










































DYNAMIC ECONOMETRIC MODELS


© 2012 Nicolaus Copernicus University Press. All rights reserved.  
http://www.dem.umk.pl/dem 

DYNAMIC ECONOMETRIC MODELS 
Vol. 12 (2012) 35−52 

Submitted April 30, 2012  ISSN 
Accepted October 8, 2012 1234-3862 

Katarzyna Bień-Barkowska*   

“Does It Take Volume to Move the EUR/PLN FX Rates?”                     
Evidence from Quantile Regressions 

A b s t r a c t This study investigates the impact of trading volume on selected quantiles of the 
EUR/PLN return distribution. Empirical results obtained with the quantile regression approach 
confirm that an increase in the turnover is associated with a significant increase in the dispersion 
of the corresponding return distribution. We divided the trading volume into its expected (antici-
pated) and unexpected (unanticipated) component and found that the unexpected volume shocks 
have a significantly larger impact on the dispersion of the return distribution. We also observed 
that the volume-return relationship is nonlinear; the dependence is stronger with more extreme 
quantiles. Moreover, after accounting for a conditional volatility measure as a controlling explan-
atory factor for the quantile dynamics, the impact of the expected volume declines yet remains 
significant especially for the most extreme quantiles. 

K e y w o r d s: volume-return relationship, market microstructure, FX trading, quantile regres-
sion.  

J E L Classification: C22, G15 

Introduction  
 Research on price – volume relationship has a long history in the literature 
of both theoretical and empirical finance. Positive contemporaneous correlation 
between trading volume and price volatility is already a well-documented ob-
servation with early studies on the topic traced back to the seventies. In this 
decade, the positive relationship between the selected measures of price varia-
bility and trading volume has been demonstrated for stock markets in various 
publications (Crouch, 1970; Epps and Epps, 1976; Morgan, 1976; Westerfield, 
1977, among others). Karpoff (1987) presents a vast survey of the early litera-

                                                 
* Correspondence to: 1. Katarzyna Bień-Barkowska, Institute of Econometrics, Warsaw 

School of Economics, ul. Madalińskiego 6/8, 02-513 Warsaw, Poland or 2. Katarzyna Bień-
Barkowska, Financial System Department, National Bank of Poland, ul. Świętokrzyska  11/21, 
00-919, Warsaw, Poland, e-mail: katarzyna.bien@sgh.waw.pl 



Katarzyna Bień-Barkowska 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

36 

ture summarizing the results of 19 empirical studies conducted throughout the 
seventies and eighties focusing on the volume-return relationship evidenced by 
daily and intraday data from the stock, bond and commodity future markets. 
Further evidence for this positive relationship can be found in numerous studies 
from the nineties and more recently (Lamoureoux and Lastrapes, 1990; Gallant 
et al., 1992; Jones et al., 1994; Bohl and Henke, 2003; Luckley, 2005; Doman, 
2008; Doman, 2011; and others). Bessembinder and Seguin (1993) suggest 
splitting the trading volume into its anticipated and unanticipated component. 
Given the well documented fact, that the volume is highly autocorrelated, it is 
also forecastable, hence the authors differentiate its expected and unexpected 
part and evidence that the unexpected volume shock has between two and thir-
teen times greater effect on the volatility of stock prices. Different informative 
meanings of the expected and the unexpected volume have also been found in 
other studies (Brown-Hruska and Kuserk, 1995; Gurgul et al., 2005; Huang et 
al., 2006).  
 There are at least three strands of the literature on market microstructure 
that could explain the relationship between trading volume and return variabil-
ity. The first one is known as the sequential information arrival hypothesis (SI-
AH) (c.f. Copeland, 1976; Jennings et al., 1981). According to this theory, all 
traders cannot simultaneously absorb the arrival of new market information. 
Therefore, a revision of their expectations occurs sequentially and the process in 
which new information is impounded into the price can spread out over time. 
Only after all traders are able to react and trade, the final equilibrium price is 
set; this explains the lead-lag relationship between volatility and trading vol-
ume. Accordingly, intensive trading and a high trading volume can help to iden-
tify periods where prices continue to adjust to informational shocks.  
 The second explanation of the positive contemporaneous correlation be-
tween return and volume arises from the idea of theoretical information models. 
In such models traders are allowed to trade different sizes; better-informed trad-
ers initiate larger transactions and their activity has an adverse selection effect 
on the price (c.f., Easley, O’Hara, 1987). In another model, the informational 
content of trading intensity has been outlined. A long duration between consec-
utive trades indicates that there was no new information, whereas a short dura-
tion increases the probability that better-informed traders have increased the 
overall trading intensity. Hence, market makers change quoted price by increas-
ing the bid-ask spread as a weapon against an adverse selection risk reflected by 
an increased number of trades (Easley and O’Hara, 1992). Other information 
models that predict a positive relationship between trading volume and price 
volatility are developed in the studies of Admati and Pfleiderer (1988), Blume 
et al. (1994), Easley, Kiefer and O’Hara (1997), and Malinova and Park (2011).  
 The third explanation for the significant positive volume-return relationship 
arises from the mixture of distributions hypothesis (MDH) and has more of 
a statistical than an economic background (Clark, 1973; Epps and Epps, 1976; 



“Does It Take Volume to Move the EUR/PLN FX Rates?”… 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

37 

Tauchen and Pitts, 1983). According to the MDH, a bivariate distribution of 
volume and price change variables is conditional upon an information variable 
such that both variables react simultaneously to the arrival of news and are driv-
en by this unobservable factor.  

The aim of this paper is to shed light on the intraday relationship between 
return and volatility in the EUR/PLN currency pair on the interbank spot mar-
ket. We will use trade data from the Reuters Dealing 3000 Spot Matching Sys-
tem, a very popular brokerage trading platform that can automatically match all 
incoming buy and sell orders once their prices agree. 

Inspired by the study of Chuang et al. (2009), we describe the return-
volume relationship with the help of quantile regressions (QR). Such an ap-
proach allows us to generalize the results of many empirical studies concerning 
the relationship between trading volume and the measure of price variability. 
The majority of empirical studies demonstrate that it is common to introduce 
volume as an additional explanatory factor into the GARCH specification for 
the conditional variance of the return distribution (Lamoureux and Lastrapes, 
1990; Bohl and Henke, 2003; Gurgul et al., 2005; Majand and Yung, 2006; and 
others). Such a modeling strategy measures only the impact of the trading vol-
ume on the second central moment of the conditional return distribution. The 
QR approach is much different in that it is semiparametric and allows for an 
analysis of the impact of some explanatory factors on the selected quantiles of 
the return distribution without making any assumptions about their parametric 
form (i.e., Gaussian, Student’s t, generalized gamma) or about the parametric 
specification of its conditional mean and variance.  

Models that are members of the GARCH family make an usual implicit as-
sumption about a type of a parametric location-scale distribution for financial 
returns where the first two moments (i.e., the conditional expectation and the 
conditional variance) are described in a dynamic fashion. The QR approach 
does not impose such parametric assumptions but instead concentrates on the 
quantiles. Accordingly, the QR approach has an obvious upper hand over the 
standard GARCH approach: the impact of the explanatory variables can be dif-
ferent for different quantiles. An impact of trading volume can be different for 
the τ-quantile than it is for the (1-τ)-quantile (where τ denotes a corresponding 
probability level). Hence, we are able to infer whether the arrival of new infor-
mation has a different impact on the probability of an extreme FX rate increase 
versus an extreme FX rate decrease. Such a situation could be explained by the 
possibly of a time-varying skewness and/or kurtosis of the return distribution 
that could also depend on a latent information arrival variable.  

Within this study we decompose trading volume into its expected (forcasta-
ble) and unexpected (unpredictable) parts and compare their impact on the se-
lected quantiles of the EUR/PLN return distribution. Moreover, we check to see 
if the trading volume captures extra information behind the quantile dynamics 



Katarzyna Bień-Barkowska 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

38 

when confronted with the standard GARCH volatility forecasts as an intuitive 
and natural explanatory factor.   

1. The Econometric Approach 

1.1. Trading Volume Decomposition  
In order to investigate the volume – return relationship one must typically 

distinguish between the so-called expected (anticipated) and unexpected (unan-
ticipated) trading volume (Andersen, 1996; Bjonnes et al., 2003). Bearing in 
mind that the volume variable is highly autocorrelated, the expected volume is 
the result of more persistent fluctuations in liquidity needs whereas unexpected 
volume should be unpredictable by traders and should approximate a new in-
formation arrival. 

Differentiation between what is expected and unexpected volume is typical-
ly performed using ARIMA models (c.f., Bessembinder and Seguin, 1993; 
Hartmann, 1999; Bjonnes et al., 2003). However, such models usually require 
logarithmic transformation of the volume variable in order to avoid its nonnega-
tivity and/or in order to diminish heteroskedasticity, especially for high fre-
quency data. Such a transformation may distort the potential relationship be-
tween the variables and so we propose a different procedure here. In order to 
preserve an original time series (unchanged due to a logarithmic transfor-
mation), we apply the Autoregressive Conditional Duration (ACD) models of 
Engle and Russell (1998). The ACD were initially used to describe a highly 
autocorrelated time series of durations (time spells) between selected events 
(i.e., transactions or price changes). More recently these models were used to 
describe other financial variables including transaction volume in the studies of 
Manganelli (2005) and Doman (2008, 2011) or the bid-ask spread in Nolte 
(2008). The ACD models are well designed for serially correlated variables 
with a strictly positive domain. Here we have used the ACD (1,1) model with 
the Burr distribution for the error term proposed by Grammig and Maurer 
(2000). The model for the trading volume variable tvol  can be written as fol-
lows:  

,= tttvol εΨ   (1) 

where )|(= 1−Ψ ttt FvolE , 1−tF  denotes an information set up at the time point 
1−t   (containing all past realizations of tvol ), tε  denotes an error term, and 

{ } ...~ diitε ),( 2σκBurr  such that 1)( =tE ε . The conditional expectation of the 
dependent variable tvol  is described as follows:  

,= 12110 −− +Ψ+Ψ ttt volβββ   (2) 



“Does It Take Volume to Move the EUR/PLN FX Rates?”… 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

39 

This model can be estimated using the ML method. The log likelihood function 
has the following form: 

(

,)(1ln11

ln1)(lnln=)(

2
2

1=





⋅⋅+⋅






 +−

⋅−+⋅−Θ

−

∑

κκξσ
σ

κξκκ

tt

tt

N

t

vol

volLogL
  (3) 

where 






 −Γ






 +Γ







 +Γ⋅

Ψ







 +

κσκ

σ
σ

ξ

κ

1111

11)(
=

2

2

11
2

tt , κσ <<0 2  and )(⋅Γ  denotes the gamma 

function.  

Accordingly, the expected volume tvolexp,  is defined as an estimate of the con-

ditional expectation tΨ̂  (i.e., it is conditional upon all past observations of the 
volume variable) whereas an unexpected volume is defined as the residual 

tttun volvol Ψ= ˆ
exp, . 

1.2. Quantile Regressions for the EUR/PLN Returns  

Taking the trading volume as an explanatory variable in the QR setup we 
are able to check its impact on the dispersion of the return distribution in a very 
explicit manner. In the QR setting we can “jointly” capture the impact that the 
trading volume exerts on the general shape (i.e., skewness, kurtosis or vari-
ance). As mentioned previously, most popular financial econometric models 
typically neglect the possible effect of explanatory variables on the skewness or 
kurtosis of the distribution. Furthermore, the popular GARCH models rule out 
a potential asymmetric impact on the trading volume on the tail probability of 
a large price upswing versus a large price falls.  

In order to check the impact of the trading volume on the selected quantiles 
of the return distribution we used simple linear QR models where each of them 
corresponds to a selected conditional quantile )|( trtQ xτ : 

,

),(=)|(

1exp,,3exp,,2exp,,1

1,1,0

−

−

+++

++

tuntunt

ttr

volvolvol

SrQ
t

τττ

τττ

γγγ

υαατ νx
  (4) 

where tr  denotes the logarithmic rate of return on the EUR/PLN exchange rate 
between the moments t  and 1−t ,τ denotes a corresponding probability level 
and ),( υτνS  depicts the intraday seasonality factor given as the fast Fourier 
form (FFF): 



Katarzyna Bień-Barkowska 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

40 

[ ]][2cos][2sin=),( ,2,12

2

1=
,0 υπνυπνυνυ ττττ llS ll

l
⋅+⋅+⋅ −∑ν  , (5) 

where υ  denotes a time-of-day variable standardised on the interval ].1,0[   
[ ,,),4cos(),4sin(),2cos(),2sin(,,,1 exp,exp,1 tunttt volvolτr πτπτπτπτ−=x

]Ttunvol 1exp, − is a vector of selected explanatory variables. The FFF diurnality 
component that we apply has been advocated by Andersen and Bollerslev 
(1996). The diurnality function can therefore be depicted as a number of sine 
and cosine functions and should smoothly depict the systematic intraday sea-
sonality pattern in the dispersion of the return distribution. This standard meth-
odology assumes a two-step procedure: the intraday returns are first deseasonal-
ized (divided by the obtained seasonality pattern) and then GARCH models are 
estimated for the filtered returns. We allow for an additive seasonality pattern 
for each of the estimated quantile regressions, which allow us to capture sys-
tematic intraday regularities in the unrestricted shape of the conditional distribu-
tion. As previously mentioned, this is done in a semiparametric setup and is 
much more general such that we can capture different diurnality patterns for 
different quantile levels. In each of QR regressions given by equation (4) we 
have also introduced a lagged tr  in order to account for possible autocorrela-
tion. The parameter corresponding to the autoregressive term can be different 
for different quantiles, as evidenced by Baur et al. (2011).  

The suggested model for the conditional quantile of the return distribution 
can be criticized as being too parsimonious. Given that it contains only the past 
return, intraday seasonality component and volume variables as the major driv-
ing forces1, its ability to account for the volatility clustering effect may be rather 
limited. Thus, in the second model that we propose we have included a return 
volatility forecast as an additional driving factor for the quantile dynamics. 
Chuang et al. (2009) proposed the addition of a lagged value of 2

tr as a natural 
proxy for the volatility. An alternative to this is to account for possible persis-
tency in the conditional quantiles with the application of the Conditional Auto-
regressive Value-at-Risk (CAViaR) models of Engle and Manganelli (2004). 
Within this framework quantile dynamics are captured in the form of auto-
regressive specifications with an absolute value for the past return as new-
information variable. However, the application of an autoregressive specifica-
tion rules out the applicability of standard linear programming algorithms to 
estimate QR. Accordingly, the estimation process based on the genetic algo-
rithm or the Nelder-Mead simplex algorithm and quasi-Newton method (with 
the necessity of computing loops for recursive quantile functions) is quite time-
consuming. Taking into account that we plan to estimate several quantile re-
                                                 

1 The lag structure for the volume variables has been selected on the grounds of their statisti-
cal significance. 



“Does It Take Volume to Move the EUR/PLN FX Rates?”… 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

41 

gression models for several probability levels, this would likely be inefficient. 
Therefore, we decided to approximate the volatility variable with the condition-
al standard deviation estimate 1ˆ −tσ , obtained from the GARCH(1,1) with a Stu-
dent’s t distribution for an error term2 model. As such, a volatility measure3 
uses whole information from the history of the return process at 1−t . It is also 
intended to describe the persistency of the quantile dynamics in a more ade-
quate manner than 2

1−tr : 

.

),(ˆ=)|(

1exp,,3exp,,2exp,,1

1,21,1,0

−

−−

+++

+++

tuntunt

tttr

volvolvol

SrQ
t

τττ

ττττ

γγγ

τνσααατ x
  (6) 

For a given probability τ , QR estimates can be obtained as a minimum of 
the following objective function of asymmetrically weighted absolute devia-
tions:  

( )∑
=

<
−−=

N

t

T
ttxr rT

tt
1

}{minargˆ ττ τ γx1γ γγ , (7) 

where [ ]Tννννν 3214321010 ,,,,,,,,, γγγαατ =γ  denotes a parameter vector and  
[ ,,),4cos(),4sin(),2cos(),2sin(,,ˆ,,1 exp,exp,1 tuntttt volvolτr πτπτπτπτσ−=x   

]Ttunvol 1exp, − is a vector of the corresponding explanatory variables. Nondifferen-
tiable objective function (7) can be minimized using the linear programming 
methods described in Koenker (2005, p. 170-202). The limiting covariance ma-
trix of ( )ττ γγ −ˆn  takes the form of the Huber sandwich (Huber, 1967): 

 ( ) ( )11)1(,0ˆ −−−→− TTT HJHNT ττττ γγ , (8) 

where 

                                                 
2 The volatility estimate 1ˆ −tσ  refers to deseasonalized returns: trtt srr ,= , thus it accounts 

for the volatility left on top of its cyclical behavior. In our empirical application an intraday sea-
sonality factor trs ,  has been estimated with the kernel regression of absolute returns on a time-of-
day variable. We use a quartic kernel with bandwidth computed as 2.78sN -1/5, where s is the 
standard deviation of the data. For details regarding the estimation procedure please refer to 
(Bauwens and Veredas, 2004). An alternative would be to estimate trs ,  by means of  cubic 
splines as suggested by Giot (2005) or by means of the fast Fourier form as suggested by Ander-
son and Bollerslev (1997).  

3  Introduction of the volatility estimate into the QR model for financial returns has been also 
adapted in Taylor (1999). Parsimonious GARCH(1,1) specification succeeded to depict the vola-
tility clustering in a satisfactory way. 



Katarzyna Bień-Barkowska 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

42 

T
t

T

t
tT TJ xx∑

=

−=
1

1  and ( ))(lim
1

1 τQfTH t
T
t

T

t
tTT xx∑

=

−

∞→
=  (Koenker, 2005, p. 74). 

The term ( ))(τQft  denotes the conditional density of tr  evaluated at the τth 
conditional quantile, )(τQ .   

In order to estimate the matrix TH , the term ( ))(τQft  must be evaluated. It 

is typically replaced by its consistent estimate ( ))(ˆ τQft  obtained with the help 
of nonparametric methods. Koenker (2005, p. 80) shows a method to estimate 
the density function evaluated at a given quantile )(τQ  with the help of the 
sparsity estimation methods proposed by Hendricks and Koenker (1991), (i.e., 
as a difference quotient): 

( ) )ˆˆ2)(ˆ
TT hh

T
tTt hQF −+ −= τττ γγ(x , (9) 

where Th denotes a bandwidth ( 0lim =
∞→ TT

h ); selecting the proper bandwidth is 

discussed by Koenker (2005, p. 139-140). Another possibility for the covariance 
matrix estimation, known as a Powell sandwich, would be to estimate TH  via 
kernel estimation: 

T
ttT

T
ttTt hrKnhH xxγx )()(ˆ 1 −= ∑− , (10) 

where )(⋅K  denotes a proper kernel function (e.g., Powell kernel) (c.f., 
Koenker, 2005, p. 80).  

2. Empirical Results 

2.1. Data  

 An empirical study of the volume-return relationship has been performed 
with trade data from the Reuters Dealing 3000 Spot Matching System. This is 
a liquid electronic brokerage system that operates as an order-driven market. It 
can be estimated that trading with the Reuters Dealing 3000 Spot Matching 
System accounts for about 60 % of all interbank spot transactions in the Polish 
zloty market in 20084. 
 The data utilized is comprised of transactions conducted between January-
June 2008 with respect to the EUR/PLN currency pair. The EUR/PLN exchange 
rate is quoted as a quantity of zlotys per one Euro. During the period of study 
the zloty followed an appreciating trend with respect to the Euro. Each transac-
tion is marked with the date, the exact time, the rate and the quantity (in mil-

                                                 
4 Trading of the Polish zloty takes place on offshore markets (mainly between London banks) 

as well as locally in Poland. The datasets used in this analysis take into account both of these 
trading venues. 



“Does It Take Volume to Move the EUR/PLN FX Rates?”… 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

43 

lions) of EUR. Trading on the interbank market is heavily concentrated on busi-
ness days between the hours of 8:00 and 18:00 Central European Time (CET). 
In order to limit the undesired impact of particularly thin trading periods we 
have excluded observations registered on weekends and on business days be-
tween the hours of 18:00 and 8:00 CET. We have also excluded days with ex-
ceptionally low liquidity due to national holidays. For data aggregated in a 15-
minute frequency, we define the following variables: (1) tvol is the trading vol-
ume (turnover) between the moments t  and 1−t , expressed in M. EUR, and (2) 

tr  is the logarithmic rate of return on the EUR/PLN exchange rate defined as 
4

1 10))()((= ⋅− −
m

t
m

tt PlnPlnr  where m
tP  denotes the mid price. The data frequen-

cy is chosen as a compromise between the need for observing the intraday in-
stantaneous fluctuation of selected market characteristics and the necessity of 
avoiding distorted results due to the effects of slow trading periods. 
 Because trading volume demonstrates strong intraday seasonality we have 
divided the volume variable by the corresponding seasonality component: 

tt svolvol = . As suggested by Bauwens and Veredas (2004), the intraday sea-
sonality factor ts  has been estimated using the kernel regression of tvol  on a 
time-of-day variable5. Estimation of the Burr-ACD models6 has been performed 
on a diurnally adjusted series7. With the obtained parameter estimates we de-
fined the expected and the unexpected volume variables. As can be observed in 
Figure 1, the expected trading volume reflects forcastable fluctuations in the 
trading turnover whereas the unexpected volume reflects unanticipated volume 
shocks.  

2.2. Modeling the volume-return relationship with the QR  
 In order to obtain an intuitive picture of the relationship between distinct 
explanatory variables and EUR/PLN return distribution, in Figure 2 we depict 
preliminary univariate quantile regressions. In the left upper corner of Figure 2 
we present a scatter plot of ( ttun rvol ,exp, ), as well as the conditional quantile 

estimates, tuntunr volvolQ
t exp,,1,0exp,

ˆˆ=)|(ˆ
ττ λλτ + , for some selected probability 

levels: { }99.0;95.0;9.0;75.0;5.0;25.0;1.0;05.0;01.0∈τ . The most striking obser-
vation is a strong positive relationship between the unexpected trading volume 

                                                 
5 We use a quartic kernel with bandwidth computed as 2.78sN -1/5, where s is the standard de-

viation of the data.  
6 Estimation has been performed in Gauss 8.0 with the application of library maxlik.  
7 The trading volume is stationary. We checked for the presence of deterministic as well as 

stochastic trends and rejected the null of unit root with the augmented Dickey-Fuller test (p-
value=0.0000).  



Katarzyna Bień-Barkowska 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

44 

0 1000 2000 3000 4000 5000

0
5

10
15

Observation number

Ex
pe

ct
ed

 v
ol

um
e

0 1000 2000 3000 4000 5000

0
5

10
15

Observation number
U

ne
xp

ec
te

d 
vo

lu
m

e

 
Figure 1.  Expected (left panel) and unexpected (right panel) volume 

and the dispersion of the return distribution. Moreover, we can also observe that 
the obtained slope parameter estimates vary across quantiles; such an observa-
tion also been found by Chuang et al. (2009). Accordingly, the largest impact 
on the unexpected volume can be observed with the most extreme quantiles 
corresponding to the tails of the return distribution. If we turn our attention to 
the expected volume variable, however, the results seem to be different. Alt-
hough this variable is also positively linked to the dispersion of the EUR/PLN 
return distribution, the scale of the effect is much smaller. Thus, the anticipated 
volume seems to have less of an impact on the probability of large price move-
ments.  
 In terms of the impact of the lagged return variable, the following tendency 
is found: after large (positive or negative) returns, the tail probability of observ-
ing further large (either positive or negative) movements increases. In order to 
confirm this effect we applied a nonparametric quantile estimation technique8. 
We can see that the dispersion of the return distribution rises in of the wake of 
large price movements (upswings or drops). To account for this effect it is rea-
sonable to allow for a forecasted volatility estimate as a factor that is positively 
related to the dispersion of the distribution. 
 We estimated the QR models given by equations (4) (model I) and (6) 
(model II) using the “quantreg” library (version 4.79) written by Roger Koenker 
under the R9. The further inference has also been carried out with the help of 
these programming codes. QR regressions have been estimated for a dense grid 
of probability levels ( 99.0,...,02.0,01.0=τ ); thus, for each model we have 
 

                                                 
8 We applied a piecewise cubic polynomial with three knots (Koenker, 2005). 
9 The library can be downloaded from the CRAN website: http://cran.r-project.org. 



“Does It Take Volume to Move the EUR/PLN FX Rates?”… 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

45 

0 5 10 15

-3
0

-2
0

-1
0

0
10

20
30

unexpected volume

EU
R

/P
LN

 re
tu

rn
 (b

as
is

 p
oi

nt
s

1 2 3 4 5 6

-3
0

-2
0

-1
0

0
10

20
30

expected volume
EU

R
/P

LN
 re

tu
rn

 (b
as

is
 p

oi
nt

s

 

-30 -20 -10 0 10 20 30

-3
0

-2
0

-1
0

0
10

20
30

return, lag1

EU
R

/P
LN

 re
tu

rn
 (b

as
is

 p
oi

nt
s

4 6 8 10

-3
0

-2
0

-1
0

0
10

20
30

volatility

EU
R

/P
LN

 re
tu

rn
 (b

as
is

 p
oi

nt
s

 
Figure 2.  Volume - return relationship. Estimates of quantile regressions for probabili-

ties: { }99.0;95.0;9.0;75.0;5.0;25.0;1.0;05.0;01.0∈τ  

allowed for 99 different vectors of parameter estimates that have been plotted in 
Figure 3 (model 1) and Figure 4 (model 2). The asymptotic standard errors for 
each of these specifications have been derived with the help of sparsity 
estimation methods (see equation (4) and (5))10. These equations have been 
used for the evaluation of the 90% confidence interval for each of the obtained 
parameter estimates.  

As can be anticipated from Figure 3, the seasonality factor of the return dis-
tribution is different across the quantiles (in the Figures 3 and 4 the symbols s1, 
s2, s3, s4, s5 are defined as τs =1 , )2sin(2 πτ=s , )2cos(3 πτ=s , 

                                                 
10 We have also experimented with the Powel kernel and the bootstrap, but it did not influence 

the further inference.    



Katarzyna Bień-Barkowska 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

46 

)4sin(4 πτ=s  and )4cos(5 πτ=s ). As the diurnality component ),( υτνS  
seems illegible in Figure 3, we decided to plot the joint diurnality pattern for all 
of the selected probability levels in Figure 5. As can be seen from the obtained 
surface, the intraday seasonality pattern is most pronounced for the most ex-
treme quantiles of the return distribution. For the middle quantiles (i.e., quan-
tiles surrounding the median,  τ=0.5), humps in the surface are rather negligible 
and the surface is rather flat. The diurnality pattern for the quantiles correspond-
ing to the lower tail of the distribution demonstrate that the probability of ob-
serving large drops in the EUR/PLN rate systematically rises early in the morn-
ing (the quantile is “shifted to the left”). This effect is rather symmetric because 
in the upper quantiles the value of the seasonality function is relatively higher 
throughout the early morning period (the quantile is “shifted to the right”). 
What is also striking is the probability of large upswings in the EUR/PLN ex-
change rate (Polish zloty depreciation) in the late afternoon as the upper tail 
probability is systematically higher late in the afternoon (just before 18.00 
CET).  

Concerning the impact of the volume variables, Figure 3 demonstrates that 
it is the unexpected component of the trading volume that is the most responsi-
ble for dispersion of the return distribution. The impact of the unexpected vol-
ume is about four times larger than that of the expected volume for the 0.99 
quantile and about three times larger for the 0.01 quantile. Therefore, the unan-
ticipated volume brings more information with regards to large upswings of the 
EUR/PLN exchange rate (i.e., the Polish zloty depreciation). Generally, the 
impact of the unexpected volume is indisputable as the variable is statistically 
significant for the probability levels { }51.0,...,02.0,01.0∈τ  and 

{ }99.0...,,6.0,59.0∈τ  (at a 5% significance level). The effect is also different 
for different quantiles with the most striking impact placed on the probabilities 
of the most extreme price movements.  

The expected volume was derived as a predictable tendency in the level of 
a trading volume. At time t this variable uses information about the turnover at 
time t-1. Although it is defined for the moment t, it is simply an anticipation of 
the trading volume given the history of its observations. Thus, it can partially 
capture a potential lead-lag relationships between returns and volumes. If the 
expected volume is high, the dispersion of the return distribution rises. The im-
pact that this variable exerts on the quantiles of the distribution is significantly 
different from zero for the probabilities { }19.0...,,02.0,01.0∈τ  and 

{ }99.0...,,65.0,64.0∈τ . However, the scale of this effect is not as strong as the 
effect evidenced in the case of unpredictable volume shocks. On top of the ex-
pected volume, significant impact on selected quantiles have also lagged unex-
pected volume shocks (recorded at t-1). However, the impact of this variable is 
significant only for { }07.0...,,04.0,03.0∈τ .  



“Does It Take Volume to Move the EUR/PLN FX Rates?”… 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

47 

0.0 0.4 0.8

-6
-2

2

(Intercept)

0.0 0.4 0.8

-2
2

6

s1

0.0 0.4 0.8

-1
0

1
2

3

s2

0.0 0.4 0.8

-1
.0

0.
0

1.
0

s3

0.0 0.4 0.8

-2
0

1
2

s4

0.0 0.4 0.8

-1
.0

0.
0

1.
0

s5

0.0 0.4 0.8

-3
-1

0
1

expected_vol

0.0 0.4 0.8

-4
0

2
4

6

unexpected_

0.0 0.4 0.8

-0
.5

0.
5

1.
0

unexpected_

0.0 0.4 0.8

-0
.1

5
-0

.0
5

return_lag1

 
Figure 3.  Parameter estimates for quantile regressions (model I). Shaded areas depict 

the 90% confidence interval 

Figure 4 shows that if we account for GARCH-type volatility forecast, 1ˆ −tσ , as 
an additional driving force of quantile dynamics, the obtained parameter esti-
mates change.  The impact of the unexpected volume remains the same as with-
out the volatile ty variable; however, the role of the expected volume declines in 
a noteworthy fashion (i.e., it is about two times smaller than in the model I) and 
it remains significantly different from zero for quantile levels { }02.0,01.0∈τ , 

{ }87.0...,,84.0,83.0∈τ  and { }98.0...,,94.0,93.0∈τ . Findings like this are ra-
ther easy to justify. The information contained in the past realizations of the 
trading volume is, to a large extent, impounded in the FX prices that are set in 
the market until time t-1. Therefore, if these trading volumes are to a large ex-
tent reflected by the volatility forecasts 1ˆ −tσ  (which condition on the infor-



Katarzyna Bień-Barkowska 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

48 

mation at t-1), the amount of information that can be attributed only to the his-
torical volume will significantly decline.  

0.0 0.4 0.8

-4
0

2
4

(Intercept)

0.0 0.4 0.8

-2
0

2
4

s1

0.0 0.4 0.8

-1
0

1
2

3

s2

0.0 0.4 0.8

-0
.5

0.
5

1.
0 s3

0.0 0.4 0.8

-1
0

1
2

s4

0.0 0.4 0.8

-1
.0

0.
0

1.
0

s5

0.0 0.4 0.8

-1
.5

-0
.5

0.
5

expected_vol

0.0 0.4 0.8
-4

0
2

4
6

unexpected_

0.0 0.4 0.8

-1
.0

0.
0

1.
0 unexpected_

0.0 0.4 0.8

-0
.1

5
-0

.0
5

return_lag1

0.0 0.4 0.8

-8
-4

0
4

volatility

 
Figure 4.  Parameter estimates for quantile regressions (model II). The shaded areas 

depict the 90% confidence interval 

The obtained parameter estimates may also suggest that the return distribution is 
skewed. This can be observed from the different parameter estimates corre-
sponding to the volatility forecasts that were obtained for lower and upper quan-
tiles (in a symmetric case they should be equal). 

Conclusions 
The results suggest that trading volume has a significant impact on the vari-

ability of the EUR/PLN rate fluctuations. We also show that the unexpected 
(unanticipated) component of this variable has a significantly stronger impact 
than the expected (predictable) component. The scale of this impact varies 



“Does It Take Volume to Move the EUR/PLN FX Rates?”… 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 35–52 

49 

across quantiles and is most pronounced in the tails of the return distribution 
(i.e., for the most extreme price movements). Our study contributes to the 
scarce literature on the volume-return relationship in FX markets.   

 
Figure 5.  The diurnality pattern for quantiles of the return distribution 

Studies on this topic have for the most part been conducted for the lower fre-
quencies including only daily or monthly data. As the FX market is extremely 
liquid and transparent in comparison to capital markets, the reaction to new 
information arrival should also be extremely prompt, which justifies the appli-
cation of high frequency data.  Moreover, as outlined by Cheung et al. (2009), 
applying the QR approach enables one to study the impact of trading on the 
general shape of the return distribution. Thus, this approach is complementary 
to the methods based solely on the conditional variance. 

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„Czy wolumen transakcji wpływa na zmiany kursu EUR/PLN?”                                           
Wnioski płynące z zastosowania regresji kwantylowych 

Z a r y s  t r e ś c i W artykule dokonano badania wpływu wolumenu transakcyjnego na wartość 
wybranych kwantyli rozkładu stóp zwrotu z kursu EUR/PLN. Wyniki empiryczne otrzymane na 
podstawie regresji kwantylowych potwierdziły, że wzrost obrotów ma statystycznie istotny 
wpływ na dyspersję rozkładu stóp zwrotu. W badaniu dokonano podziału wolumenu 
transakcyjnego na dwie części: tzw. wolumen oczekiwany przez uczestników rynku i tzw. 
wolumen nieoczekiwany przez uczestników rynku oraz wykazano, że to wolumen nieoczekiwany 
ma dużo większy wpływ na dyspersję badanego rozkładu. Zaobserwowano również, że relacja 
pomiędzy wolumenem a stopą zwrotu ma charakter nieliniowy, tzn. jest najsilniejsza dla 
najbardziej ekstremalnych kwantyli. Wykazano, że w konsekwencji uwzględnienia miary 
warunkowej zmienności (jako dodatkowego czynnika wyjaśniającego dynamikę kwantyli stóp 
zwrotu) wpływ oczekiwanej wartości wolumenu transakcyjnego ulega zmniejszeniu, ale wciąż 
pozostaje istotny statystycznie, szczególnie dla najbardziej ekstremalnych kwantyli. 

S ł o w a  k l u c z o w e: relacja wolumen-stopa zwrotu, mikrostruktura rynku, obrót na rynku 
walutowym, regresja kwantylowa  

Acknowledgements 

The author wants to thank the Thomson Reuters for providing the data from the 
Reuters Dealing 3000 Spot Matching System and the two anonymous referees 
for their valuable comments. The views and opinions presented in the paper are 
those of the author and do not necessary reflect those of the National Bank of 
Poland. 


	Introduction
	1. The Econometric Approach
	2. Empirical Results
	Conclusions
	References

