Sugiyanto, E. Zukhronah
SWUP
MA.95
3. Results and discussion
Based on plot of the real exchange rate data, it appears that the data fluctuate from time to time. It gives the allegation that the data is not stationary on the average and the
variance Therefore,it needs transformation and difference to obtain the stationary data, namely in the form of log returns.
Plot of log returns of the real exchange rate indicates that the data has been stationary against average and variance is not constant. Then log returns of real exchange rate data that
has been stationary can be modeled by ARMA model.
3.1 ARMA model
ARMA model is used to model the stationary time series data. ARMA model can be done by looking at the ACF and PACF plots of log returns of the real exchange rate data. Value
of ACF and PACF is interrupted after the first lag and it is out of bounds confidence interval. The best model of ARMA model parameter estimation is ARMA1,0 which can be written as
= 0.011916 + 0.188511
o
+ .
1 Based on Lagrange multiplier test, the residue of ARMA1,0 model until the 10th lag
generated probability value 0.000056 that of less than 0.05, so that the ARMA1,0 model still pregnant heteroscedasticity. This means that the ARMA1,0 model can not explain the
heteroscedasticity. Furthermore, heteroscedasticity will be explained by ARCH model.
3.2 ARCH model
The result of ARCH model with average conditional ARMA1,0 shows that the best model is ARCH4 which can be written as
= 0.000142 + 1.002690ε
o
+ 0.227968ε
o
− 0.090551ε
o‰
+0.396207ε
oï
. 2
Furthermore, a diagnostic test of residual is done to determine the feasibility of the model. Based on Ljung-Box test, the residue of ARCH4 models to lag the 10th known that
the probability is 0.986175 that of more than 0.05, so that residual of ARCH4 models does not contain autocorrelation.
Based on Lagrange multiplier test, the residual of ARCH4 models until the 10th lag generated probability value of 0.986175 greater than 0.05, so that residual of ARCH4
models does not have the effect of heteroscedasticity. Based on Jarque Bera test, residue of ARCH4 models is not normal. Therefore, ARCH4 model was re-estimated using QMLE
methods Rosadi, 2012, and obtained the best model was the model of ARCH4 model with the average conditional ARMA1,0. Therefore, all assumptions of ARCH models have been
fulfilled, the model does not need to be taken to GARCH or EGARCH. Based on the test of structural changes, there is a structural changes of the real exchange rate on period of
February 1998 and July 1998.
3.3 SWARCH model
Results of the SWARCH2,4 model estimation with an average of conditional ARMA1,0 is as follows
= S0.0000791077 ,
for state 1
0.0000344499 ,
for state 2
3 This value indicates that the average of log return of real exchange monthly data in state 1
Combination of volatility and Markov-switching models for financial crisis in Indonesia based on real exchange rate indicators
SWUP
MA.96
stable is 0.0000791077, in state 2 volatile is 0.0000344499. Heteroscedasticity model of the SWARCH2,4 model can be written as
= J
K L
K M0.0000972 + 0.9648948ε
o
+ 0.257537ε
o
+2.4764 ∙ 10
o
+ 0.476999 , for state 1
0.0000133 + 0.9648948ε
o
+ 0.257537ε
o
+2.4764 ∙ 10
o
+ 0.476999 , for state 2
4
Transition probability matrix of data the real exchange rate can be written as x = •0.018495753 0.18535501
0.981504250 0.81464499– 5
Matrix P explaines that the probability of a change from stable state to stable state is 18.5335501, from volatile state to stable state is 98.150425.
The results of SWARCH3,4 estimation model with an average of conditional ARMA1,0 is as follows
= ß 0.0000853095 , for state 1
0.0000314552 0.0001923780
, for state 2 , for state 3
6 This value indicates that the average of log return of real exchange rate monthly data
in state 1 low volatility is 0.0000853095, in state 2 moderate volatility is 0.0000314552 and in state 3 high volatility is 0.0000192378. Heteroscedasticity model of SWARCH3,4
model can be written as
=
J K
K K
L K
K K
M0.0000545 + 1.0664938ε
o
+ 1.0664938ε
o
+0.1160877ε
o‰
+ 0.224554ε
oï
, for state 1 0.0000174 + 1.0664938ε
o
+ 1.0664938ε
o
+0.1160877ε
o‰
+ 0.224554ε
oï
, for state 2 0.0000023 + 1.0664938ε
o
+ 1.0664938ε
o
+0.1160877ε
o‰
+ 0.224554ε
oï
, for state 3 7
Transition probability matrix of real exchange rate data can be written as x = ;
0,45020043 8,819365 × 10
o ò
0,55972078 0,41756084
0,77295701 1,7102414 × 10
o ï
0,13223873 0,22704299
0,44027922 ?
Matrix P explaines that the probability of a change from state 1 low volatility to state 1 is 45.020043, from state 1 to state 2 moderate volatility is 41.756084, from state 1 to
state 3 high volatility is 13.223873. Detection of crisis using a SWARCH2,4 model with an average of conditional
ARMA1,0 can be done by looking at the value of inferred probabilities. There are some period of data that has inferred probabilities value more than 0.5. It shows periods of data in
volatile conditions and indicates the occurrence of a crisis. For SWARCH3,4 model, there are some period of data that has inferred probabilities
value between 0.4 to 0.6 that indicated in a state of moderate volatility. And there are inferred probability values more than 0.6 that indicated in a state of high volatility, and may
indicate the occurrence of a crisis.
Sugiyanto, E. Zukhronah
SWUP
MA.97
4. Conclusion and remarks
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