plots of the conditional lower tail dependence coeffi-
cients are presented. This type of dependence is observed for the pairs 
(BUX, PX) and (BUX,WIG20). It does not occur when we analyze the link-
ages for the pair (BUX, S&P 500(–1)). Some very weak dependence is visi-
ble for the pairs (BUX, DAX) and (BUX, S&P 500), but it disappears at the 
beginning of 2006.  

In the case of the PX index, the results are similar to those for the BUX 
in the part dealing with the emerging markets, but different when consider-
ing the DAX and S&P 500 (Table 3). First observation is that the depend-
ence between the PX and DAX, measured by means of Spearman’s rho 
(Figure 7), is very strong during almost all the period under scrutiny (from 

0

0,05

0,1

0,15

0,2

0,25

05/05/2004 02/25/2005 12/28/2005 10/20/2006 08/24/2007 06/24/2008 04/21/2009 02/17/2010 12/14/2010 10/10/2011

PX WIG20 DAX S&P500 S&P LAG



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

22

the end of 2005). Some decrease in the strength of dependencies is visible 
from July 2009 to February 2010. The dependence between the returns on 
the PX and S&P 500 is quite significant for both the returns from the same 
day and in the case of lagged returns on the S&P 500. The pair (PX, S&P 
500) is the only one for which the value of Spearman’s rho in the regime 
with tail dependence is higher than in that with the Gaussian copula. Lower 
tail dependence coefficient for (PX, S&P 500) is higher than for (PX, DAX). 
The periods of stronger dependencies in lower tail for the pair (PX, DAX) 
occur in the beginning of the sample period and in late 2009. 

Table 3. Linkages of the PX: parameter estimates for the MSC models. Standard 
errors in parentheses 

PX   and WIG20 DAX S&P500 S&P 500(–1) 

11p  0.9589 0.9960 0.9903 0.9932 

22p  0.9702 0.9849 0.9909 0.9916 
Copula 

 in regime 1 
Gauss
ρC  Gauss

ρC  Gauss
ρC  Gauss

ρC  

ρ  0.6796 
(0.0216) 

0.6028 
(0.0219) 

0.2305 
(0.0504) 

0.3209 
(0.0471) 

Spearman’s rho 0.6621 0.5848 0.2206 0.3078 
Copula 

 in regime 2 
Clayton
γC  Clayton

γC  ClaytonJoe
,
−

γκC  Clayton
γC  

κ    
1.2935 

(0.0733)  

γ  0.6991 
(0.1286) 

0.3991 
(0.1227) 

0.4484 
(0.0866) 

0.2832 
(0.0637) 

Lλ  0.3710 0.1761 0.2132 0.0865 

Uλ    0.2911  
Spearman’s rho 0.3779 0.2465 0.4013 0.1848 

Table 4 and Figures 9–10 present the estimation results for dependencies 
with the WIG20. The estimates for (WIG20, DAX) are very similar to those 
for (WIG20, BUX) and (WIG20, PX). The linkages between the WIG20 and 
DAX, however, seem to be stronger than for (PX, DAX) or (BUX, DAX). 
The results concerning dependencies between the returns on the WIG20 and 
S&P 500 (Table 4) could seem surprising, but are in agreement with practi-
tioners’ beliefs. The best models describing the dependencies are in this case 
the static Gaussian copula for the returns from the same day, and the static 
Joe-Clayton copula in the case of lagged S&P 500 returns. This supports the 
established opinion about the stability of the US market impact on the War-
saw Stock Exchange. The plots in Figure 9 show that the estimates  of  dyna- 



The Dynamics and Strength of Linkages between the Stock Markets…                                                  

DYNAMIC ECONOMETRIC MODELS 3 (2013) 5–31 

23

 

 
Figure 7.  Dependencies between the PX and the other indices. Estimates of Spear-

man’s rho  

 
Figure 8.  Dependencies between the PX and the other indices. Estimates of lower 

tail dependence coefficient 

mic Spearman’s rho for the pairs (WIG20, BUX) and (WIG20, PX) are 
changing between 0.4 and 0.7. In the case of linkages with the DAX, in prin-
ciple only values 0.34 (until July 2006) and 0.63 (from December 2006) are 
observed. Tail dependence for the WIG20 and DAX has disappeared since 
December 2006, and tail dependence between the returns on the WIG20 and 
lagged S&P 500 is present during all the sample period, but is very weak. 

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

05/05/2004 02/25/2005 12/28/2005 10/20/2006 08/24/2007 06/24/2008 04/21/2009 02/17/2010 12/14/2010 10/10/2011

BUX WIG20 DAX S&P500 S&P500 LAG

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

05/05/2004 02/25/2005 12/28/2005 10/20/2006 08/24/2007 06/24/2008 04/21/2009 02/17/2010 12/14/2010 10/10/2011

BUX WIG20 DAX S&P500 S&P500 LAG



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

24

Table 4. Linkages of the WIG20: parameter estimates for the MSC models. Standard 
errors in parentheses 

WIG20   and DAX S&P 500 S&P 500(–1) 

11p  0.9995   

22p  0.9962   
Copula 

in regime 1 
GaussCρ  GaussCρ   

ρ  0.6529 
(0.0127) 

0.3936 
(0.0177)  

Spearman’s rho 0.6531 0.3783  
Copula 

in regime 2 
Clayton
γC   ClaytonJoe

,
−

γκC  

κ    1.0406 
(0.0205) 

γ  0.6132 
(0.0737)  0.1895 

(0.0291) 

Lλ  0.3229  0.0258 

Uλ    0.0534 
Spearman’s rho 0.3440  0.1570 
 
As it was mentioned earlier, we used the Model Confidence Set method-

ology, described in Section 3, to compare the average strength of dependen-
cies for the considered pairs of indices. Table 5 presents the comparison 
results for the strength of dependencies in the form of a ranking, where 
a higher score means stronger average dependence. The MCS procedure is 
applied sequentially – after each run, the series constituting the MCS obtain 
the subsequent score and are excluded. In the case where the MCS consists 
of at least two elements, the arithmetic mean of the corresponding scores is 
assigned to each of them. The procedure is applied to the series of the 
smoothed values of Spearman’s rho and tail dependence coefficients. All the 
MCSs have been estimated (with the significance level 0.1α = ) using the 
package MulCom of Hansen and Lunde (2010). 
 The ranking results for Spearman’s rho differ from those concerning the 
lower tail dependence coefficient. Generally, however, we can say that in 
average the linkages between the BUX, PX and WIG20 are stronger than the 
dependencies between each of them and the DAX or S&P 500. The only 
exception is for the PX index where the mean levels of the lower tail de-
pendence coefficient for (PX, WIG20) and (PX, S&P 500) are statistically 
indistinguishable. The results indicate the importance of the WIG20 as far as 
we measure average dependence using Spearman’s rho. The pattern for de-



The Dynamics and Strength of Linkages between the Stock Markets…                                                  

DYNAMIC ECONOMETRIC MODELS 3 (2013) 5–31 

25

pendencies in lower tail is more complicated. In the case of the BUX, the 
highest score is assigned to the pair (BUX, PX). Accordingly, for the PX this 
is so for the pairs (PX, WIG20) and (PX, S&P 500), and for the WIG20 – for 
the pair (WIG20, BUX). 

 

 

Figure 9.  Dependencies between the WIG20 and the other indices. Estimates of 
Spearman’s rho  

 

Figure 10. Dependencies between the WIG20 and the other indices. Estimates of 
lower tail dependence coefficient 

  

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

05/05/2004 02/25/2005 12/28/2005 10/20/2006 08/24/2007 06/24/2008 04/21/2009 02/17/2010 12/14/2010 10/10/2011

BUX PX DAX S&P500 S&P500 (‐1)

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

05/05/2004 12/15/2004 07/29/2005 03/08/2006 10/20/2006 06/11/2007 01/25/2008 09/04/2008 04/21/2009 12/03/2009 07/19/2010 02/25/2011 10/10/2011 05/25/2012

BUX PX DAX S&P500(‐1)



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

26

Table 5. Rankings of average strength of dependencies 
BUX 
 & 

Spearman’s 
rho Lambda_L PX 

 & 
Spearman’s 

rho Lambda_L WIG20 
& 

Spearman’s  
rho Lambda_L 

PX 4 5 BUX 4 3 BUX 5 3 
WIG20 5 4 WIG20 5 4.5 PX 4 5 
DAX 3 3 DAX 3 1.5 DAX 3 4 
S&P 
500 2 2 S&P 

500 2 4.5 S&P 
500 2 1 

S&P 
500  
(-1) 

1 1 
S&P 
500 
 (-1) 

1 1.5 
S&P 
500  
(-1) 

1 2 

 

 

Figure 11. Smoothed probabilities of the regime with tail dependence for pairs 
(BUX, PX), (BUX,WIG20) and (PX,WIG20) 

Usually in literature, the presence of tail dependence is linked with the 
turmoil periods in markets. The plots presented in Figures 11–13 allow to 
determine the moments of switching on the regime with tail dependence. 
First observation is that the changes of regimes are very frequent as far as we 
consider the three pairs of the analyzed emerging markets (Figure 9). If tail 
dependence is present for the pair (BUX, WIG20) it is usually present for the 
two other pairs. However, for the pairs (BUX, PX) and (PX, WIG20), there 
occur some additional periods with tail dependence. Tail dependence be-
tween the considered emerging markets and the German market disappeared 
in 2006. In the case of the pair (PX, DAX), it appeared again during a short 
period from July 2009 to February 2010. For the pair (BUX, S&P 500(–1)), 
tail dependence has occurred since September 2008 (the crisis effect), and 
for (WIG20, S&P500(–1)), it is present during all the sample period. In the 

0

0,2

0,4

0,6

0,8

1

1,2

05/05/2004 12/15/2004 07/29/2005 03/08/2006 10/20/2006 06/11/2007 01/25/2008 09/04/2008 04/21/2009 12/03/2009 07/19/2010 02/25/2011 10/10/2011 05/25/2012

BUX‐PX BUX‐WIG20 PX‐WIG20



The Dynamics and Strength of Linkages between the Stock Markets…                                                  

DYNAMIC ECONOMETRIC MODELS 3 (2013) 5–31 

27

case of (PX, S&P 500(–1)), the pattern is more complicated because periods 
with tail dependence appear and disappear cyclically. Tail dependence in the 
case of (WIG20, S&P 500) is absent. For the pair (BUX, S&P 500) it occurs 
in pre-crisis period, and for (PX, S&P 500) it is present during most of the 
time in the recent crisis years. 

 
Figure 12. Smoothed probabilities of the regime with tail dependence for pairs 

(BUX, DAX), (PX, DAX) and (WIG20, DAX) 

Our findings can be sum up as follows. Dependencies between the three 
considered emerging markets are stronger than the one of each of them with 
the German or the US markets, regardless of the applied dependence meas-
ure. In almost all cases the dynamics of the dependencies is rich, indicating 
sensitivity on information process. The periods with tails dependence occur 
very often and they are not necessary connected with crisis periods, though 
this type of dependence is present during these periods too. The linkages 
between the considered emerging markets and the developed ones are very 
stable and mostly do not change during the crises. The extreme example 
involves the WIG20 index for which the dependencies with contemporary 
and lagged S&P 500 returns are described by means of static copulas. As 
regards the dynamics of dependencies between the Czech, Hungarian and 
Polish markets, the crucial relation is that between the BUX and WIG20. 
The importance of the influence of major European markets and the US 
market on the analyzed emerging markets can be perceived as comparable if 
one takes into account that due to the no-synchronization effect the impact of 
the US market is divided between two days. 
 

0

0,2

0,4

0,6

0,8

1

1,2

05/05/2004 12/15/2004 07/29/2005 03/08/2006 10/20/2006 06/11/2007 01/25/2008 09/04/2008 04/21/2009 12/03/2009 07/19/2010 02/25/2011 10/10/2011 05/25/2012

BUX PX WIG20



Małgorzata Doman, Ryszard Doman 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 5–31 

28

 
Figure 13. Smoothed probabilities of the regime with tail dependence for pairs 

(BUX, S&P 500), (PX, S&P 500) and (WIG20, S&P 500) 

 
Figure 14. Smoothed probabilities of the regime with tail dependence for pairs 

(BUX, S&P 500(–1)), (PX, S&P500(–1)) and (WIG20, S&P500(–1)) 

Conclusions 
In the paper we analyzed the dynamics and strength of linkages between 

the Czech, Hungarian and Polish stock markets. In addition, we examined 
linkages between each of these markets and developed markets (European 
and US). The analysis was based on the daily quotations of the main repre-
sentative stock indices (PX, BUX, WIG20, DAX, S&P 500). The period 

0

0,2

0,4

0,6

0,8

1

1,2

05/05/2004 12/15/2004 07/29/2005 03/08/2006 10/20/2006 06/11/2007 01/25/2008 09/04/2008 04/21/2009 12/03/2009 07/19/2010 02/25/2011 10/10/2011 05/25/2012

BUX PX WIG20

0

0,2

0,4

0,6

0,8

1

1,2

05/05/2004 12/15/2004 07/29/2005 03/08/2006 10/20/2006 06/11/2007 01/25/2008 09/04/2008 04/21/2009 12/03/2009 07/19/2010 02/25/2011 10/10/2011 05/25/2012

BUX PX WIG20



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DYNAMIC ECONOMETRIC MODELS 3 (2013) 5–31 

29

under scrutiny was from May 5, 2004 to July 20, 2012. So, it starts after the 
EU accession of the corresponding countries and includes recent financial 
crises. Our tool to model the dynamics of dependencies were Markov-
switching copula models. Due to this choice, we were able to use two kinds 
of measure of the strength of the linkages: dynamic Spearman’s rho and tail 
dependence coefficients. Our results show that the dependencies between the 
three considered emerging markets are stronger than those between each of 
them and the German or the US markets, regardless of the applied measure. 
The dynamics of dependence in almost all cases is rich, clearly indicating 
sensitivity on information process. The tail dependence appears and disap-
pears cyclically and is not necessary connected with the crisis periods, 
though this type of dependence is present during these periods too. The link-
ages of the examined emerging markets with the considered developed mar-
kets are very stable, not sensitive on present information, and mostly do not 
change during the crises. The crucial relation for the considered region is the 
dependence between the Hungarian and Polish markets. The importance of 
the impact of the developed European market and the US market on the ana-
lyzed emerging markets can be viewed as comparable. 

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The Dynamics and Strength of Linkages between the Stock Markets…                                                  

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Dynamika i siła zależności pomiędzy rynkami giełdowymi Czech, 
Węgier i Polski po ich wejściu do Unii Europejskiej 

Z a r y s  t r e ś c i. W pracy analizowana jest dynamika i siła powiązań pomiędzy rynkami 
giełdowymi Czech, Węgier i Polski. Badanie obejmuje okres po wejściu wymienionych kra-
jów do Unii Europejskiej. Ponadto oceniamy powiązania pomiędzy każdym z wymienionych 
rynków a wybranymi rynkami rozwiniętymi (europejskim i amerykańskim). Analiza oparta 
jest na dziennych notowaniach głównych indeksów giełdowych (PX, BUX, WIG20, DAX, 
S&P 500) i obejmuje okres od 5 maja 2004 r. do 20 lipca 2012 r. Dynamika zależności jest 
opisywana za pomocą modeli kopuli z przełączaniem typu Markowa, a stosowanymi miarami 
siły powiązań są dynamiczne współczynniki rho Spearmana i dynamiczne współczynniki 
zależności w ogonach rozkładów. Uzyskane wyniki pokazują, że zależności pomiędzy rozwa-
żanymi rynkami wschodzącymi są bardzo wrażliwe na sytuację rynkową, natomiast powiąza-
nia z rynkami rozwiniętymi są stabilne. 

S ł o w a  k l u c z o w e: Środkowoeuropejski rynek giełdowy, zależność warunkowa, modele 
kopuli z przełączaniem typu Markowa, współczynnik rho Spearmana, zależność w ogonie 
rozkładu, zbiór ufności modeli, indeks giełdowy. 






