In the present study we develop and implement a short term exchange rate forecasting methodology using dynamic confidence intervals based on GARCH processes and we analyze whether this methodology can be used to model a regime switch in the volatility ofconditional heteroskedasticity, regime switch, exchange rates, long memory

Necula Ciprian

Radu Alina-Nicoleta

English

Research Papers in Economics

610 
 
DETECTING REGIME SWITCHES IN THE EUR/RON EXCHANGE RATE 
VOLATILITY  
 
Necula Ciprian 
The  Academy  of  Economic  Studies  The  Faculty  of  Finance  and  Banking  Bucharest  
ciprian.necula@fin.ase.ro 
Radu Alina-Nicoleta 
The  Academy  of  Economic  Studies    The  Faculty  of  Finance  and  Banking  Bucharest  
alinanicoleta.radu@gmail.com 
 
In the present study we develop and implement a short term exchange rate forecasting methodology using 
dynamic confidence intervals based on GARCH processes and we analyze whether this methodology can 
be used to model a regime switch in the volatility of the EUR/RON exchange rate generated by the change 
of the reference currency from USD to EUR in March 2003. In order to capture this switch we use in our 
analysis daily exchange rate returns from 1st of January 1999 to 1st of January 2004. We model the 
dynamics of the daily returns for the exchange rate by estimating a series of GARCH models, with various 
specifications  for  the  conditional  mean  and  for  the  conditional  variance.  The  best  specification  is  a 
FIGARCH (1, d, 0), a long memory process accounting for volatility persistence. The main finding is that 
there was a significant decrease in the volatility of the EUR/RON exchange rate after March 2003. 
 
Keywords: conditional heteroskedasticity, regime switch, exchange rates, long memory 
 
JEL Classification: C01, C15, C51, C87, E44, E47 
 
1. Introduction 
Daily frequency financial data series present some specific characteristics, such as the „volatility 
clustering‖  phenomenon.  This  phenomenon  refers  to  the  fact  that  on  the  capital  market  the 
conditional  variance  of  the  return  series  is  not  constant,  but  variable  in  time.  Nowadays, 
modeling the volatility of assets returns is the research frontier in financial theory. In order to 
have a proper analysis of the „volatility clustering‖ phenomenon, Engle (1982) introduced ARCH 
(AutoRegressive Conditional Heteroskedasticity) processes and Bollerslev (1986) developed a 
more parsimonious model, GARCH (Generalized ARCH). 
To account for the high levels of kurtosis in the distribution of daily returns, a series of GARCH 
models with ―fat-tails‖ innovations were developed. The Student distribution was employed by 
Bollerslev  (1987)  and  Kaiser  (1996),  Nelson  (1991)  analyzed  the  „Generalized  Error 
Distribution‖  (GED)  and  Lambert  and  Laurent  (2001)  developed  a  GARCH  model  with  an 
asymmetric Student distribution. Numerous studies (Harvey, 1993; Ding, Granger and Engle, 
1993; Briedt, Crato and Lima, 1998) conclude that the volatility of financial assets is persistent. 
To model this persistence various GARCH processes with long memory were proposed in the 
literature. In this category one can mention FIGARCH models (Fractionally Integrated GARCH) 
developed by Baillie, Bollerslev and Mikkelsen (1996), Bollerslev and Mikkelsen (1996) and 
Chung (1999).  
In  the  present  study  we  develop  and  implement  a  short  term  exchange  rate  forecasting 
methodology using dynamic confidence intervals. The confidence intervals length is variable, 
since it depends on the volatility forecast obtained from a GARCH process. We analyze whether 
this methodology based on GARCH stochastic processes can be used to model a regime switch in 
the volatility of the EUR/RON exchange rate generated by the change of the reference currency 
from USD to EUR in March 2003. We model the dynamics of the daily return for the exchange 
rate by estimating a series of GARCH models, with various specifications for the conditional 
mean and for the conditional variance. 611 
 
The paper is organized in three sections. In the first section we develop a dynamic confidence 
interval forecasting methodology based on GARCH processes. In the second section we estimate 
a series of GARCH model specifications using daily EUR/RON the exchange rate returns. The 
final section concludes. 
 
2. Exchange Rates Forecasting using Dynamic Confidence Intervals 
In order to model the dynamics of daily exchange rate returns, we employ a series of GARCH 
models with various specifications for the conditional mean and for the conditional variance. 
Therefore, the daily return series is modeled as 
 
  t t t t r E r    1                           (1) 
where    t E   is  the  conditional  mean,  and  t    represents  the  innovations,  with  the  following 
properties      s t E E s t t     , 0 , 0    . GARCH models imply that conditional variance is not 
constant in time. Therefore, one can write 
t t t z                              (2) 
where  t z   i.i.d    with     1 , 0   t t z Var z E ,  and 
2
t    is  the  conditional  variance  that  will  be 
modeled using different specifications.  
In order to discriminate between various model specifications we employ several informational 
criteria. We also perform a series of stability tests for the parameters of these models.  
Regarding exchange  rate forecasting, we  employ a  dynamic  confidence interval methodology 
based on the conditional variance forecast obtained from the GARCH models. Hence, the 95% 
confidence interval for the one day return is 
  t t t t t t t t z r z r | 1 975 . 0 | 1 | 1 025 . 0 | 1 ˆ ˆ , ˆ ˆ                          (3) 
where  t t r | 1 ˆ  is the forecast for the  expected one day return,  t t | 1 ˆ    the one day forecast of the 
volatility, and  025 . 0 z  and  975 . 0 z  are the 2.5% and 97.5% quantiles of the theoretical distribution 
employed in the GARCH model. In conclusion, the 95% confidence interval for  1 ln  t P  (i.e. the 
logarithm of the spot exchange rate at 1  t ) is 
  t t t t t t t t t t z r P z r P | 1 975 . 0 | 1 | 1 025 . 0 | 1 ˆ ˆ ln , ˆ ˆ ln           .        (4) 
In case one wants to obtain confidence intervals for a period of h days, one can use the h -days 
expected return forecast 


  
h
i
t i t t h t r R
1
| | ˆ ˆ                       (5) 
and the h-days volatility forecast 


  
h
i
t i t t h t V
1
2
|
2
| ˆ ˆ                   (6) 
In these conditions, the 95% confidence interval for the h-days return is 
  t t t t t t t t V z R V z R | 1 975 . 0 | 1 | 1 025 . 0 | 1 ˆ ˆ , ˆ ˆ
                       (7) 
and the 95% confidence interval for  h t P ln  is 
  t h t t h t t t h t t h t t V z R P V z R P | 975 . 0 | | 025 . 0 | ˆ ˆ ln , ˆ ˆ ln                 (8) 
 
3. Forecasting the EUR/RON exchange rate volatility  612 
 
In this section we analyze whether the methodology based on GARCH processes can accurately 
model a regime switch in the volatility of the EUR/RON exchange rate generated by the change 
of the reference currency from USD to EUR in March 2003. In order to capture this switch we 
use in our analysis daily exchange rate returns from 1st of January 1999 to 1st of January 2004. 
First we tested for normality and for heteroskedasticity in the daily EUR/RON exchange rate 
returns. The Jarque-Bera test rejects the null hypothesis of normal returns. The existence of the 
autocorrelation in the squared returns (according to Box Pierce Q test) and the existence of the 
ARCH effects (according to the Engle‘s ARCH LM test) entail the usage of a GARCH model to 
account for volatility clustering. 
The first estimated model is a classical GARCH (1, 1) model with normal innovations and a 
constant  in  the  equation  of  the  conditional  mean.  The  estimated  parameters  are  statistically 
significant, the GARCH process is stationary, but with volatility persistence. The BoxPierce Q 
test and the ARCH LM test for the squared standardized residues imply that the conditional 
variance  equation  is  correctly  specified.  The  BoxPierce  Q  test  for  the  standardized  residues 
suggests that the mean equation is also correctly specified. Since only a constant is required to 
explain the conditional mean, the EUR/RON exchange rate return dynamics is quite difficult to 
forecast. The Nyblom stability test rejects the null hypothesis that parameters of the estimated 
model are stable (i.e. constant in time). As a consequence, we introduced a dummy variable to 
account  for  the  moment  the  Central  Bank  changed  the  reference  currency  in  March  2003. 
Henceforth, we estimated a GARCH (1, 1) model with normal innovations and a dummy variable 
in the conditional variance equation. The parameters of this model are stable, implying that there 
are  no  more  volatility  switches  in the analyzed  period.  Also, according  to  the  informational 
criteria, this model is superior to the previous one. Figure 1 depicts 1, 5, 10 and 20 days forecasts 
for the EUR/RON exchange rate return generated by the dummy – GARCH (1, 1) model with 
normal innovations. 
 
Figure 1 - 95% confidence intervals for the EUR/RON exchange rate return for the estimated dummy - 
GARCH (1, 1) model with normal innovations and a constant in the mean equation  
As  one  can  notice,  the  EUR/RON  exchange  rate  volatility  decreased  from  the  moment  the 
 613 
 
Central Bank introduced euro as the reference currency. This shift in volatility was probably 
generated by Central Bank interventions on the FOREX market.  
The  tests  conducted  on  the  residues  of  the  two  estimated  GARCH  models  imply  that  the 
innovations are not normally distributed. This distribution is leptokurtic and asymmetrical. As a 
result we estimated a series of dummy - GARCH (1, 1) models having innovations with GED 
distribution, Student distribution or asymmetric Student distribution. Table 1 presents quality 
indicators  for  these  models:  Akaike  informational  criterion  (AIC),  Schwartz  informational 
criterion (BIC), Pearson distribution comparison test, and Nyblom stability test.   
 
Table 1 Quality indicators for the estimated dummy - GARCH (1, 1) models with various distributions for 
the innovations  
   Indicator 
Innovations` distribution 
Normal  GED  Student  Asymmetric 
Student  
AIC statistic  1.932326    1.908004    1.894860    1.889276   
BIC statistic  1.952563    1.932288    1.919145    1.917608   
Pearson p-value  0.021586  0.059488  0.056443  0.176441 
Nyblom statistic  0.970891  1.42561  1.32591  1.43361 
 
The Pearson test for the estimated GARCH (1, 1) model with an asymmetric distribution of the 
innovations indicated a higher probability than for the other estimated models that the theoretical 
distribution is identical to the empirical one. In addition, according to the informational criteria, 
the asymmetric Student distribution model is superior to the other GARCH (1, 1) processes. This 
can be explained by the fact that the theoretical distribution is not only leptokurtic, but also 
asymmetrical, implying a better fit to the empirical distribution. 
Next, we used some other specifications for the conditional variance equation. For the beginning, 
we tested for the existence of a leverage effect in the EUR/RON exchange rate return series. The 
test was conducted using two asymmetrical GARCH models. The estimations of the TARCH and 
APARCH  models  concluded  that  the  parameter  that  account  for  the  leverage  effect  is  not 
statistically significant. It is important to mention that all the estimated models present a high 
persistence of the volatility. In order to model this persistence we estimated a series of integrated 
GARCH  models.  First  an  IGARCH  (1,  1)  model  was  used.  The  parameters  are  statistically 
significant and stable in time. But, according to the informational criteria, this model is not 
superior to the estimated GARCH (1, 1) models. As a consequence, we modeled the persistence 
in volatility using a long memory process. Therefore, we estimated a FIGARCH (1, d, 0) model 
with asymmetric Student distribution. The Box Pierce and ARCH LM tests imply that the mean 
and variance equations are correctly specified and the Nyblom test suggests that the parameters 
are  stable.  Also,  the  Pearson  test  can  not  reject  the  null  hypothesis  that  the  empirical  and 
theoretical  distributions  of  the  innovations  are  identical.  In  addition,  according  to  the 
informational criteria, this model is the best from the ones estimated for the EUR/RON exchange 
rate. Figure 2 depicts 1, 5, 10 and 20 days forecasts for the EUR/RON exchange rate return 
generated by the dummy – FIGARCH(1, d, 0) model with asymmetric Student innovations. Also, 
as  in  the  case  of  the  other  models,  one  can  notice  a  significant  decrease  in  the  EUR/RON 
exchange rate volatility after the moment the Central Bank introduced euro as the reference 
currency.    
 
   614 
 
Figure  2  -  95%  confidence  intervals  for  EUR/RON  exchange  rate  return  for  the  estimated  dummy  - 
FIGARCH (1, d, 0) model with asymmetric Student innovations and a constant in the mean equation  
 
Having  identified  the  best  specification  for  the  variance  equation,  next,  we  modeled  the 
conditional mean using autoregressive processes. The only statistically significant specification 
consists of an ARFIMA (1, d, 0), a long memory process. The Nyblom test implies that the 
parameters are stable, and the Box Pierce Q and ARCH LM tests suggest that the mean equation 
and the conditional variance are correctly specified. However, according to the informational 
criteria, this model is not superior to the models that have only a constant in the equation of the 
conditional mean. 
 
4. Concluding remarks 
In  the  present  study  we  analyzed  whether  a  dynamic  confidence  intervals  forecasting 
methodology based on GARCH processes can be used to model a regime switch in the volatility 
of the EUR/RON exchange rate generated by the change of the reference currency from USD to 
EUR in March 2003. In order to capture this switch we used in our analysis daily exchange rate 
returns from 1st of January 1999 to 1st of January 2004.  
We estimated a series of GARCH models, with various specifications for the conditional mean 
and  for  the  conditional  variance.  The  best  specification  for  the  mean  equation  is  a  constant 
specification. Due to the simplicity of the mean equation the EUR/RON exchange rate return 
dynamics is quite difficult to forecast.  The best specification for the variance equation consists of 
a FIGARCH (1, d, 0), a long memory processes that accounts for the persistence in volatility. The 
results of the parameter stability tests entailed the introduction of a dummy variable to account 
for the moment the Central Bank changed the reference currency. 
The main finding of the study is that there was a significant decrease in the volatility of the 
EUR/RON exchange rate after March 2003. This shift in volatility was probably generated by 
Central Bank interventions on the FOREX market. 
 
   
 615 
 
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DETECTING REGIME SWITCHES IN THE EUR/RON EXCHANGE RATE VOLATILITY

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DETECTING REGIME SWITCHES IN THE EUR/RON EXCHANGE RATE VOLATILITY

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