Early Detection of South Korean Financial Crisis using MS- GARCH Based on Term of Trade Indicator

The 1997 Asian financial crisis, which occurred until 1998, had a significant impact on the economies of Asian countries, including South Korea. The crisis brought down the South Korean currency quickly and sent the economy into sudden decline. Because the impact of the financial crisis was severe and sudden, South Korean requires a system which able to sight crisis signals, therefore that, the crisis will be fended off. One in all the indicators that can detect the financial crisis signals is that the term of trade indicator which has high fluctuation and change in the exchange rate regime. The mixture of Markov Switching and volatility models, Generalized Autoregressive Conditional Heteroscedasticity (GARCH), or MSGARCH could explain the crisis. The MS-GARCH model was built using data from the South Korean term of trade indicator during January 1990 until March 2020. The findings obtained in this research can be inferred that the best model of the term of trade is MS-GARCH (2,1,1). Term of trade indicator on that model could explain the Asian monetary crisis in 1997 and also the global monetary crisis in 2008. The smoothed probability of term of trade indicators predicts in April till December 2020 period, there will be no signs of the monetary crisis in South Korea.


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Chang et al. [4] used a combination of Markov switching and volatility models to examine the volatility and exchange rate of the Korean stock market, as well as the global currency crisis, using Markov switching autoregressive conditional heteroscedasticity (SWARCH). Sugiyanto and Hidayah [5] were using a composite of the Markov switching and the GARCH models to detect financial crises using an indicator of interest rates on loans and deposits. According to the findings of that study, the MS-ARCH(2,1) model for the real interest rate on deposits indicator and the MS-GARCH(3,1,1) model for the lending interest rate/deposit interest rate indicator might explain the financial crisis in Indonesia. As a result, these models were used to forecast Indonesia's financial catastrophe in 2019. The MS-GARCH model will be used to detect financial crises based on indicators of South Korea's terms of trade in this study.

2.1.
Augmented Dickey Fuller (ADF) Test. The ADF test was performed to assess the data stationarity [6]. The ADF test's null hypothesis is that time series data are not stationary, while the alternative hypothesis is that time series data are stationary. The ADF test statistic is denoted as where and are parameter estimator and the standard deviation of the autoregressive model, respectively. If p-value of the ADF test statistic is less than α, the 115 null hypothesis should be rejected. If the data is not stationary, it is necessary to transform it.

2.2.
Log Return Transformation. According to Tsay [7], the return has better statistical properties than the actual data. In economic analysis, the return value is more emphasized than the actual value, and the formula is R t represents return value at time-t, z t represents observational data at time-t, and z t-1 represents observational data at time t-1. It is possible to write the log return transformation as . where , is the AR model parameter, , is the MA model parameter, and a t is the residual of ARMA models at time-t.

2.4.
Information Criteria. The optimum model is chosen based on information criteria. One of the information criteria approaches is the Akaike Information Criterion (AIC). The AIC is formulated by Akaike [9] (5) where l represents the log-likelihood function, h represents the number of parameters to be estimated, and T represents the total number of observations.

Generalized Autoregressive Conditional Heteroscedasticity (GARCH)
Model. The GARCH model is a volatility model that utilizes previous variation to explain variance in the future, according to Bollerslev, who initially identified it in 1986 [2]. The GARCH(m,s) model is defined as (6) where m 0, s 0 for i=1,2, ..., m and j=1,2, ...,s. is the conditional variance of the residual at time-t [7].

2.6.
Dynamic Time Warping (DTW). DTW is a method for describing the best resemblance between collections by computing the shortest distance between them. A dynamic program method based on the distance accumulation matrix can be used to determine the DTW distance of two-time series. After we have determined the optimum number of clusters, we could search for a Markov switching model using the same number as the best number of clusters.

2.7.
Markov Switching Model. Markov switching is a type of time series data modeling that can be used to explain how events or states change. Hamilton [3] said that the Markov switching model for the state at time-t in the time series approach can be expressed as (7) where r t is the observed variable, a t is the residual of conditional mean ARMA(p,0) model, and is the mean of the Markov switching model depending on the state (s t ).

2.8.
The Mixture of Markov Switching and GARCH Model. According to Gray [10], the mixture model of Markov switching and GARCH, MS-GARCH, can be written as (8) where m and s are the orders of the GARCH model.

2.9.
Transition Probability Matrix. According to Hamilton [3], s t is an unobserved random variable with the values 1, 2, 3, …, k assuming it follows a first-order Markov chain process with a transition probability p ij . The transition probability s t is equal to a certain value of j which depends on the s t-1 value of i and can be written in the following form (9) where P can be written in matrix form in equation (10): (10)

Smoothed Probability.
Smoothed probability is the probability value of a condition at time t based entirely on observational data from start to finish. The smoothed probability value can be represented in equation (11) based on Kim and Nelson [11]: (11) The anticipated value of the smoothed probability at-t+1 is formulated as equation (12), according to Guidolin and Pedio [12]: where is the smoothed probability value when for state and p ij is the transition probability of a state. Short-term indicators of a crisis on an economic indicator can be predicted by looking at the sign of the smoothed probability's expected value.

Results and Discussion
Data on South Korea's term of trade indicator was obtained from the website of the International Monetary Fund (IMF) [13]. The term of trade is defined as (13) where Px is export price index and Pm is import price index. The data taken is monthly data from January 1990 to March 2020. The period of January 1990 to March 2019 is used as training data while April 2019 to March 2020 is used as test data.
The stages in obtaining predictions for financial crisis signals in South Korea start from determining the appropriate data pattern through data plotting, stationarity testing, determining the best ARMA pattern based on the smallest AIC of each model combined with the order of the disconnected ACF and PACF lag combinations. Figure 1 illustrates a time series plot of the term of trade, which indicates that the data is not stationary because there is a fluctuation from time to time. Furthermore, the ADF test reveals a probability value greater than 0.05. This indicates that the data is not stationary, necessitating the use of the log return transformation. Figure 2 shows that the log return transformed data does not indicate that the data is stationary. The probability value in the ADF test is substantially less than 0.05, indicating that the data is stationary. After the data has stabilized, ACF and PACF tests are run on each data set to determine which ARMA model should be utilized. The ACF and PACF plots from the log return converted data in Figure 3 and Figure 4 identify the highest order ARMA model. The ACF plot in Figure 3 shows that the ACF value is disconnected and exits the confidence band at lag 1. Figure 4 shows that the PACF value is disconnected after the second lag. Consequently, the usable ARMA models are ARMA(1,0), ARMA(1,1), ARMA(2,0), and ARMA(2,1). Estimated parameters of each ARMA model are shown in Table 1.   In Table 1, some parameters are not significant so that the ARMA model with insignificant parameters is ignored. The ARMA model is obtained with three significant parameters: ARMA(1,0), ARMA (2,0), and ARMA (3,0). (2,1). The ARMA model with the smallest AIC is obtained using the AIC information criteria, which is ARMA (2,1).
However, in this study, the simple principle of the model is considered so that the ARMA (2,0) or AR (2) model is used. The ARMA(2,0) model on the transformation data log return of the South Korean term of trade indicator is written in equation (15): where r t is the log return of the South Korean term of trade indicator at time t. Figure 5. ARMA model residual curve Figure 5 demonstrates that the ARMA model's residual distribution has a high peak, indicating that it is a leptokurtic distribution. Since this pattern shows that there is a range value that differs from the residual, the residuals must be grouped. The DTW distance algorithm is used to properly group time series data. The best number of clusters is found based on the grouping findings, which is two clusters as shown in Figure 6.   Table 2. The predicted and actual conditions are identical, as shown in Table 2. In addition, the MS-GARCH(2,1,1) is utilized to predict future financial crises. Table 3 shows the expected value of smoothed probability in South Korea.  Table 3 shows that the smoothed probability prediction value is steady, indicating that the MS-GARCH(2,1,1) model of the term of trade indicator predicts that no financial crisis will occur between April and December 2020. Next, the plotting is carried out.   Figure 8 shows that in the period April -December 2020 it is predicted that there will be no crisis. The data used in this research is the ratio of the export price to the import price. In 2020, when there was a global pandemic due to the COVID-19 virus, the two indicators both dropped so that the comparison between the two was balanced. As a result, the term of trade indicator had a balanced comparison value, and the term of trade indicator was unable to alert a financial crisis in the case of a COVID-19 pandemic.

Conclusion
The composite Markov switching model and the GARCH volatility model that is appropriate for the South Korean term of trade indicator is MS-GARCH(2,1,1). In South Korea, this indicator detects the 1990-1991 crisis, the 1997-1998 Asian crisis, and the 2008 global financial crisis. The combination model was used to detect crises in April -December 2020 based on term of trade indicator and the results showed that there will no crisis signal in that period in South Korea.