334 Finance a úv?r – Czech Journal of Economics and Finance, 59, 2009, no. 4
JEL Classification: C1, C5, G1
Keywords: intraday data, realized variance, return and volatility distributions, heterogeneous autoregressive
Distribution and Dynamics of Central-European
Exchange Rates: Evidence from Intraday Data*
Vít BUBÁK – Institute of Economic Studies, Charles University in Prague and CES, Université
Paris I. Panthéon-Sorbonne (email@example.com)
Filip ŽIKEŠ – Imperial College London, Business School (firstname.lastname@example.org)
This paper investigates the behavior of the EUR/CZK, EUR/HUF and EUR/PLN spot ex-
change rates in the period 2002–2008, using 5-minute intraday data. We find that daily
returns on the corresponding exchange rates scaled by model-free estimates of daily re-
alized volatility are approximately normally distributed and independent over time. On
the other hand, daily realized variances exhibit substantial positive skewness and very
persistent, long-memory type of dynamics. We estimate a simple three-equation model
for daily returns, realized variance and the time-varying volatility of realized variance.
The model captures all salient features of the data very well and can be successfully em-
ployed for constructing point, as well as density forecasts for future volatility. We also
discuss some issues associated with measuring volatility from the noisy high-frequency
data and employ a simple correction that accounts for the distortions present in our data-
The recent economic downturn has put an end to a period of relative stability
that the Czech koruna, Hungarian forint and Polish z?oty enjoyed over the last years.
The considerable increase in the volatility of these currencies raises a question about
the ability of the Czech Republic, Hungary and Poland to fulfill the exchange rate
stability criteria stipulated in the Maastricht Treaty. Indeed, these criteria require that
for at least two years prior to the entry into the Eurozone, the applicant country's cur-
rency remain within a normal fluctuation band around the central parity, effectively
setting limits to the currency’s volatility during the pre-accession period (Antal and
Holub, 2007). There is no doubt that while the choice of the appropriate monetary
and exchange rate policies will be crucial to ensure that the currency meets the con-
vergence criteria, the design and implementation of such policies would not be pos-
sible without a thorough understanding of the statistical properties of the currencies
in question. A practical framework for accurate modeling and forecasting of the ex-
change rate volatility in particular could ultimately help in making the relevant poli-
cies more efficient.
A good knowledge of the Central European (CE) exchange rates dynamics is
equally relevant for asset pricing and risk management. Understanding the condition-
al probability distribution of the exchange rate returns and their volatility is critical
for accurate estimation of various models used in pricing and hedging derivative se-
curities written on the exchange rate. On a more general level, frequent and poten-
* The authors thank Jozef Baruník for helpful comments on an earlier version of this paper. Bubak grate-
fully acknowledges financial support from the Czech Ministry of Education, grant code MSM0021620841.
Finance a úv?r – Czech Journal of Economics and Finance, 59, 2009, no. 4 335
tially large unexpected exchange rate movements adversely affect the performance of
export-oriented businesses. Papaioannou (2006) discusses specific types of exchange
rates risk that these companies face at times of increased currency volatility, include-
ing transaction costs associated with hedging against unfavorable exchange rate
movements and economic costs arising from increased uncertainty about future rela-
tive competitiveness. As the CE currencies continue to suffer from relatively high
volatility triggered by the global economic crisis, containing these and related risks
demands effective risk management decisions that are impossible without a sound
knowledge of the underlying exchange rate behavior.
The CE currencies have been subject to a wide range of studies. The most re-
cent focus on understanding the effectiveness of foreign exchange interventions con-
ducted by Central Banks (see Geršl, 2004; Geršl, 2006; Geršl and Holub, 2006; Égert
and Komárek, 2006; Égert, 2007), the sustainability of the real exchange rates (Bulí?
and Šmídková, 2005), or the equilibrium real exchange rate determination (Melecký
and Komárek, 2008), among others.
In contrast, only a limited number of studies have attempted to model the dy-
namics of the spot exchange rates for the CE currencies. Ko?enda and Valachy (2006)
provide a detailed analysis of the exchange rate volatility in the Visegrád countries,
with a particular focus on the period in which these countries abandoned tight FX
regimes for more flexible ones. Using daily nominal exchange rate data, the authors
employ an augmented version of a threshold GARCH-in-Mean (T-GARCH) model
to study the effects of path dependency, asymmetric shocks, and movements in in-
terest rates on exchange rate volatility during the regime transition. The study shows
that the introduction of the more flexible regime lead to a general increase in ex-
change rate volatility, with the level of volatility persistence becoming roughly the same
across the exchange rates analyzed. The authors also find a significant and negative
effect of asymmetric shocks on the volatility of Polish z?oty and Hungarian forint under
the floating regime.
In a related paper, Fidrmuc and Horváth (2008) analyze the exchange rate dy-
namics in the selected EU members including the Czech Republic, Hungary and Po-
land, using daily data from 1999 to 2006. The authors apply both a GARCH model
and an extended version of the TARCH model to assess the exchange rate volatility
in connection with the estimated target exchange rate and the credibility of exchange
rate management. Among other findings, the study shows that the daily exchange rate
volatility exhibits strong persistence as well as systematic asymmetric effects, with
the latter being especially pronounced during the periods of exchange rate appre-
Horváth (2005) investigates the medium-term determinants of the bilateral ex-
change rate volatility of Central and Eastern European countries (CEEc) based on
the optimal currency area criteria. As part of the analysis, the author also compares
the actual and predicted exchange rate variability between the Euro area countries
and the CEEc. Although limited to the use of quarterly data and a relatively short
sample period from 1999 to 2004, the study shows that the actual exchange rate vari-
ability is larger in the CEEc compared to what it had been in the Euro area before its
creation. In addition, the author finds the predicted exchange rate variability to be
close to the Eurozone levels, with the difference between the latter and the actual
336 Finance a úv?r – Czech Journal of Economics and Finance, 59, 2009, no. 4
variability caused by the Euro area countries participating in the ERM during the sam-
Finally, Frömmel (2007) provides an interesting investigation of the changes
between volatility regimes in five Central and Eastern European countries, including
the Czech Republic, Poland and Hungary. Frömmel employs a Markov-Switching
GARCH model to study whether the changes between the volatility regimes are consist-
ent with changes in the official exchange rate arrangements. Among other findings,
the author concludes that an increase in the flexibility of the exchange rate regime
leads to an increase in exchange rate volatility.
The goal of this paper is to examine the conditional distribution of the Czech
koruna, Hungarian forint and Polish z?oty exchange rates vis-à-vis the Euro in the pe-
riod 2002–2008. Employing a 5-minute intraday data, we examine the distributional
properties and time-series dynamics of both daily exchange rate returns, as well as
daily realized variance. Unlike the existing empirical literature that employs almost
exclusively a GARCH framework to study the dynamics of the exchange rate, our work
relies on model-free nonparametric measures of ex-post volatility based on the use of
intraday data. This approach, pioneered by Andersen and Bollerslev (1998), has at-
tracted substantial attention in the recent financial econometric literature; see e.g.
McAleer and Medeiros (2008) for a recent review. It offers a number of advantages.
First, no parametric assumptions are needed to ensure that the realized vari-
ance and related measures are consistent for the true, unobserved volatility, apart
from some mild regularity conditions. This is in stark contrast to the GARCH frame-
work, where all results concerning the behavior of volatility hinge on a particular
specification of the GARCH variance equation.
Second, realized variance captures the total variation in the price or exchange
rate over a given period of time, unlike a GARCH-type model that focuses on condi-
tional volatility of the price at time t, given the information set available at time t – 1.
In other words, realized variance combines both the volatility expectations as well as
the innovations to volatility. This carries important implications for studying the con-
ditional distributions of one-period returns as pointed out by Andersen, Bollerslev
and Dobrev (2007): while the one-period financial returns standardized by condition-
al volatility typically appear to be leptokurtic, standardizing by realized volatility
produces approximately Gaussian innovations. This in turn lends empirical support to
a large class of continuous-time stochastic volatility models widely employed in the as-
set pricing literature.
Finally, since the realized variance and alternative related measures render vol-
atility essentially observable up to a measurement error that vanishes as the sampling
frequency increases, simple time-series models can be used to model and accurately
forecast future volatility (see Andersen, Bollerslev, Diebold and Labys, 2003; Ander-
sen, Bollerslev and Dobrev, 2007, among others). This includes not only point fore-
casts, that is, the expected future volatility, but the entire predictive density for future
volatility, allowing for construction of confidence intervals around the point forecast
or, similarly, estimation of the probability that future volatility remains within a cer-
tain fluctuation band. The ability to provide the predictive density for future volatility
also facilitates the measurement and management of risk associated with trading re-
alized volatility, which has become very popular in recent years (e.g. Bondarenko,
Finance a úv?r – Czech Journal of Economics and Finance, 59, 2009, no. 4 337
2007). In this paper, we only focus on a simple model for returns and variance since
our primary interest lies in studying the dynamics and conditional distributions of
the EUR/CZK, EUR/HUF and EUR/PLN spot exchange rates.
Our empirical results confirm some stylized facts about the behavior of re-
turns and volatility of foreign exchange rates. We find that daily returns on the ex-
change rates are approximately normally distributed and independent over time, when
properly scaled by model-free estimates of daily realized variance. Daily realized
variance, on the other hand, exhibits substantial positive skewness as well as a very
persistent, long-memory type of dynamics. We propose a relatively simple model for
daily returns, realized variance and the time-varying volatility of realized variance,
finding that it very well captures all salient features of the data. In addition, the model
is shown to perform remarkably well out-of-sample, delivering accurate volatility fore-
casts. It may therefore serve well as an auxiliary model for estimating various con-
tinuous-time stochastic volatility models used for pricing derivative securities written
on the exchange rate (Bollerslev, Kretschmer, Pigorsch and Tauchen, 2009).
The rest of the paper is organized as follows. In Section 2 we describe our
theoretical framework and discuss some distributional predictions that it generates
for the EUR/CZK, EUR/HUF and EUR/PLN returns. In Section 3, we follow with
a definition of the realized variance as a model-free measure of variation in asset
prices and some of the issues associated with measuring volatility from noisy high-
-frequency data. In Section 4 we describe the data and in Section 5 we report the em-
pirical results. In particular, we present the results of the tests of normality and in-
dependence of returns standardized by realized volatility, the estimation of a joint
model for daily returns, realized variance and the volatility of realized variance, and
the results of an out-of-sample volatility forecasting exercise. Section 6 concludes
the paper with some suggestions for future work.
2. Theoretical Framework
Following a vast body of recent literature in financial econometrics, we adopt
a relatively simple, yet very general continuous-time framework. Working in con-
tinuous time has a number of technical advantages, but more importantly it provides
a direct link to the asset pricing literature, which establishes a number of important
results concerning the restrictions on admissible models governing asset prices in
an arbitrage-free environment (Back, 1991). A detailed overview of this and related
issues is beyond the scope of this paper and we refer the interested reader to an ex-
cellent discussion in Andersen, Bollerslev, Diebold and Labys (2003).
We assume that the logarithmic spot exchange rate, st, follows a stochastic
volatility model given by
where ?t and ?t denote the drift and volatility processes, respectively, and Wt is
a standard Brownian motion. Both ?t and ?t are allowed to be general stochastic pro-
cesses and we do not impose any parametric assumption regarding their respective
laws of motion. Also, no restrictions are placed on the dependence between volatility
(?t) and the Brownian motion (Wt) driving the exchange rate innovations.
356 Finance a úv?r – Czech Journal of Economics and Finance, 59, 2009, no. 4
the models achieve the best results with the logarithmic realized variance (Panel A),
in which case the R2 is found to be just over 0.60 for EUR/CZK and nearly 0.84 for
the EUR/PLN case. The explanatory power of the models seem to deteriorate by 5
and 30 percentage points on average in case of the forecasts of realized volatility
(Panel C) and the realized variance (Panel B), respectively. The relatively worse per-
formance for the realized variance forecasts is hardly surprising, given the fact that
the time series of RVt exhibits several “outliers” associated with periods of high
volatility and/or potential jumps in the exchange rates. These outliers tend to be
attenuated by taking the square root and especially logarithmic transformations re-
sulting into better forecasting performance.
Comparing the relative performance of the simple HAR versus the more
elaborate HAR-GARCH model, we observe that the former provides consistently
albeit marginally better forecasting power across all three exchange rates and loss
functions, the only exception being the forecasts of realized variance (Panel B) for
EUR/HUF. To see whether the difference between the competing models is statisti-
cally significant we employ a test developed by Giacomini and White (2006). Note
that this test is valid despite the fact that the two models are nested. This is due to
the non-vanishing parameter estimation error implied by the rolling forecasting
scheme, which prevents the test statistics from degenerating in the limit. Based on
the Giacomini-White test we find that the HAR and HAR-GARCH perform equally
well in forecasting the various volatilities of EUR/CZK and EUR/HUF. Some statis-
tically significant difference is detected for EUR/PLN when the QLIKE loss function
is employed, with the simple HAR beating the more complicated HAR-GARCH.
To summarize our forecasting exercise, we find that despite the HAR-GARCH
model having a better in-sample fit, the simple HAR model offers equally or in some
cases even significantly better forecasting performance. The fact that the simple
HAR can be estimated by ordinary least squares makes it a particularly attractive
Our study extends the current understanding of the Central European ex-
change rates behavior by describing the conditional distribution and dynamics of
EUR/CZK, EUR/HUF, and EUR/PLN exchange rate returns and volatility in the pe-
riod from 2002 to 2008. Relying on model-free nonparametric measures of ex-post
volatility based on the use of 5-minute intraday returns, our approach contrasts with
the existing literature that almost invariably employs a parametric framework to
model the exchange rate volatility.
Our findings show that daily returns on the EUR/CZK, EUR/HUF and EUR/
/PLN exchange rates are approximately normally distributed and independent over
time, when properly scaled by model-free estimates of daily volatility. Given the pro-
perties of the 5-minute intraday returns, we find that a relatively simple correction to
the realized variance suffices to account for the bias arising from the microstructure
noise contaminating the data. The resulting daily realized variance exhibits substan-
tial positive skewness and very persistent, long-memory type of dynamics.
We estimate a simple time series model for daily returns, realized variance
and the time-varying volatility of realized variance. We show that the particular spec-
Finance a úv?r – Czech Journal of Economics and Finance, 59, 2009, no. 4 357
ification of the model that we suggest captures very well all salient features of
the data and can be successfully employed for constructing point as well as density
forecasts of future volatility. It can also serve very well as an auxiliary model for es-
timating stochastic volatility models often employed in derivatives pricing. The results
from an out-of-sample forecasting exercise provide evidence of excellent forecasting
performance of the HAR-GARCH model, especially in forecasting the logarithmic
realized variance. It remains to be noted that a simple and computationally less de-
manding HAR model performs at least as well as and sometimes even better than
the HAR-GARCH model.
Our findings provide a natural starting point for future investigation of the Cen-
tral European exchange rates. The flexible and computationally simple non-para-
metric approach for measuring ex-post volatility that we employ can be used in areas
ranging from volatility forecasting, to testing the efficiency of central bank’s inter-
vention along the lines of Beine, Lahaye, Laurent, Neely and Palm (2006), or
analyzing the response of the volatility of the exchange rate to macroeconomic
announcements (jumps). The simple, but highly empirically successful model for
daily returns and volatility we propose in this paper could be employed to investigate
and compare alternative continuous-time models and their ability to accurately price
derivative securities written on the Czech koruna, Hungarian forint and Polish z?oty
In Section 5.2 we employ the rotated Clayton and the Gaussian copulas to
model the dependence between the two innovation processes in the HAR-GARCH
model. The rotated Clayton copula CRC (u,v|?) is given by
( , | ) u v 1 (1)
? ? ? ???
where ? ? [0,?) governs the degree of dependence. The structure of dependence
implied by the rotated Clayton copula is asymmetric in the sense that upper-tail
extreme events are more dependent than lower-tail extremes.
The Gaussian copula CG (u,v|?) reads
C u v
? ? ??
( , | ) ( ),u ( )v
where ?? denotes the joint distribution function of a bivariate standard normal vector
with correlation ? and ? denotes the univariate standard normal distribution function.
Contrary to the rotated Clayton copula, the dependence structure associated with
the Gaussian copula is symmetric.
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