Combination of volatility and Markov-switching models for financial
crisis in Indonesia based on real exchange rate indicators
Sugiyanto† and Etik Zukhronah
Department of Mathematics, FMIPA UNS Ir. Sutami Street 36A Surakarta, Central Java, Indonesia
Abstract
Financial crisis that happened in 1997 to 1998 resulted in decline of the economy in Indonesia. Therefore in this study will be built a model of the financial crisis in Indonesia which can be used in anticipation of or preparation for what to do in the future. The model is based on indicators of the real exchange rate from January 1990 to December 2014 using a combination of volatility and Markov_Switching models. The results showed that the model SWARCH(2,4) and SWARCH(3,4) can catch a signal crisis in Indonesia on February 1998 and July 1998.
Keywords financial crisis, volatility model, Markov-Switching model, real exchange rate, SWARCH
1.
Introduction
The crisis that hit the Indonesian economy in 1997 to 1998 is caused by the fall of bath Thailand exchange rate in July 1997. The impact of the crisis in 1997 to 1998 are quite severe makes researchers interested in establishing a model that illustrates the crisis. The model can be built through the monitoring of a number of macroeconomic indicators (Abimanyu & Imansyah, 2008). According to Fordet al. (2007), one of the indicators that can be used to detect the currency crisis in Indonesia is the real exchange rate indicators.
The real exchange rate is the relative price of goods between the two countries (Mankiw, 2003). The real exchange rate can be calculated from the nominal exchange rate multiplied by the price level. Price level used is the consumer price index (CPI). Kaminsky et al. (1997) states that a high real exchange rate will reduce exports so as to reduce the supply of foreign currency is entered. That led to the weakening of the domestic currency and will likely result in a huge crisis.
Monthly data of real exchange rate is a time series data. Cryer (1986) introduced one model of stationary time series data, namely autoregressive moving average(ARMA). ARMA models have the assumption of constant residual variance (homoscedasticity). Real exchange rate data have indicated volatility or volatility clustering. Volatility clustering of data that is gathering a bunch of great value and followed a group of small-value data. These circumstances indicate that the variance is not constant, so the real exchange rate data does not meet the homoscedasticity assumptions.
Engle (1982) introduced a model of autoregressive conditional heteroscedasticity (ARCH) which can model the data that has heteroscedasticity. However, the financial time series data can undergo structural changes caused by changes in policy, war or natural
SWUP
disasters and ARCH model does not take into account the structural changes that occur in such volatility.
Hamilton (1989) introduced Markov switching models as an alternative modelling of time series data that undergo structural changes. Hamilton combined Markov switching and autoregressive models resulting in a Markov switching autoregressive models (SWAR).
Hamilton & Susmel (1994) introduced a model that combined ARCH models and Markov_Switching models then called Markov Switching ARCH (SWARCH). SWARCH model can explain changes in the structure and illustrates the volatility. Some researchers have applied SWARCH model to detect crisis that occur in a country. Among these researchers were Chen & Lin (2000) which apply SWARCH models to identify the stock market volatility in Taiwan. Then Chang et al. (2010) also apply SWARCH models to identify the volatility of the stock market and the exchange rate in Korea as well as the financial crisis global.
This research will be carried out modeling of the financial crisis in Indonesia is based on indicators of the real exchange rate using combined of volatility and Markov switching models. The real exchange rate data that indicated heteroscedasticity and undergo structural changes can be modeled by SWARCH model of two and three states.
2. Materials and methods
This research uses monthly real exchange rate data of the January 1990 to December 2014 periods. Data are obtained from the International Financial Statistics (IFS).
In conditions of crisis or impending crisis turmoil, the financial data unlucky in particular real exchange rate will experience high fluctuation and structural changes. When this happens, the combined of volatility and structural changes models are suitable for use. If the real exchange rate does not have heteroscedasticity, then SWAR model is used. However, when real exchange rate has heteroscedasticity, SWARCH models is more suitable for use. High order on the SWARCH models can lead to biased interpretations on the model, so SW-GARCH model can be used to overcome this problem (1996). Some lack of proper economic policy or the contagion from abroad will have an impact on the real exchange rate, this information is often referred to as a bad-new. While the precise economic policy or foreign trust towards Indonesia will give a good impact on the value of the real exchange rate, information like this is often referred to as a good-new. The existence of bad-new and good-new that does not contribute to balanced then it is used SW- EGARCH models (2007). Crisis situation can be seen from the inferred probabilities generated by the models: SWARCH, SW-GARCH and EGARCH. According to Hamilton (1989), inferred probabilities written as
x
jVæ = 2
|
T
W
1 −
x
jVæ = 1
|
T
W
for two states and
x
jVæ
3
|
T
W
1 −
x
jVæ = 1
|
T
W
x
jVæ
2
|
T
W
for three states.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 ARMA(1,0) which can be written as
= 0.011916 + 0.188511
o+ .
(1)Based on Lagrange multiplier test, the residue of ARMA(1,0) model until the 10th lag generated probability value 0.000056 that of less than 0.05, so that the ARMA(1,0) model still pregnant heteroscedasticity. This means that the ARMA(1,0) 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 ARMA(1,0) shows that the best model is ARCH(4) 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 ARCH(4) models to lag the 10th known that the probability is 0.986175 that of more than 0.05, so that residual of ARCH(4) models does not contain autocorrelation.
Based on Lagrange multiplier test, the residual of ARCH(4) models until the 10th lag generated probability value of 0.986175 greater than 0.05, so that residual of ARCH(4) models does not have the effect of heteroscedasticity. Based on Jarque Bera test, residue of ARCH(4) models is not normal. Therefore, ARCH(4) model was re-estimated using QMLE methods (Rosadi, 2012), and obtained the best model was the model of ARCH(4) model with the average conditional ARMA(1,0). 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 SWARCH(2,4) model estimation with an average of conditional ARMA(1,0) is as follows
= S0.0000791077 ,0.0000344499 ,
for state 1
for state 2
(3)SWUP
(stable) is 0.0000791077, in state 2 (volatile) is 0.0000344499. Heteroscedasticity model of the SWARCH(2,4) model can be written as
=
J K L K
M0.0000972 + 0.9648948εo + 0.257537εo
+2.4764∙10o + 0.476999 , for state 1
0.0000133 + 0.9648948εo + 0.257537εo
+2.4764∙10o + 0.476999 , for state 2
(4)
Transition probability matrix of data the real exchange rate can be written as
x = •0.018495753 0.185355010.981504250 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 SWARCH(3,4) estimation model with an average of conditional ARMA(1,0) is as follows
= ß0.0000853095 , for state 10.0000314552
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 SWARCH(3,4) model can be written as
M0.0000545 + 1.0664938ε o + 1.0664938εo
+0.1160877ε o‰+ 0.224554εoï , for state 1
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 × 10o 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 SWARCH(2,4) model with an average of conditional ARMA(1,0) 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.
4.
Conclusion and remarks
Financial crisis in Indonesia based on indicators of the real exchange rate can be made using the model SWARCH(2,4) and SWARCH(3,4) with ARMA (1,0) as the conditional average model. Based on the test of structural changes, it is known that the period of February 1998 and July 1998 to change the structure. Then reinforced with inferred probabilities value in these months is more than 0.6. So it can be said that in February 1998 and July 1998 occurred a big crisis. Volatile real exchange rate in February 1998 and July 1998 is a result of the crisis in Indonesia middle 1997. Therefore, the detection of a currency crisis in Indonesia use SWARCH(2,4) and SWARH(3,4) with ARMA(1,0) as the conditional average model.
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