




































© 2016 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.2016.006  Vol. 16 (2016) 87−116 

Submitted November 30, 2016  ISSN (online) 2450-7067 

Accepted December 18, 2016 ISSN (print) 1234-3862 

Aneta Włodarczyk, Iwona Otola
*
 

Analysis of the Relationship between Market Volatility 
and Firms Volatility on the Polish Capital Market 

A b s t r a c t. In this paper we investigate if the strength of firm-market volatility relationship 

has changed after subprime crisis on the Polish Capital Market. The empirical study concern 

the selected companies listed on the Warsaw Stock Exchange (WSE) from the construction 

and IT sectors in the 2004–2011 period. The volatility measures were computed on the basis 

of daily low and high prices for companies shares and WIG index. For each company   

ARFIMAX-FIGARCH model with additional exogenous variables, which represented market 

volatility, was estimated in the stable and the turbulent period. Conducted empirical studies 

have not shown that the negative shocks flowing from the American stock market through 

investors' behavior channel contributed to the increase in the fraction of firms of the construc-

tion and IT sectors listed on the WSE whose volatility is shaped by market volatility. 

K e y w o r d s: ARFIMAX-FIGARCH, firm volatility, market volatility, subprime crisis, 

Warsaw Stock Exchange.  

J E L Classification: G12; D40; C58. 

Introduction  

Volatility of prices of listed companies shares is the subject of interest not 

only to stock exchange investors but also companies which emit them. High 

volatility means high probability of change of company market value in the 

future and this in turn influences its competitiveness on the market. This is 

                                                 
* Correspondence to: Aneta Włodarczyk, Czestochowa University of Technology, Faculty 

of Management, 36b Armii Krajowej Street, 42-200 Częstochowa, Poland, e-mail: 

aneta.w@interia.pl; Iwona Otola, Czestochowa University of Technology, Faculty of Man-

agement, 19b Armii Krajowej Street, 42-200 Częstochowa, Poland, iwotola@gmail.com. 



Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

88 

connected with the fact that high market value of an enterprise in relation to 

its book value is connected with a simultaneous high market share of a given 

subject (Grabowska, 2013). Enterprise competitiveness depends, among 

others, on the value for the shareholders and clients, financial capability, 

determining its ability to act and react quickly in the competitive environ-

ment and human potential and technologies used in implementing strategic 

changes (Feurer and Chaharbaghi, 1994). Moreover, the knowledge about 

linkages between market volatility and firm volatility is of great importance 

in risk management process and determining the investment portfolio struc-

ture, because it helps to understand the nature of individual firm volatility 

and identify this process determinants. It is not surprising that there exist 

many articles that were devoted to this issue. We may summarize some im-

portant facts about firm volatility on the basis of literature studies. As sug-

gest Karolyi (2001) the existence of excessive volatility in stock prices un-

dermines the usefulness of the information about the true value of the com-

pany. This clearly does not mean that high volatility is proof of the irrational 

behavior and inefficient markets and investors. No signals from the market 

to volatility of stock prices, affirms the conviction that it is the correct meas-

ure of risk. Interest in the subject matter of volatility, in particular, the possi-

bility of its forecasting is related to the ability to reduce the risk of invest-

ment or achieving higher returns from investments. In the literature, there are 

already several well-documented facts concerning volatility. Chen and Lai 

(2013) and other researchers (Whaley, 2009; Simon, 2003; Giot, 2005; Peng 

and Ng, 2012) showed a significant feature, which is the asymmetry of vola-

tility. Shin and Stulz (2000) decomposed shares risk into its market and firm-

specific components in order to show that changes in market risk are posi-

tively correlated with changes in firm value, but changes in firm- specific 

risk are negatively correlated with changes in firm value. Campbell et al. 

(2001) used a disaggregated approach to study the volatility of common 

stocks at the market, industry and firm level. They proposed three variance 

components, which were estimated monthly using daily data, so their further 

analysis about volatility components were conducted on the basis of monthly 

frequency indicators and for this reason they could not consider the impact 

of volatility clustering effect on evaluation of risk measurement process. 

Phylatkis and Xia (2009) investigated the equity market comovement at the 

sector level and confirmed the sector heterogeneity of the contagion. They 

showed that investors might find the profitable sectors on the capital markets 

despite of the prevailing contagion on the market level. Chuliá and Torró 

(2011) estimated a conditional CAPM with multivariate GARCH-M struc-

ture in order to investigate an asymmetric volatility spillover effect between 



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

89 

large and small firms in the Spanish stock market and they proved the exist-

ence of  bidirectional relationship between these volatility processes with 

asymmetric influence of bad and good news for firm volatility. Sharma et al. 

(2011, 2014) showed that firms belonging to different sectors experienced 

different degrees of association with market volatility, what caused that in 

some cases firm volatility might be predicted on the basis of market volatil-

ity. They proved that commonality in volatility increases with the firm's size. 

Sequeira and Lan (2003) found that, the most significant component of ag-

gregate volatility in the international market, with firm-level volatility form-

ing the largest component of total volatility is unsystematic variance of the 

stock return. They also claim that volatility of the market-level is more im-

portant than the volatility of the sector-level in the explanation of the total 

volatility of stock return, which is also confirmed in earlier research con-

ducted by Cavaglia et al. (2000) or Griffin and Karolyi (1998). That is why 

both managerial staff in enterprises and investors should be interested in 

knowing the strength and direction of relationships between shares volatility 

of particular enterprises and stock market volatility. 

Previous studies on the volatility in the majority relate to market volatili-

ty. A small part of the study is devoted to the volatility of the firm-level. 

Volatility of asset prices is also often explained by the mechanism of trans-

mission of crises and the related phenomenon of contagion (Baur, 2003; 

Corsetti et al., 2005; Claessens and Forbes, 2004; Le and David, 2014). Re-

searchers examining the contagion effect on the capital market level concern 

only a chosen stock indices, which do not reflect the impact of the volatility 

of share prices of companies in different sectors. In such an approach the 

heterogeneity effect of the sectors selected within a given capital market and 

their various immunity to external shocks and different sensitivity to effects 

of a financial crisis are omitted (Phylatkis and Xia, 2009).  

The impact of the subprime crisis on individual segments of the Polish fi-

nancial market were presented by Konopczak et. al. (2010). The analysis 

shows the local and global conditions that made the interaction of disorders 

associated with the global financial crisis on the Polish financial market was 

as strong as in developed markets. Empirical studies, including the period of 

the subprime crisis, conducted by Otola (2013), concerning the relationship 

between the WIG index and the S&P500 index, had to indicate whether neg-

ative shocks arising in the United States have been transferred to Polish Cap-

ital Market by stock exchange channel. The high volatility in the capital 

market, which has been observed in an unstable period is not only the result 

of the interdependence between the markets but the result of the financial 

contagion of Polish Capital Market. In this context, we rightly seem to con-



Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

90 

duct the further research on the volatility of the Polish Capital Market on the 

firm level. 

Taking above into consideration we are interested in examining the direc-

tion and strength of relationship between firm-level volatility and market-

level volatility on the Polish Capital Market in the period of pre- and post- 

subprime crisis. The aim of this paper is to investigating if the market vola-

tility and firm volatility are related and if the strength of this relationship 

increase significantly in the turbulent period compared to the stable period. 

The empirical study concerns the selected companies listed on the Warsaw 

Stock Exchange from the construction and IT sectors in the period from 2 

January 2004 to 31 December 2011. In this respect, our contribution to the 

literature is connected with the calibration of Sharma et al. model (2011, 

2014) through introducing long memory dynamics and skewed fat-tailed 

distributions of innovations into the basic model describing the relationship 

between firm volatility and market volatility. Following Sadigue and 

Silvapulle (2001) and Kang and Yoon (2012) we expect that on the Polish 

capital market some investors reacted to new information immediately, 

whereas others postpone making the investment decision until they confirm 

the information. It causes that their actions form a non-linear pattern, which 

characterizes statistical persistence in a time series. We also taking into con-

sideration the possible structural changes that may have affected the long 

memory property, so we divide the analyzed period into two sub-periods, 

taking the subprime financial crisis of July 2007 as the structural change 

point. The above considerations allow us to formulate the following hypoth-

esis: There is no significant increase in the fraction of firms from a given 

sector of Polish Capital Market whose volatility is strongly and positively 

related with market volatility in pre-crisis period compared with post-crisis 

period. 

The remainder of the paper is organized as follows. Section 2 describes 

the methodology, data properties are presented in section 3. In Section 4 we 

verify the hypothesis about the commonality in volatility in stable and turbu-

lent period. And finally, Section 5 concludes the  paper.  

2. Methodology 

We have modified the model of Sharma et al. (2011, 2014), which de-

scribes the relationship between firm volatility and stock market volatility by 

capturing the possible long memory effect in both firm and market volatility 

process. Theoretical frames of the volatility model determines Capital Asset 



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

91 

Pricing Model (CAPM) and Fractionally Integrated Generalized Autoregres-

sive Conditional Heteroscedasticity (FIGARCH).  

In empirical research presented in the paper the authors use the following 

regression equation, in which firm volatility is conditioned by previous and 

present market volatility and also by present return on investment into the 

market portfolio and squared return of market index (Sharma et al., 2011):  

,2
,4,31,2,10, ittmitmitmitmiitf RRVVV

i
        (1) 

where: Vm – stock market volatility, 
if

V  – share volatility of i-nth company  

(i=1, 2, ..,N), Rm,t – logarithmic return of stock market index. 

Sharma et al. (2011) incorporated market return and squared market return 

factors into above equation in order to control for possible spurious depend-

ence between returns and volatility measures.  

Price range estimators are used as volatility estimators that are computed 

on the basis of full publicly available set of information about financial in-

strument prices what make them more efficient than volatility estimators 

calculated as the squared return (Fiszeder and Perczak, 2013; Molnár, 2012; 

Sharma et al., 2014): 

 daily volatility estimator created by Parkinson (1980): 

,)]ln()[ln(361.01 2
itit PLPHV       (2) 

where: PHit – highest price of i-nth financial instrument on t day, PLit – 

lowest price of i-nth financial instrument on t day; 

 daily volatility estimator proposed by Garman and Klass (1980): 

,)]ln()][ln(12ln2[)]ln()[ln(5.02 22
itititit POPCPLPHV   (3) 

where: PCit – closing price of i-nth financial instrument on t day, POit – 

opening price of i-nth financial instrument on t day; 

 daily volatility estimator defined by Rogers and Satchell (1991): 

)].ln())][ln(ln()[ln(

)]ln())][ln(ln()[ln(3

itititit

itititit

PCPLPOPL

PCPHPOPHV




                 (4) 

Originally, the Parkinson, Garman-Klass, Rogers-Satchell volatility 

measures of financial instruments prices are the estimators of uncondition-

ally volatility for the geometric Brownian motion determined for time inter-

val [0, T]. Therefore, all of analysed here estimators are derived under the 

assumptions of continuous sampling, no bid-ask spread and constant volatil-

ity. Moreover, in the case of the Parkinson and Garman-Klass estimators an 

additional assumption refers to zero drift. It is worth attracting attention on 



Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

92 

some properties of range-based volatility estimators, especially in the case 

when one day is used as a unit of time. It was proved that the Garman-Klass 

estimator characterized by the highest efficiency in the case when the as-

sumption of zero drift was met. The efficiency of range- based volatility 

estimators for zero drift are as follow: the Parkinson – 4.9, the Garman-Klass 

– 7.4, the Rogers-Satchell – 6.0 and they are significantly higher than the 

efficiency of simply volatility estimator (based on squared daily returns) 

equals by definition 1 (Molnár, 2012). For daily financial time series, mean 

return is often much smaller than its standard deviation, which is in line with 

the assumption of zero drift. Fiszeder and Perczak (2013) derived the ex-

pected values of the Parkinson and Garman-Klass estimators for the arithme-

tic Brownian motion with non-zero drift and they proved the unbiasedness of 

the Parkinson and Garmann-Klass estimators for the process with a zero drift 

and of the Rogers-Satchell estimator for any drift. It is worth stressing that 

the square root of any range-based volatility estimators is a biased estimator 

of standard deviation of a Brownian motion, but this bias is rather small (3–

4%) compared to bias of the square root of the simply volatility estimator 

(25%). The questionable issue is the use of the range-based volatility estima-

tors for the standardization of the returns. It was shown that returns normal-

ized by means of the Garman-Klass estimator were approximately normally 

distributed. Another disadvantage concerning the use of range estimators in 

practice is failure to comply with the assumptions of continuous sampling. 

Prices are observed at discrete points in time (vector of POt, PHt, PLt, PCt for 

each day) and it causes that the observed high price is below the true high 

price and observed low price is above the true low price. Bid-spread effect 

works in the opposite direction. These two effects are small for liquid stocks 

(Molnár, 2012). A debatable question is also the adjustment of range-based 

volatility estimators for the opening jumps, resulting from the situation that 

most of the assets are not traded continuously for 24h a day (Molnár, 2012; 

Fiszeder and Perczak, 2013).  

Sharma et al. (2014)  limited their empirical studies to modelling the firm 

volatility shocks (   error term) by using GARCH(1,1) model with the con-

ditional normal distribution of innovations. In the above equation the authors 

used full available on a given day information on the market portfolio (open-

ing price, the lowest and the highest price, closing price), which will allow 

us to eliminate the effect of influencing the research results with one type of 

data only – closing price. For each analyzed series of share prices volatility 

of the given enterprises the ARFIMA(P,D,Q)-FIGARCH(p,d,q) models were 

chosen individually in accordance with the following stages: 



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

93 

 specification of the equation describing the relation between market 

volatility and firm volatility (1), adjusted for possible autocorrelation de-

pendencies occurring in the company share volatility series;  

 specification of the conditional variance equation describing the ARCH 

effect in the series of residuals from the equation (1) and the selection of 

the form of innovation density function. 

The fractionally integrated autoregressive moving average process  

(ARFIMA) is more flexible econometric tool for modelling the conditional 

mean process than ARMA model in the situation when it exhibits long 

memory properties. Similarly, the fractionallly integrated generalized auto-

regressive conditional heteroskedasticity process, constituting a generaliza-

tion of the GARCH model, enables for capturing the persistence in the con-

ditional variance process (Bollerslev and Mikkelsen, 1996). However, mar-

ket shocks have a simultaneous impact on the conditional mean and condi-

tional variance. Therefore, some recent empirical studies have focused on 

the analyzing the relationship between the conditional mean and the condi-

tional variance of the process that simultaneously exhibits long memory 

properties (Beine et al., 2002; Fiszeder, 2009; Kang and Yoon, 2012). The  

ARFIMA(P,D,Q)-FIGARCH(p,d,q) model is defined in the following way 

(Arouri et al., 2012):  

,

)](1[)1)((

)()()1)((

2

2

ttt

tt
d

ttt

ttt
D

h

LLL

h

LyLL

















     (5) 

where: L denotes a lag operator;  








 













00 )()1(

)(
)1()1(

j

jjj

j

D L
Dj

Dj
L

j

D
L  – differential filter of D 

order, where, )(  denotes gamma function;  

,...1)( 1
P

PLLL  
Q

QLLL   ...1)( 1  are respectively lags 

polynomials for the autoregressive part of P order and moving average of Q 

order, whose all roots lie outside the unit circle, i, i are the model parame-

ters; 






 













00 )()1(

)(
)1()1(

s

sss

s

d L
ds

ds
L

s

d
L – differential filter of d 

order; ,...1)( 1
q

qLLL   p
pLLL   ...1)( 1  are respectively 



Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

94 

lags polynomials for the ARCH part of q order and GARCH part of p order, 

all the roots of )](1[),( LL   lie outside the unit circle, αi, βi are the model 

parameters;
 t is an innovations series, ).1,0(..~ diit  

On the basis of D parameter value one can identify the memory type of 

the process (Hosking,1981): 

            means that the process exhibits negative dependencies 

between distant observations (anti-persistence, but stationary process),  

          corresponds to the long-memory stationary process,  

     means reduction of the ARFIMA(P,D,Q) to the stationary  

ARMA(P,Q) model (short memory process), 

       indicates a non-stationary process (in particular for     the 

process follows a unit root process  – ARIMA(P,1,Q) model).  

For the FIGARCH model the influence of current shocks for volatility fore-

casts decreases to zero, but at a slower rate than for GARCH processes. 

Moreover, the autocorrelation function of FIGARCH squared residuals de-

creases at a hyperbolic rate to zero, which indicates long memory in volatil-

ity of series described by this class models. The existence of long memory in 

volatility process may be recognized on the basis of estimated value of d 

parameter (Fiszeder, 2009): 

         means that volatility process exhibits long memory property, 

     means reduction of the FIGARCH(p,d,q) to the GARCH(p,q) 

process for which the influence of current volatility on forecasts of con-

ditional variance decays at fast rate (also short memory process  in sense 

of “influence of current volatility for the true conditional variance proc-

ess”), 

     means reduction of the FIGARCH(p,d,q) to the IGARCH(p,q) 

process for which current volatility has permanent impact on forecasts of 

conditional variance (short memory in above explained sense). 

This class of models is estimated by using the quasi-maximum likelihood 

(QML) estimation method, based on the following log-likelihood function 

(under the assumption about Gaussian distribution of innovations) (Fiszeder, 

2009; Kang and Yoon, 2012):  

,])[ln(
2

1
)2ln(

2

1

1

2




T

t

ttGaussian hTLL       (6) 

where T denotes the number of observation.  

It is worth stressing that one of stylized facts of high – frequency time series 

of financial prices is excess kurtosis and skewness of returns distributions 

(Fiszeder, 2009; Laurent, 2013; Włodarczyk, 2010). In order to capture the 



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

95 

excess kurtosis and fat-tailed effect in the residuals, the Student t-distribution 

may be used as the innovation distribution in ARFIMA-FIGARCH model, 

and then the log-likelihood function is defined as follows (Kang and Yoon, 

2012; Laurent, 2013 ):  

,
2

1ln)1()ln(
2

1

)]2(ln[
2

1

2
ln

2

1
ln

1

2


 




































































 


T

t

t
t

Student

h

TLL









               

(7) 

where         
Parameter   measures the degree of fat tails of the density function and the 

lower its values is, the fatter tails of distribution are. The latest specification 

of ARFIMA-FIGARCH models, which be considered in this work, allows 

for both the excess skewness and kurtosis of residuals by using the skewed 

Student t-distribution. In this case the log-likelihood function is as follows 

(Kang and Yoon, 2012; Laurent, 2013 ):  

 

,
2

)(
1ln)1()ln(

2

1

ln
1

2
ln)]2(ln[

2

1

2
ln

2

1
ln

1

2
2













































































































 


T

t

IStS
t

SentSkewedStud

tkh

k
k

TLL









   

(8)

 

where: 

,
/ if  1

/ if     1

t

t










SS

SS

tI



     (9) 

is the indicator function, which is determined on the basis of the mean (S) 

and standard deviation (σS) of the skewed Student t-distribution (Kang and 

Yoon, 2012; Laurent, 2013 ):  

,
1

2

2
2

1




























 



k

kS 





      (10) 



Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

96 

.1
1 2

2

22
SS

k
k  








      (11) 

The value of the asymmetry parameter ln(k) determined the type of skew-

ness, that is, if  0)ln ( k , the density is right skewed and if 0)ln( k , the 

density is left skewed. 

3. Data Description 

Empirical research were conducted for the chosen companies from con-

struction and IT sector listed on the main market of the Warsaw Stock Ex-

change whereas restrictive provisions which these companies had to meet in 

order to be able to exist on it. To the research 17 companies from the con-

struction sector were chosen in the stable period and during a turbulent three 

more. The IT sector study involved 10 companies during the stable period 

and 20 in a turbulent period. The authors excluded from the research sample 

enterprises which in the given sub-period withdrew from the market or their 

debuts took place in the course of the given sub-period. Data were obtained 

from the Notoria Service and consist of 2013 daily observations of high, 

low, open and close prices for analyzed companies from January 2, 2004 to 

December 30, 2011. 

The starting point is determining the breakthrough on the basis of which 

it is possible to distinguish two sub-periods: the stable period which corre-

sponds to low stock market volatility and the turbulent period characterized 

by high market volatility. First symptoms of growing volatility of main in-

dexes of American market (DJIA, NASDAQ, S&P500) can be observed in 

July and August of 2007. They are accompanied by bankruptcy of two hedg-

ing funds of Bear Stearns bank connected with the mortgage market in the 

USA (July 2007), as well as the insolvency of three funds of the French bank 

BNP Paribas investing in the bonds market secured with mortgages sub-

prime (9 August 2007) (Otola, 2013; Burzała, 2013; Dungay et al., 2011). 

The analyzed period was divided into two sub-samples:  

 the stable period (02.01.2004–25.07.2007) – 899 observations; 

 the turbulent period (26.07.2007–31.12.2011) – 1114 observations. 

Due to the prolonging period of instability on the European financial market, 

caused not only by the occurrence of the subprime crisis, but also the debt 

crisis in the peripheral countries of the EU zone, the turbulent period in the 

present analysis was lengthened to the end of the year 2011.  

Selection of sectors was conducted on the following basis. The construc-

tion sector is most connected with the country's economy and most suscepti-



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

97 

ble to GDP changes. It is also most strongly represented sector on the Polish 

stock market. Moreover, since 2004 Poland as a member of the European 

Union has been receiving financial resources within European funds to im-

prove the living conditions of inhabitants. In the course of the second pro-

gramming period (2007–2013) Poland received about 242,3 billion PLN, the 

part of which was destined for public infrastructural investments, both in the 

scope of road construction as well as other public facilities. About 48% of 

allocated within structural funds resources were used to execute the Infra-

structure and Environment Programme. Additionally, the decision of UEFA 

in the II quarter of 2007 to give the right to organize the European Football 

Championship – Euro 2012 in Poland and Ukraine was also connected with 

the necessity to complete numerous construction investments in short time. 

According to the Central Statistical Office since the year 2005 the construc-

tion sector was the fastest growing sector of Polish economy. Moreover, this 

sector is the most abundantly represented sector on the Warsaw Stock Ex-

change. We claim that there is no significant increase in the fraction of firms, 

belonging to the construction sector, whose volatility is shaped by market 

volatility in the turbulent period compared to the stable period. Thus, one 

can expect that external shocks transmitted on the stock market in Poland in 

the subprime crisis period and the debt crisis in the Euro zone should not be 

noticeable by the enterprises of this sector. Claessens and Forbes (2004) 

emphasised the importance of investor reactions in the contagion process in 

the liquidity risk context. Referring to this theory one can expect that inves-

tors having in mind good development perspectives resulting from a substan-

tial financing of this sector with structural funds should not withdraw capital 

located in the stocks of construction companies. 

The second select sector, namely IT, may be considered as the one based 

on knowledge, most intellectual and innovative one. The IT sector may be 

divided into three groups due to the form of conducted activity: 

 production of IT equipment (among others Comp, Elzab, Novitus); 

 software related services (among others Asseco Poland, Comarch, Syg-

nity); 

 distribution of IT solutions (among others Arcus, B3System, NNT Sys-

tem). 

Comparing it with the construction sector one should notice that in the 

analyzed period a lot of enterprises from the IT sector put on acquiring capi-

tal to conduct activity through emission of shares (see table 1). The resources 

acquired from the shareholders for development of this sector are used not 

only on tangible investments but also investments in intellectual capital. 

Moreover, development of new and growth of awareness of needs in the 



Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

98 

scope of IT also in the sector of Small and Medium Enterprises, the use of 

structural funds to liquidate disproportions in access to tele-informatic tech-

nologies in rural areas are only some of the factors conditioning continuity 

of operations of this sector companies. The IT sector is perceived in the 

world as one of the most perspective ones, the one which creates new inno-

vative products, such as for example mobile product applications or devel-

opment of cloud services. Customers of products and services of the IT sec-

tor are primarily enterprises from the public administration sector that to 

a large extent use for this purpose the resources from the European funds. 

More important customers of services and products from the IT sector are 

enterprises operating in the banking and tele-communication sectors. Such 

a perception of the IT sector by the investors should contribute to the fact 

that the enterprises listed on the stock market should show resistance to 

shocks coming from the market. Thus, in our opinion commonality in vola-

tility did not  increase significantly in the turbulent period compared to the 

stable period in  the IT sector on the Polish Capital Market.   

Table 1. Descriptive statistics for volatility measures – stable period 

Variable Minimum Mean Maximum Standard deviation Skewness Kurtosis 

V1_WIG 0.0004 0.008 0.157 0.012 
5.577 
[0.000] 

47.622 
[0.000] 

V2_WIG 0.0003 0.008 0.195 0.011 
7.348 
[0.000] 

85.857 
[0.000] 

V3_WIG 0 0.008 0.269 0.013 
9.764 
[0.000] 

147.92 
[0.000] 

V1_Construction 0.013 0.136 1.303 0.130 
3.042 
[0.000] 

14.837 
[0.000] 

V2_Construction 0.011 0.131 1.786 0.146 
4.248 
[0.000] 

28.550 
[0.000] 

V3_Construction 0.006 0.158 3.506 0.241 
5.418 
[0.000] 

47.534 
[0.000] 

V1_IT 0.009 0.116 1.046 0.119 
2.759 
[0.000] 

10.424 
[0.000] 

V2_IT 0.010 0.084 1.397 0.081 
6.675 
[0.000] 

78.417 
[0.000] 

V3_IT 0.011 0.092 2.179 0.103 
10.018 
[0.000] 

165.52 
[0.000] 

Note: all volatility series were scaled by 100, p-value in brackets. 

On the basis of daily information on four price categories (open, close, 

high and low) of the WIG stock index and shares of particular companies the 

authors determined volatility series in the stable and turbulent period accord-

ing to the price range volatility measures (2)–(4). For each sector the authors 

estimated series of average firm volatility in each of the analyzed sub-



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

99 

periods and then on their basis they  determined descriptive statistics (Tables 

1–2).  

Table 2. Descriptive statistics for volatility measures – turbulent period 

Variable Minimum Mean Maximum Standard deviation Skewness Kurtosis 

V1_WIG 0.0002 0.015 0.373 0.028 
6.125 
[0.000] 

53.180  
[0.000] 

V2_WIG 0.0002 0.013 0.305 0.027 
6.340 
[0.000] 

50.279 
[0.000] 

V3_WIG 0 0.013 0.357 0.029 
6.651 
[0.000] 

55.075 
[0.000] 

V1_Construction 0.012 0.205 2.481 0.351 
2.176 
[0.000] 

3.837 
[0.000] 

V2_Construction 0.010 0.120 3.394 0.195 
7.707   
[0.000] 

103.24   
[0.000] 

V3_Construction 0.010 0.100 3.623 0.253 
10.149  
[0.000] 

112.55 
[0.000] 

V1_IT 0.061 0.289 1.224 0.170 
1.861 
[0.000] 

4.802 
[0.000] 

V2_IT 0.011 0.092 0.571 0.075 
2.919 
[0.000] 

11.721 
[0.000] 

V3_IT 0.010 0.104 0.697 0.084 
2.626 
[0.000] 

9.510 
[0.000] 

Note: all volatility series were scaled by 100, p-value in brackets. 

One can observe that the average volatility in the IT sector was relatively 

lower than in the construction sector for all three measures. A similar de-

pendence can be observed for the maximum value of each volatility meas-

ures evaluated for the firms in both sectors. It is worth emphasizing that in 

the stable period market volatility was substantially lower than volatility of 

firms in both sectors, comparing volatility range determined in accordance 

with the three analyzed measures. Also determined skewness and kurtosis 

indicate sector differentiation of the volatility process, which may indicate 

heterogeneity of the construction and IT sectors on the Warsaw Stock Ex-

change. Similar conclusions were formulated for the American stock ex-

change in the paper of  Sharma, Narayan and Zheng (2014).  

The determined average statistics for the series of firm and market volatility 

took higher values in the turbulent period in comparison with the stable pe-

riod. Also in this period market volatility was substantially lower than the 

firm volatility in both sectors. Due to high kurtosis and skewness of the vola-

tility series determined in accordance with the Rogers and Satchel formula 

only volatility calculated according to the Parkinson method has been in-

cluded in the further part of the analysis. Shaping of  daily  volatility  for  the  



Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

100 

 

Figure 1.  Shaping of daily volatility for the companies from the construction sector 

in the stable period
1
 

 

Figure 2.  Shaping of daily volatility for the companies from the construction sector 

in the turbulent period
2
 

                                                 
1 Explanations of used abbreviations for listed companies can be found in Table 5. 
2 Explanations of used abbreviations for listed companies can be found in Table 6. 



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

101 

 

Figure 3. Shaping of daily volatility for the companies from the IT sector in the 

stable period
3
 

 

Figure 4. Shaping of daily volatility for the companies from the IT sector in the 

turbulent period
4
 

                                                 
3 Explanations of used abbreviations for listed companies can be found in Table 7. 
4 Explanations of used abbreviations for listed companies can be found in Table 8. 

SGN 

2008 2010

2

4
SGN CTC 

2008 2010

2

4
CTC ELZ 

2008 2010

2.5

7.5 ELZ ACP 

2008 2010

2.5

7.5
ACP 

CMR 

2008 2010

2

4
CMR MCL 

2008 2010

2

4
MCL TLX 

2008 2010

2

4
TLX SME 

2008 2010

2

4
SME 

WAS 

2008 2010

2

4
WAS CDR 

2008 2010

2

4 CDR BCM 

2008 2010

2

4
BCM ATM 

2008 2010

2

4
ATM 

CMP 

2008 2010

2

4
CMP PCG 

2008 2010

5

15 PCG QSM 

2008 2010

2

4
QSM U2K 

2008 2010

2

4
U2K 

LSI 

2008 2010

2

4
LSI IMX 

2008 2010

2

4
IMX PRD 

2008 2010

2

4
PRD NTT 

2008 2010

2

4
NTT 



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DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

102 

companies from the construction and IT sectors in the stable and turbulent 

periods show Figures 1–4. 
In the stable period the biggest range of daily share price volatility fell for 

Budopol SA company. High daily spread of volatility was also characteristic 

for such companies as: Awbud SA, Energopol Południe SA, Ulma Construc-

cion SA. In the turbulent period two companies Elkop SA and Erbud SA 

were characterized by very high daily volatility spread.  

In the stable period the highest spread in daily volatility was observed for the 

companies: Simple SA, Wasko SA and Calatrava Capital SA. In the turbu-

lent period a high daily spread of volatility was observed in the companies: 

ZUK Elzab, Asseco Poland SA, CD Project Red SA, Calatrava Capital SA, 

Simple SA, PC Guard SA, LSI Software SA, NTT System SA. 

The presented above descriptive statistics for enterprises listed on the 

Warsaw Stock Exchange from the construction and IT sectors let us notice 

differences both between sectors as well as the stable and turbulent periods. 

4. Verifying the Hypothesis about the Commonality  in Volatility 
in Stable and Turbulent Period 

Time series volatility V1 of share prices of enterprises from the construc-

tion and IT sectors in the stable period i.e. 02.01.2004.–25.07.2007 and the 

turbulent one 26.07.2007–31.12.2011 were subject to modelling in order to 

verify the occurrence of significant relationships between firm volatility and 

WIG index volatility. Due to the characteristic properties of volatility time 

series, which were the subject of modelling: skewness, high kurtosis, fat-

tailed distribution, autocorrelation dependencies (Box-Pierce test), occur-

rence of long memory effect (GPH test), occurrence of volatility clustering 

effect (Engle test, McLeod and Li test) (see Table 3), for each volatility se-

ries individual specification of the model in the form (5)–(8) were selected 

with t-Student distribution or skewed t-Student distribution (Laurent, 2013).  

Additionally, in the conditional mean equation is assumed that the firm 

volatility is dependent on previous, present and future market volatility and 

also expected daily change of the WIG index and the squared WIG index 

return. The choice of the final form of the firm volatility model has been 

performed on the basis of :  

 evaluating significance of the model parameters estimations; 

 minimizing information criteria of Akaike’a (AIC) and Bayesian 

Schwarz (SC); 



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

103 

 test results of standardized models residuals which verified the correct-

ness of the model dynamic specification: Box-Pierce test, Engle test, 

McLeod and Li test; 

 Nyblom test for checking the constancy of model parameters over time; 

 Engle and Ng set of tests for existing leverage effect and investigating 

possible misspecification of the conditional variance equation (FI-

GARCH vs. FIEPARCH), with in particularly covered Negative Sign 

Bias test and Positive Sign Bias test for verifying the effect of negative 

and positive shocks on the conditional variance (Laurent, 2013).  

Table 3. Descriptive statistics and diagnostic tests for volatility series of MSW in 

stable period 

Parameter/Test Value of statistics 

Mean 0.868 
Standard deviation 1.410 

Minimum 0 
Maximum 14.537 
Skewness 5.239   [0.000] 
Kurtosis 38.493 [0.000] 

Jarque-Bera statistics 59616  [0.000] 
ADF  statistics –6.588 

D-GPH statistics 0.259   [0.000] 

Q Box-Pierce statistics 

Q(5) 71.1948   [0.000] 
Q(10) 120.783   [0.000] 
Q(20) 145.085   [0.000] 
Q(50) 172.831   [0.000] 

Q McLeod-Li statistics 

Q(5) 117.096   [0.000] 
Q(10) 182.624   [0.000] 
Q(20) 204.178   [0.000] 
Q(50) 214.615   [0.000] 

Engle LM statistics 

ARCH(1–1) 46.606   [0.000] 
ARCH(1–2) 25.877   [0.000] 
ARCH(1–5) 23.281   [0.000] 
ARCH(1–10) 15.902   [0.000] 
ARCH(1–20) 9.590     [0.000] 

 

Note: p-value in brackets. 

Below we present the detailed results of the estimation of ARFIMAX-

FIGARCH model with t-Student innovations for the chosen enterprise from 

the construction sector – Mostostal Warszawa SA (MSW; see Table 4a–4b).   



Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

104 

Table 4a. Estimation results of ARMAX(1,2)-GARCH(1,1) for MSW in stable  

period 

Parameter Parameter estimates 

Cst(M) 0.223    [0.000] 
Vm,t_WIG 0.369    [0.374] 

AR(1) 0.858    [0.000] 
MA(1) –0.712   [0.000] 
MA(2) –0.049   [0.044] 
Cst(V) 0.221    [0.025] 
ARCH1 0.165    [0.003] 

GARCH1 0.757    [0.000] 
Df-Student 2.258    [0.000] 

AIC 2.029 SC 2.072 
 

Note: p-value in brackets. 

Table 4b. Diagnostic residuals tests for MSW 

Test Estimates of the test statistics 

Q Box-Pierce statistics for standardized residuals 

Q(5) 8.183        [0.037] 
Q(10) 11.812      [0.107] 
Q(20) 19.714      [0.289] 
Q(50) 54.719      [0.205] 

Q Box-Pierce statistics for squared standardized residuals 

Q(5) 0.660        [0.883] 
Q(10) 0.916        [0.999] 
Q(20) 2.187        [0.999] 
Q(50) 3.857        [0.999] 

Engle LM statistics  

ARCH(1–2) 0.035       [0.965] 
ARCH(1–5) 0.128       [0.986] 
ARCH(1–10) 0.088       [0.999] 

Jarque-Bery for normality 27151      [0.000] 
Joint Nyblom test of stability 1.2021 

Nyblom for Cst(M) 0.1501 
Nyblom for Vm,t_WIG 0.0541 

Nyblom for AR(1) 0.0577 
Nyblom for MA(1) 0.0505 
Nyblom for MA(2) 0.0803 
Nyblom for Cst(V) 0.1432 
Nyblom for ARCH1 0.2187 

Nyblom for GARCH1 0.2149 
Nyblom for Df-Student 0.0712 

Sign Bias Test 0.899      [0.369] 
Negative Sign Bias Test 0.381      [0.703] 
Positive Sign Bias Test 0.275      [0.783] 
Jointly Engle–Ng test 2.227      [0.527] 

Note: p-value in brackets, p-value (5%) = 0.47 for individual Nyblom test. 



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

105 

It is worth emphasizing that for each estimated model for the Mostostal 

Warszawa company, the parameters indicating the strength and direction of 

dependencies between enterprise volatility and market volatility was statisti-

cally insignificant. 

The results summarizing estimation of ARFIMAX-FIGARCH class 

models with included variables describing volatility of the stock market for 

particular companies from the construction sector in the stable period and 

turbulent period have been presented in Tables 5–6. 

The analysis of data included in Table 5 allows us to formulate the following 

conclusions. In case of Energopol-Południe and Budopol-Wrocław enter-

prises the relationship between the market volatility and volatility of their 

share prices was statistically insignificant. For the remaining enterprises the 

relationship between the WIG index volatility and firms volatility was statis-

tically significant  and positive. All additional variables describing market 

volatility  (Vm,t-1_WIG, Rm,t, Rm,t
2
) turned out to be statistically insignificant 

in case of all estimated models.  

Table 5. Results on commonality in volatility for construction sector in stable period 

Company Model specification 
Estimate of  
Vm,t_WIG 
parameter 

Significance of the influence of others 
market variables (Vm,t-1_WIG, Rm,t, Rm,t

2)  
on firm volatility 

Mostostal 
Export (MSX) 

ARMAX(1,1)-
FIGARCH(1,0.54,1),  
t-Student distribution 

2.069    
[0.000] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Prochem 
(PRM) 

ARFIMAX(1,0.121,1)- 
GARCH(1, 1), 

t-Student distribution 

0.390    
[0.005] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Mostostal 
Zabrze Hol-
ding (MSZ) 

ARFIMAX(1,0.049,1)- 
GARCH(1, 1), 

t-Student distribution 

1.191    
[0.013] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Budimex 
(BDX) 

ARFIMAX(1,0.021,1)- 
GARCH(1, 1), skewed 
t-Student distribution 

0.090    
[0.006] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Elektrobudo-
wa (ELB) 

ARFIMAX(1,0.105,1)- 
GARCH(1, 1), 

t-Student distribution 

0.677    
[0.010] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Energoapara-
tura (ENP) 

ARFIMAX(1,0.086,0)- 
ARCH(1), 

t-Student distribution 

0.539   
[0.022] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Energopol- 
Południe 

(EPL) 

ARFIMAX(1,0.185,1)- 
GARCH(1, 1), 

t-Student distribution 

0.075   
[0.410] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

 



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DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

106 

Table 5. continued 

Company Model specification 
Estimate of  
Vm,t_WIG 
parameter 

Significance of the influence of others 
market variables (Vm,t-1_WIG, Rm,t, Rm,t

2)  
on firm volatility 

Projprzem 
(PJP) 

ARFIMAX(1,0.027,0)- 
ARCH(1), 

t-Student distribution 

0.167   
[0.003] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Elkop (EKP) 
ARMAX(1,1)- 
GARCH(1, 1), 

t-Student distribution 

0.023   
[0.018] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Ulma 
Construccion 
Polska (ULM) 

ARFIMAX(0,0.06,1)- 
FIGARCH(1,0.57,1), 
t-Student distribution 

0.041  
[0.355] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Energomon-
taż-Południe 

(EDP) 

ARFIMAX(1,0.042,1)-
GARCH(1,1), 

t-Student distribution 

0.815  
[0.045] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Mostostal 
Płock (MSP) 

ARX(2)-GARCH(1,1), 
t-Student distribution 

3.642   
[0.000] 

Rm,t:  0.081      [0.027] 
Rm,t

2:  –0.069   [0.001] 

Budopol-
Wrocław 

(BDL) 

ARFIMAX(0,0.06,1)- 
FIGARCH(1,0.79,1), 
t-Student distribution 

0.024  
[0.283] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Awbud (AWB) 
ARFIMAX(0,0.06,1)- 

GARCH(1,1), 
t-Student distribution 

0.921   
[0.005] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Pemug (PMG) 
ARX(2)-GARCH(1,1), 
t-Student distribution 

0.748   
[0.099] 

All additional market variables have statisti-
cally insignificant impact on the firm volatili-

ty – elimination from the model 

Instal Kraków 
(INK) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

2.618   
[0.000] 

Rm,t
2:  –0.076      [0.001] 

Note: p-value in brackets. 

In the turbulent period for five enterprises: Awbud, Projprzem, Prochem, 

Elkop, Ulma Construccion the relationship between the WIG index volatility 

and firm volatility was statistically insignificant. For the remaining 15 enter-

prises statistically significant influence of market volatility on firm volatility 

was confirmed, while the direction of this dependence was positive. Addi-

tionally, share price volatility of Mostostal Warszawa was significantly 

shaped by market volatility observed on the previous day. In case of the 

remaining enterprises additional variables did not significantly influence 

share price volatility. The conducted commonality in volatility analysis for 

the enterprises listed on the Warsaw Stock Exchange shows that in the stable 

period 82% of analyzed enterprises were sensitive to the WIG index volatili-

ty, the appropriate ratio in the turbulent period reached the value of 75%. 



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

107 

Table 6. Results on commonality in volatility for construction sector in turbulent 

period 

Company Model specification 
Estimate of  
Vm,t_WIG 
parameter 

Significance of the influence of others 
market variables (Vm,t-1_WIG, Rm,t, Rm,t

2) 
on firm volatility 

Mostostal Export 
(MSX) 

ARFIMAX(1,0.07,1)- 
GARCH(1,1), 

t-Student distribution 

0.949   
[0.007] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Mostostal 
Warszawa 

(MSW) 

ARX(2)-GARCH(1,1), 
t-Student distribution 

0.171   
[0.006] 

Vm,t-1_WIG:   0.176 [0.040] 

Prochem 
(PRM) 

ARMAX(1,1)-
FIGARCH(1,0.68,1), 
t-Student distribution 

0.138   
[0.483] 

 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Budimex 
(BDX) 

ARFIMAX(1,0.103,1)- 
GARCH(1,1), 

t-Student distribution 

0.206   
[0.000] 

 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Mostostal 
Zabrze Holding 

(MSZ) 

ARFIMAX(1,0.076,0) -
GARCH(1,1), 

t-Student distribution 

0.867    
[0.000] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Elektrobudowa 
(ELB) 

ARFIMAX(1,0.121,1)- 
GARCH(1,1), 

t-Student distribution 

0.122   
[0.082] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Ulma 
Construccion 
Polska (ULM) 

ARFIMAX(1,0.041,1)- 
GARCH(1,1), 

t-Student distribution 

0.227    
[0.454] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Energoaparatura 
(ENP) 

ARFIMAX(1,0.111,0)- 
GARCH(1,1), 

t-Student distribution 

0.508    
[0.005] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Polimex-
Mostostal 

(PXM) 

ARMAX(1,1)- 
GARCH(1,1), 

t-Student distribution 

1.639    
[0.000] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Mostostal Płock 
(MSP) 

ARMAX(1,1)-
ARCH(1), 

t-Student distribution 

0.401    
[0.000] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Energopol- 
Południe 

(EPL) 

ARFIMAX(1,0.045,1)- 
GARCH(1,1), 

t-Student distribution 

0.521  
[0.012] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Instal Kraków 
(INK) 

ARFIMAX(0,0.12,1)-
FIGARCH(1,0.75,1), 
t-Student distribution 

0.541    
[0.000] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Projprzem 
(PJP) 

ARMAX(1,1)- 
GARCH(1,1), 

t-Student distribution 

0.065    
[0.562] 

 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Elkop 
(EKP) 

ARFIMAX(1,0.999,0)-
ARCH(1), 

t-Student distribution 

0.054    
[0.189] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 



Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

108 

Table 6. continued 

Company Model specification 
Estimate of  
Vm,t_WIG 
parameter 

Significance of the influence of others 
market variables (Vm,t-1_WIG, Rm,t, Rm,t

2) 
on firm volatility 

PBG (PBG) 
ARFIMAX(1,0.236,1)- 

GARCH(1,1), 
t-Student distribution 

1.041  
[0.000] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Herkules 
(HRS) 

ARFIMAX(1,0.063,1)- 
GARCH(1,1), 

t-Student distribution 

1.016  
[0.000] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Erbud 
(ERB) 

ARFIMAX(1,0.04,1)- 
GARCH(1,1), 

t-Student distribution 

0.269  
[0.020] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Energomontaż-
Południe (EDP) 

ARFIMAX(1,0.14,1)- 
GARCH(1,1), 

t-Student distribution 

0.457   
[0.009] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Budopol-
Wrocław (BDL) 

ARFIMAX(1,0.087,1)- 
GARCH(1,1), 

t-Student distribution 

0.972  
[0.000] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Awbud (AWB) 
ARMAX(1,1)- 
GARCH(1,1), 

t-Student distribution 

–0.018   
[0.735] 

All additional market variables have 
statistically insignificant impact on the firm 

volatility – elimination from the model 

Note: p-value in brackets. 

Estimation of volatility models for the IT sector enterprises in both ana-

lyzed periods was conducted in the same manner as in case of the construc-

tion sector enterprises (Tables 7–8).  

The estimated models indicate a statistically insignificant relationship be-

tween market volatility and share price volatility of IT sector companies only 

in case of Macrologic and Talex. Moreover, included in the modelling pro-

cess the additional variables describing market volatility, did not have a sta-

tistically significant impact on shares volatility of the analyzed enterprises. 

In the turbulent period for the seven analyzed enterprises from the IT sector:  

Comarch, Talex, Simple, Wasko, PC Guard, Unima 2000, Infovide-Matrix 

the relationship between the WIG index volatility and share price volatility 

was statistically insignificant at 10% significance level. In addition, for three 

enterprises: Comarch, Procad and NTT System market volatility from the 

previous day significantly affected share price volatility of these enterprises. 

On the basis of empirical studies results for IT sector one may draw the con-

clusion that ARFIMAX-FIGARCH specification has been chosen more fre-

quently for the post-crisis period compared to pre-crisis period. Therefore, 

long memory property is not an inherent feature of firm volatility process 

and the structural change connected with the subprime crisis may influence 



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

109 

to the assessment of the long memory property in the volatility
5
. The con-

ducted commonality in volatility analysis for the IT sector  enterprises  listed  

Table 7. Results on commonality in volatility for IT sector in stable period 

Company Model specification 
Estimate of  
Vm,t_WIG 
parameter 

Significance of the influence of others 
market variables (Vm,t-1_WIG, Rm,t, Rm,t

2)  
on firm volatility 

Calatrava 
Capital 
(CTC) 

ARFIMAX(1,0.104,1)-
GARCH(1,1), 

t-Student distribution 

1.186    
[0.002] 

 

All additional market variables have statisti-
cally insignificant impact on the firm volatility 

– elimination from the model 

ZUK Elzab 
(ELZ) 

ARFIMAX(1,0.044,1)-
GARCH(1,1), 

t-Student distribution 

0.362    
[0.030] 

 

All additional market variables have statisti-
cally insignificant impact on the firm volatility 

– elimination from the model 

Asseco Po-
land 

(ACP) 

ARFIMAX(1,0.108,1)- 
GARCH(1,1), 

t-Student distribution 

0.536    
[0.000] 

All additional market variables have statisti-
cally insignificant impact on the firm volatility 

– elimination from the model 

Comarch 
(CMR) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.349   
[0.003] 

All additional market variables have statisti-
cally insignificant impact on the firm volatility 

– elimination from the model 

Macrologic 
(MCL) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.392    
[0.133] 

All additional market variables have statisti-
cally insignificant impact on the firm volatility 

– elimination from the model 

Talex 
(TLX) 

ARMAX(1,1)-
GARCH(1,1) with t-
Student distribution 

0.362    
[0.155] 

All additional market variables have statisti-
cally insignificant impact on the firm volatility 

– elimination from the model 

Simple 
(SME) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

1.414    
[0.061] 

All additional market variables have statisti-
cally insignificant impact on the firm volatility 

– elimination from the model 

CD Project 
Red 

(CDR) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.949    
[0.001] 

 

All additional market variables have statisti-
cally insignificant impact on the firm volatility 

– elimination from the model 

Sygnity 
(SGN) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.349   
[0.086] 

All additional market variables have statisti-
cally insignificant impact on the firm volatility 

– elimination from the model 

Wasko 
(WAS) 

ARMAX(1,1)- 
GARCH(1,1), 

t-Student distribution 

0.719   
[0.056] 

All additional market variables have statisti-
cally insignificant impact on the firm volatility 

– elimination from the model 

Note: p-value in brackets. 

                                                 
5 It is worth underlining that for both the construction and IT sectors there were no rea-

sons for changing the basic specification of firm volatility models to Exponential GARCH 

model, which enables capturing the asymmetric effect of negative and positive shocks for 

conditional variance (results of Sign Bias tests). But for deepening the studies over the link-

age between market volatility and firm volatility on the Polish Capital Market we will use the 

asymmetric multivariate GARCH structure in near future.  



Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

110 

on the Warsaw Stock Exchange shows that in the stable period 80% of ana-

lyzed enterprises were sensitive to the WIG index volatility, while in the 

turbulent period the fraction of these enterprises dropped to 65%. 

Table 8. Results on commonality in volatility for IT sector in turbulent period 

Company Model specification 
Estimate of  
Vm,t_WIG 
parameter 

Significance of the influence of others 
market variables (Vm,t-1_WIG, Rm,t, Rm,t

2)  
on firm volatility 

Sygnity 
(SGN) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.633    
[0.005] 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

Calatrava 
Capital 
(CTC) 

ARFIMAX(1,0.049,1)-
GARCH(1,1), 

t-Student distribution 

1.401   
[0.013] 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

ZUK Elzab 
(ELZ) 

ARMAX(1,1)-
FIGARCH(1,0.39,1), 
t-Student distribution 

1.494      
[0.036] 

 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

Asseco 
Poland 
(ACP) 

ARFIMAX(1,0.64,1)-
GARCH(1,1),skewed 
t-Student distribution 

1.381    
[0.000] 

 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

Comarch 
(CMR) 

ARFIMAX(1,0.07,1)-
FIGARCH(1,0.31,1), 
t-Student distribution 

0.085    
[0.410] 

Rm,t
2:  0.011  [0.005] 

Macrologic 
(MCL) 

ARFIMAX(1,0.08,1)-
FIGARCH(1,0.7,1), 

t-Student distribution 

0.020      
[0.000] 

 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

Talex 
(TLX) 

ARFIMAX(2,0.044,0)-
GARCH(1,1), 

t-Student distribution 

–0.008     
[0.942] 

 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

Simple 
(SME) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.365   
[0.203] 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

Wasko 
(WAS) 

ARMAX(1,1)-
GARCH(1,1), skewed 
t-Student distribution 

0.073   
[0.326] 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

CD Project 
Red (CDR) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

2.180    
[0.000] 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

Betacom 
(BCM) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.706    
[0.000] 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

ATM 
(ATM) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.554    
[0.049] 

 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

Comp 
(CMP) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.188    
[0.080] 

 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

111 

Table 8. continued 

Company Model specification 
Estimate of  
Vm,t_WIG 
parameter 

Significance of the influence of others 
market variables (Vm,t-1_WIG, Rm,t, Rm,t

2)  
on firm volatility 

PC Guard 
(PCG) 

ARFIMAX(1,0.002,1)-
GARCH(1,1), 

t-Student distribution 

0.003  
[0.731] 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model, 

problem with parameters’ stability 

Qumak-
Sekom 
(QSM) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.271    
[0.021] 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

Unima 2000 
SystemyTele-
informatycz-

ne (U2K) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

–0.009    
[0.661] 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

LSI Software 
(LSI) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.807   
[0.016] 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

Infovide-
Matrix 
(IMX) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.043   
[0.568] 

 

All additional market variables have statis-
tically insignificant impact on the firm 
volatility – elimination from the model 

Procad 
(PRD) 

ARMAX(1,1)-
FIGARCH(1,0.29,1), 
t-Student distribution 

0.896   
[0.004] 

Vm,t-1_WIG :   0.644   [0.005] 

NTT System 
(NTT) 

ARMAX(1,1)-
GARCH(1,1), 

t-Student distribution 

0.733   
[0.000] 

Vm,t-1_WIG :   0.539  [0.000] 

Note: p-value in brackets. 

In order to verify the hypothesis assuming that within a given sector the 

percentage of enterprises in the stable and turbulent period, for which a sig-

nificant positive dependence between their share price volatility and stock 

market volatility is the same, we used a statistical test (Krysicki et al. 2012):   

.:

:

211

210

ppH

ppH




      

The test statistics under the null hypothesis has a standardized normal distri-

bution:  

),1,0(arcsin2arcsin2
21

21

2

2

1

1 N
nn

nn

n

k

n

k
U 


















      (12) 

where: p1 – fraction of the firms in the given sector for which the commonal-

ity in volatility effect was confirmed in stable period, p2 – fraction of the 



Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

112 

firms in the given sector for which the commonality in volatility effect was 

confirmed in turbulent period, 
  

  
 and 

  

  
  – sample proportions corresponding 

to p1 and p2. 

Table 9. Statistics for similarity of commonality in volatility effect in stable and 

turbulent period 

U statistic 

(1.95 – 5% critical value) 

Construction sector IT sector 

0.546 0.875 

At 5% significance level there is no reasons for rejecting the hypothesis that 

commonality in volatility didn’t differ significantly in the turbulent period 

compared to the stable period in construction sector as well as in IT sector 

on the Polish Capital Market (Table 9).  

The conducted research show that the fractions of enterprises, in the sta-

ble and turbulent period, for which the occurrence of significant relation-

ships between  their share price volatility and the WIG index volatility was 

proved, did not significantly differ one from the other. This may confirm that 

analyzed sectors were characterized by resistance to external shocks ab-

sorbed by Polish stock market through  the investor behaviour channel. 

Conclusions 

The analysis of relationships between market volatility and volatility of en-

terprises from the construction and IT sectors has shown that there is not an 

increase in the fractions of firms, for which their share volatility in a signifi-

cant and positive way was connected with stock market volatility in the pe-

riod corresponding to the subprime crisis and the debt crisis in the Euro 

zone. Moreover, one can observe a different relation of these sectors to ex-

ternal shocks coming to Polish market, namely in the IT sector the fraction 

of enterprises sensible to the WIG index volatility decreased, while in the 

construction sector it increased. However, the changes were not statistically 

significant. The financial situation of the enterprises from these sectors was 

conditioned not only by unforeseen factors connected with reaction of inves-

tors to the information about crisis, but first of all economic factors and 

skills of managers in the scope of adjusting enterprise strategies to the 

changeable conditions of external environment, making the use of the oppor-

tunities and threats filter in building and maintaining enterprise competitive 

position. On the basis of conducted empirical studies (Otola, 2013) concern-

ing financial condition of enterprises from the construction and IT sectors we 

can draw the following conclusions. Majority of the analyzed enterprises 



Analysis of the Relationship between Market Volatility and Firms Volatility…  

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

113 

from the construction sector did not possess financial liquidity which is the 

determinant of the ability to pay back their liabilities. Moreover, in case of 

over 65% of the examined enterprises their rates of debt exceeded 70%. In 

addition, majority of the discussed enterprises achieved low sales profitabil-

ity already at the level of gross profit from sales or operational profit. There 

were such enterprises among all the examined ones which were character-

ized by high negative sales profitability. The situation was different in the IT 

sector. This sector enterprises were characterized by average debt level and 

maintained financial liquidity on the proper level (in accordance with the 

assumed norms of indexes), and a part of them possessed surplus of turnover 

assets with reference to the current liabilities, which indicates the excess of 

liquidity. Sales profitability indexes in the stable period were on a higher 

level than in the turbulent period, in which they can be considered as low 

and unsatisfactory for investors, nonetheless they were better than the ones 

from the construction sector.  

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Whaley, R.E. (2009), Understanding the VIX, Journal of Portfolio Management, 35, 98–105, 

 DOI: http://dx.doi.org/10.3905/jpm.2009.35.3.098. 

Włodarczyk, A. (2010), Testowanie efektu długiej pamięci w zmienności cen metali szlachet-

nych (Testing for Long Memory in Volatility of Precious Metal Prices), Roczniki Na-

ukowe. Seria B, Nauki Ekonomiczne i Informatyka (Scientific Annals. Series B, Eco-

nomic Science and Informatics), 1–2, 151–170. 

Analiza relacji między zmiennością rynku a zmiennością firm           
na polskim rynku kapitałowym 

Z a r y s  t r e ś c i. W artykule analizowano kształtowanie się zależności między zmiennością 

rynku a zmiennością cen akcji w spółkach z wybranych sektorów Giełdy Papierów Warto-

ściowych w Warszawie przed i po kryzysie subprime. Badania empiryczne dotyczą wybra-

nych przedsiębiorstw z sektorów budownictwo i IT w latach 2004–2011. Miary zmienności 

zostały obliczone na podstawie najniższego i najwyższego kursu dziennego spółek należących 

http://dx.doi.org/10.1016/j.irfa.2011.06.012
http://dx.doi.org/10.1016/S1042-444X(03)00015-X
http://dx.doi.org/10.1016/j.ecosys.2013.12.003
http://dx.doi.org/10.3905/jpm.2009.35.3.098


Włodarczyk, Otola 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 87–116 

116 

do indeksu WIG. Dla każdej firmy został oszacowany, zarówno dla okresu stabilnego, jak 

i niestabilnego, model ARFIMAX-FIGARCH z dodatkowymi zmiennymi egzogenicznymi, 

odzwierciedlającymi zmienność rynku. Przeprowadzone badania empiryczne nie wykazały, 

że negatywne szoki płynące z rynku amerykańskiego przez kanał zachowań inwestorów 

przyczyniły się do wzrostu frakcji firm z sektorów budownictwa i IT notowanych na GPW, 

których zmienność jest kształtowana przez zmienność rynku. 

S ł o w a  k l u c z o w e: ARFIMAX-FIGARCH, kryzys subprime, zmienność firm, zmien-

ność rynku, Giełda Papierów Wartościowych w Warszawie. 
 


