Transcript A comparison of the exchange rate volatility between

A comparison of the exchange rate
volatility between Central-Eastern
European Currencies and Euro
Student: Nechita Laura
Coordinator:Professor Moisă Altăr
Objectives

To approach the volatility of CEE countries (Czech, Hungary,
Poland, Slovakia and Romania) exchange rates from the
perspective of the permanent and transitory dimensions using
Component GARCH model

To explore the question regarding the convergence between
CEE economies and Euro area by the comparison of long-run
volatility trends in CEE currencies and the Euro
Literature review
The
studies on exchange rate volatility in major currencies often have used conditional
variance measures of volatility and have focused on the analysis of long-run trends in exchange
rate volatility.
Pramor
and Tamirisa (2006) - a lower degree of commonality within CEE area, which is less
than what Black and McMillan(2004) found for major industrial countries in Europe before the
introduction of the euro
Kobor
and Szekely (2004) - research on a sample of four countries ( Poland, Hungary, Czech
and Slovak) during a period of three years (2001-2003), revealing that volatilities were highly
variable from one year to another
Horvath
(2005) pointed out that excessive exchange rate volatility triggers macroeconomic
instability, being perceived as a bad signal by investors
Fidrmuc
and Korhonen (2006) reviewed the literature on business cycle correlation between
the euro area suggesting that several new Member States have already achieved a comparably
high degree of synchronization with the euro area business cycle
Literature review
Beveridge and
Nelson (1981) showed that the permanent component is a random
walk with drift and the transitory component is a stationary process
Engle
and Lee (1993) applied that decomposition on US and Japanese stock indices
developing a statistical component model (CGARCH) in order to investigate the longrun and the short-run movement of volatility in the stock market
Data
 EUR-CZK, EUR-HUF, EUR-PLN, EUR-RON, EUR-USD
 the period January 1999 – June 2009 (except SKK – only the
period January 1999-December 2008) with the following sub
periods:
the full period: January 1999 – June 2009
the late period: January 2004 – December 2008
the last semester: January 2009 – June 2009
Data
HUF
CZK
USD
1.7
40
320
36
300
32
280
28
260
24
240
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
220
20
0.8
99
00
01
02
03
04
05
06
07
08
99
09
00
01
02
PLN
03
04
05
06
07
08
99
09
00
01
02
04
05
06
07
08
09
SKK
RON
5.0
03
48
4.4
4.0
44
4.5
3.6
3.2
4.0
40
2.8
36
2.4
3.5
2.0
32
1.6
3.0
28
1.2
99
00
01
02
03
04
05
06
07
08
09
99
00
01
02
03
04
05
06
07
08
09
99
00
01
02
03
04
05
06
07
08
09
Data

All series present unit root

log-differences:
xt  100* (ln(S t )  ln(St 1 )

ADF Test & PP Test– the absence of the unit root of the logdifferences
Null Hypothesis: D_L_CZK has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic based on SIC, MAXLAG=27)
Augmented Dickey-Fuller test statistic
Test critical values:
1% level
5% level
10% level
*MacKinnon (1996) one-sided p-values.
t-Statistic
Prob.*
-51.18178
-3.432607
-2.862423
-2.567285
0.0001
Model C-GARCH
Conditional variance of the model GARCH(1,1):
ht2       t21    ht21
2 

1  (   )
ht2   2    ( t21   2 )    (ht21   2 )
Model C-GARCH


2
Replacing  with a time-varying trend qt
Long run component:
qt2      qt21    ( t21  ht21 )

Transitory component:
ht2  qt    ( t21  qt 1 )    (ht21  qt 1 )    ( t21  qt 1 )  Dt 1

Constrains :
0      1
0   
 ,  0
CGARCH Estimates

Jan99-Dec08
Jan1999-Dec 2008
Trend Intercept
Trend AR Term
Forrecast Error
ARCH Term
Assymetric Term
GARCH Term
α+β
CZK
0.000015
0.981705
0.057896
0.033464
0.047886
0.693173
0.726637
HUF
0.000069
0.998972
0.030877
0.131043
_
0.64983
0.780873
PLN
0.000044
0.990685
0.062736
0.059544
_
0.758766
0.81831
RON
0.000412
0.999143
0.117011
0.139125
_
-0.13035
0.008774
SKK
0.000017
0.997584
0.034834
0.081904
_
0.835732
0.917636
EUR
0.000061
0.998195
0.027709
0.023276
-0.08502
0.444306
0.467582
ω
ρ
φ
α
γ
β
 coefficients corresponding to the long-run component are significant at level 1% and
higher than the ones associated with the transitory component
 the AR coefficient of permanent volatility (ρ) is highly significant (almost 1) and its size
exceeds the coefficients of the transitory component => model is stable and long run
component tends to be a random walk with drift
PLN and SKK present shocks mostly of transitory nature (the coefficients almost 1)
RON – especially long nature (forrecast error is positive and significant)
CGARCH Estimates
Dependent Variable: D_L_CZK
Method: ML - ARCH
Date: 06/14/09 Time: 19:29
Sample (adjusted): 1/05/1999 6/11/2009
Included observations: 2671 after adjustments
Convergence achieved after 24 iterations
Variance backcast: ON
Q = C(1) + C(2)*(Q(-1) - C(1)) + C(3)*(RESID(-1)^2 - GARCH(-1))
GARCH = Q + (C(4) + C(5)*(RESID(-1)<0))*(RESID(-1)^2 - Q(-1)) +
C(6)*(GARCH(-1) - Q(-1))
Coefficient
Std. Error
z-Statistic
Prob.
10.80765
230.1517
5.343732
1.940132
2.035239
7.938400
0.0000
0.0000
0.0000
0.0524
0.0418
0.0000
Variance Equation
C(1)
C(2)
C(3)
C(4)
C(5)
C(6)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
1.46E-05
0.981705
0.057896
0.033464
0.047886
0.693173
-0.000620
-0.002497
0.004097
0.044736
11299.96
1.35E-06
0.004265
0.010834
0.017248
0.023529
0.087319
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Durbin-Watson stat
-0.000102
0.004092
-8.456725
-8.443493
1.979188
CGARCH Estimates

Jan04-Dec08
Jan 2004 - Dec 2008
Trend Intercept
Trend AR Term
Forrecast Error
ARCH Term
Assymetric Term
GARCH Termn
α+β
CZK
0.000013
0.98625
0.056155
0.076902
-0.05571
-0.85752
-0.78062
HUF
0.000028
0.995044
0.044871
0.120597
-0.07272
0.801309
0.921906
PLN
0.000031
0.993352
0.046684
0.078535
-0.09769
0.842474
0.921009
RON
0.000378
0.998989
0.13162
0.180497
_
0.28093
0.461427
SKK
0.000264
0.999037
0.184954
0.149343
-0.31008
0.602871
0.752214
EUR
0.000408
0.999883
0.032341
0.018926
_
-0.98407
-0.96515
ω
ρ
φ
α
γ
β
 stability of the model is given by the AR coefficient which is almost 1
 CZK and EUR have a negative short term component (α + β inferior to 1),
confirming the long term nature of shocks
 The assymetric term is negative and significant (especially for Czehia,
Hungary, Poland and Slovakia ), suggesting higher volatility in case of currency
depreciation
CGARCH Estimates
CZK
EUR
CGARCH Estimates

Last Semester
Jan 2009 – Jun 2009
Trend Intercept
Trend AR Term
Forrecast Error
ARCH Term
Assymetric Term
GARCH Termn
α+β
CZK
-0.00013
0.994299
0.044625
0.086282
-0.23089
0.775026
0.861308
HUF
0.000162
0.715081
-0.21497
0.0904
-0.09531
0.642694
0.733094
PLN
0.000189
0.727395
0.352466
-0.30143
-0.22536
0.642414
0.340984
RON
0.000025
0.944272
0.247012
-0.12335
-0.21886
0.786753
0.663408
EUR
0.000105
0.585094
-0.20478
0.217061
0.107044
-0.0676
0.149462
ω
ρ
φ
α
γ
β
The currencies strongly depreciated – the asymmetric term is negative
 HUF and EUR have a negative forecast error => suggesting a lower shock
impact on the permanent component of the volatility
The model still confirms to be stable
Permanent vs. transitory component
Hodrick Prescott Filter
.00025
.0006
.0005
.00020
.0005
.0004
.0004
.0003
.0003
.0002
.00015
.00010
.0002
.00005
.0001
.0001
.00000
.0000
.0000
-.00005
-.0001
-.0001
99
00
01
02
03
04
05
06
07
08
99
00
01
02
03
04
05
06
07
-.0002
08
99
Cond_var_CZK
Perm_CZK
Trans_CZK
Cond_var_HUF
Perm_HUF
00
01
02
03
cond_var_pln
.004
04
05
06
07
08
Trans_HUF
perm_pln
trans_pln
.00014
.00025
.00012
.003
.00020
.00010
.00015
.00008
.002
.001
.00006
.00010
.00004
.00005
.00002
.00000
.000
.00000
-.00005
-.00002
-.001
99
00
01
02
cond_var_ron
03
04
05
perm_ron
06
07
08
trans_ron
99
00
01
02
cond_var_skk
03
04
05
perm_skk
06
07
08
trans_skk
-.00010
99
00
01
02
cond_var_eur
03
04
05
perm_eur
06
07
08
trans_eur
Permanent vs. transitory component
Jan99-Dec2008
PERM_CZK
Mean
Std. Dev.
PERM_HUF
0.000015
0.000010
TRANS_CZK
Mean
Std. Dev.
PERM_PLN
0.000025
0.000021
TRANS_HUF
0.0000000
0.0000105
PERM_RON
PERM_SKK
PERM_EUR
0.000053
0.000010
0.000042
0.000053
0.000004
0.000019
TRANS_RON
TRANS_SKK
TRANS_EUR
-0.0000003
0.0000003
0.0000000
-0.0000004
0.0000326
0.0001220
0.0000073
0.0000091
0.000042
0.000024
TRANS_PLN
0.0000001
0.0000263
Jan04-Dec2008
PERM_CZK
Mean
Std. Dev.
PERM_HUF
0.000014
0.000014
TRANS_CZK
Mean
Std. Dev.
PERM_PLN
0.000031
0.000028
TRANS_HUF
0.0000000
0.0000118
PERM_RON
PERM_SKK
PERM_EUR
0.000035
0.000011
0.000034
0.000024
0.000004
0.000021
TRANS_RON
TRANS_SKK
TRANS_EUR
0.0000000
0.0000000
0.0000000
0.0000000
0.0000262
0.0000537
0.0000131
0.0000108
0.000030
0.000026
TRANS_PLN
0.0000000
0.0000339
Jan09-Jun09
PERM_CZK
Mean
Std. Dev.
PERM_HUF
0.000059
0.000024
TRANS_CZK
Mean
Std. Dev.
PERM_PLN
0.000162
0.000011
TRANS_HUF
0.0000000
0.0000179
TRANS_PLN
0.0000000
0.0000598
PERM_RON
PERM_EUR
0.000026
0.000106
0.000013
0.000000
TRANS_RON
TRANS_EUR
0.0000000
0.0000000
0.000000
0.0000704
0.0000179
0.000025
0.000193
0.000036
Full period
CZK
HUF
PLN
RON
SKK
EUR
Std. Dev.Longrun/Std.Dev.Trans Short-run
0.95
0.78
0.73
0.44
0.48
2.04
Late period
Std. Dev.Longrun/Std.Dev.Trans Short-run
1.18
0.83
0.99
0.44
0.34
1.94
Last semester
Std. Dev.Longrun/Std.Dev.Trans Short-run
1.36
0.19
0.51
0.72
_
0.01
Principal Components Analysis - Long run
component – jan99-dec08
-0.6
-0.5
-0.4
-0.3
-0.2
RM
PE
RM
PE
_E
N
LN
UR
_P
O
_R
RM
PE
0
UF
_H
-0.1
RM
PE
Cattell criterion
delta
1.05141
-0.105502
0.465487
0.159829
-0.085941
0.103
ZK
_C
epsilon
1.588283
0.536873
0.642375
0.176888
0.017059
0.103
RM
PE
Full period
eigen value
3.064478
1.476195
0.939322
0.296947
0.120059
0.103
Pairwise Covariance Matrix - Long run
component –jan99-dec08
the weights on the first component are similar in sigh and absolute value => the
common trend for the currencies CZK, PLN and EUR
 the covariance matrix underlines also the same couples : CZK, PLN and EUR
the same conclusion Fidrmuc&Korhonen(2006) si Kobor&Szekely(2004)
The model still confirms to be stable
Principal Components Analysis - Long run
component – jan04-dec08
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
PE
RM
_
CZ
K
PE
RM
_
HU
F
PE
RM
_
PL
N
PE
RM
_
RO
N
PE
RM
_
EU
R
Pairwise Covariance Matrix - Long run
component –jan04-dec08
both methods confirm the same trend for the currencies:
CZK- HUF- PLN – EUR
the same correlation was found by:
Horvath(2007):
CZK-PLN
Kobor&Szekely(2006): PLN-HUF
Principal Components Analysis - Long run
component – jan09-jun09
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
PE
RM
_
CZ
K
PE
RM
_
HU
F
PE
RM
_
PLN
PE
RM
_
RO
N
PE
RM
_
EU
R
Pairwise Covariance Matrix - Long run
component –jan09-jun09
Estimated coefficients from CGARCH were less significant than in the
previous sub periods => twisted results: a strong correlation between CZK,
PLN and RON
EUR-HUF correlation (78%) –beginning with 2008, Hungary adopted a
free floating regime regarding the exchange rate policy
Principal Components Analysis: Transitory
component –jan04-dec08
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
TR
AN
S_C
Z
-0.1
TR
K
TR
AN
S_H
U
F
AN
S_P
LN
TR
AN
S_R
O
TR
N
AN
S_S
KK
0
Euro has a common trend with SKK in the last period as it has been
shown also by Pramor & Tamirisa findings (2006)
TR
AN
S_E
U
R
Principal Components Analysis: Transitory
component –jan09-jun09
-0.8
-0.6
-0.4 T
RA
NS
_C
-0.2
ZK
TR
AN
S_
HU
F
TR
AN
S_
PLN
0
0.2
0.4
0.6
0.8
For the last semester, we can not conclude about the common trend
between the currencies based on the transitory component
TR
AN
S_
RO
N
TR
AN
S_
US
D
Conclusions

Permanent component coefficients were positive and higher than the ones
corresponding to the transitory component, reflecting the fact that permanent
volatility component is stronger than the short term one

The dispersion and overall variability of weights for the short-run component are
significantly higher than for the long-run component – not surprisingas the shortrun component of volatility reflects transitory and unsystematic disturbances

The most volatility components (both for the permanent component and transitory
one) belong to Romania while the lowest one to Slovakia.

For the full period, the weights of the first component revealed that Czech koruna,
Polish Zloty and Euro have similar long term volatility component

SKK seemed to have a common trend with euro in the last period

Romanian currency is slowly correlated not only with the other CEE currencies but
also with euro .
References
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Beveridge, S. and C. R. Nelson (1981), “A New Approach to Decomposition of Economic Time Series into
Permanent and Transitory Components with Particular Attention to Measurement of the ‘Business Cycle’,
Journal of Monetary Economics, Vol. 7, 151–74.
Black, Angela J. and D.G.McMillan (2004), “Long-Run Trends and Volatility Spillovers in Daily Exchange
Rates”, Applied Financial Economics, Vol.14, 895-907
Bollerslev, T. (1986), “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of
Econometrics, Vol. 31, 307–27.
Engle, R.F. and G.G.J Lee (1993), “A Permanent and Transitory Component Model of Stock Return
Volatility”, Discussion Paper 92-44R, University of California, San Diego
Engle, Robert F. (1982), “Autoregressive Conditional Heteroscedasticity with Estimates for the Variance of
United Kingdom Inflation,” Econometrica, Vol. 50, No. 4, 987–1008.
Fidrmuc, J. and I. Korhonen (2006), “Meta-analysis of Business Cycle Correlation between the Euro Area
and the CEECs,” Journal of Comparative Economics, 34, 518–537
Fidrmuc, J. and R. Horvath (2007), “Volatility of Exchanges Rates in Selected New EU Members:
Evidence from Daily Data”, CESifo Working Paper No.2107, 10/2007
Horvath, R. (2005), “Exchange Rate Variability, Pressures and Optimum Currency Area Criteria:
Implications for the Central and Eastern European Countries,” CNB Working Paper No. 8 (Czech Republic:
Czech National Bank).
Kóbor, A. and I. P. Székely (2004), “Foreign Exchange Market Volatility in EU Accession Countries in the
Run-Up to Euro Adoption: Weathering Uncharted Waters,” Economic Systems, 28(4), 337–352
Mundell, R. (1961), “A Theory of Optimum Currency Areas,” American Economic Review, Vol. 51, 657–
65.
Pramor, M. and N.T. Tamirisa (2006), “Common Volatility Trends in the Central and Eastern European
Currencies and the Euro”, IMF Working Paper, 06/2006
Schnabl, G. (2007), “Exchange rate Volatility and Growth in Small Open Economies at the EMU
Periphery”, ECB Working Paper No. 773, 07/2007