Analysis Volatility Spillover of Stock Index in ASEAN (Case Study: Indonesia, Singapore, Malaysia)

Every country has its own income, including ASEAN countries such as Indonesia, Singapore, and Malaysia. One source of national income can come from stocks, which can be measured by the stock index. The income of each country depends on each other and can be influenced by a phenomenon, such as the Covid-19 pandemic. The Covid-19 pandemic can also cause volatility spillover. This research aims to analyze volatility spillover in ASEAN countries (Indonesia, Singapore, and Malaysia) before and during Covid-19 by looking at the effects of asymmetric volatility. Volatility spillover testing in this study uses the Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) model, starting with creating a time series model and then modeling the residuals from that model, then finding the estimated parameter results of asymmetric volatility effects. The results of this study indicate that during the period before Covid-19, there is volatility spillover for Indonesia and Malaysia. Then, during the Covid-19 period, there is volatility spillover for Indonesia and Malaysia, for Indonesia and Singapore, and for Singapore and Malaysia.


Introduction
The Association of Southeast Asian Nations (ASEAN) is an organization consisting of countries in the Southeast Asian region.One of the goals of this organization is to enhance economic growth (Prajanto, 2022).Each ASEAN member has its own economic market and national income.In December 2019 in Wuhan, China, the Corona Virus Disease 2019  emerged.The impact of Covid-19 affected the stock markets of ASEAN countries, including a significant decline in the Indonesian stock market in March 2020, when Covid-19 began spreading.
According to the Indonesia Stock Exchange (2022), a stock index is a statistical measure that represents the movement of prices for a group of stocks.Each country has its own stock index, including those in ASEAN, such as the Jakarta Stock Exchange Composite (JKSE) for Indonesia, Straits Times Singapore (STI) for Singapore, and Malaysia KLCI (KLSE) for Malaysia.
The emergence of the Covid-19 pandemic has a significant impact on the economic conditions of each country, especially on the stock markets, and can influence the volatility of each country's returns.Volatility is a measure that indicates how much prices fluctuate within a period (Mieg, 2022).Additionally, the Covid-19 pandemic can also lead to volatility spillover.Volatility Spillover is a condition where volatility in one market affects the volatility in another market.Another term for Volatility Spillover is also used to express a situation where there is instability that transmits from one market to another (Arini et al., 2016).
Based on the above explanation, this research uses conventional stock index data in Indonesia, Singapore, and Malaysia with the aim of analyzing whether there is Volatility Spillover in the stock indices of ASEAN, especially in Indonesia, Singapore, and Malaysia.The results of this research can be utilized by investors to understand the stock market conditions before and during the Covid-19 pandemic.

Stock Return
Return is the income or yield obtained from financial assets.Stock return is the excess of the selling price of stocks over their purchase price.The higher the selling price of stocks over their purchase price, the higher the return obtained by the investor (Garcia-Vega, Zeng and Keane, 2020).The value of stock return can be calculated using equation (1). (1) : Stock return at time : Closing stock price at time : Closing stock price at time

Volatility Spillover
Volatility is the change in the rate of return of securities or portfolios over time.Volatility can also be interpreted as the standard deviation of the existing rate of return against the continuously increasing rate of return per unit of time.One type of volatility is asymmetric volatility, which can be defined as the uneven or unbalanced changes in the rate of return of securities or portfolios.Volatility Spillover is a condition where volatility in one market affects the volatility in another market.Another term for Volatility Spillover is also used to express a situation where instability transmits from one market to another (Arini, et al, 2016).

Stationarity Test
In analyzing time series data, the data used must be stationary; hence, a stationarity test is conducted.Data is considered stationary if it has constant mean and variance (E.P. Box et al., 2004).
For testing the stationarity of data regarding the mean, a Unit Root Test is performed using the Augmented Dickey-Fuller Test (ADF Test).The hypotheses of the ADF test are outlined as follows: , indicating the presence of a unit root, and the data is non-stationary., indicating the absence of a unit root, and the data is stationary Test statistic, ̂ ̂ : The ratio value between the estimated parameter and standard error.

̂
: The estimated value of ̂ : The standard error of ̂ The test criteria used at a significance level of 5% are as follows: 1.
If or p-value , then is rejected.

2.
If or p-value , then is not rejected.
Subsequently, for testing the stationarity of data concerning variance, the Box-Cox transformation can be applied.The Box-Cox transformation is formulated as follows (Osborne, 2010) : : The transformation parameter The estimation of the parameter can be obtained using the Maximum Likelihood method, where the value of is chosen based on the minimum residual sum of squares.The transformation is performed if the value of is not yet obtained, indicating stationarity in variance.

Autoregressive Moving Average (ARMA) Model
The autoregressive moving average model is a combined model consisting of the Autoregressive (AR) model and the Moving Average (MA) model.The Autoregressive (AR) model is a stationary model that utilizes time series data, where the observed value at time is influenced by the observed value at the previous time.Meanwhile, the Moving Average (MA) model is a stationary model that utilizes time series data, depending on the previous residuals.The ARMA model of order is symbolized as ARMA( ) and is represented by the following equation ( 4). (

Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) Model
The Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) model is a model that does not restrict the parameters used to ensure that the variance is always positive.This model frees the estimation of non-negative sizes to form a non-negative conditional variance, and the current residual variance is not only influenced by the residuals of the previous period but also influenced by the residual variances from the past.According to Tsay (2002), the EGARCH( ) model has the following equation.
: EGARCH model : Intercept : ARCH effect parameter, : GARCH effect parameter, : Leverage effect/asymmetric effect parameter, According to Brooks (2019), the gamma parameter represents asymmetric volatility as follows:  If it implies the non-existence of asymmetric volatility. If it implies that positive shocks (good news) will amplify volatility more than negative shocks (bad news). If it implies that negative shocks (bad news) will amplify volatility more than positive shocks (good news).

Materials
The data used is secondary data, index stock closing data every day of Indonesia, Singapore, and Malaysia from www.investing.com.The period of data is during January 2018 -December 2021.The applications used are R Studio and Microsoft Excel.

a) Stationarity tests
The stock index return data is calculated using equation (1) and then this data is tested for stationarity against the mean and variance.Testing the stationarity of data against the mean is conducted using the ADF test, and the results can be seen in Table 1.  1, a p-value of is obtained, indicating the absence of a unit root, thus the data is stationary regarding the mean.Subsequently, the data is tested for stationarity against variance using the Box-Cox Transformation, and the results can be seen in Table 2.The next step is create ARMA models for each dataset and later the residual of the ARMA models will be used to build EGARCH models.The ARMA models for each dataset are obtained as shown in Table 3.To analyze the asymmetric volatility occurring in each stock of Indonesia, Singapore, and Malaysia, one can observe the gamma values in the EGARCH model.The gamma value for each pair of data shown in Table 5.
Based on Table 5, it can be concluded that for JKSE and KLSE before Covid-19, there is asymmetric volatility where bad news increases volatility more that good news.Then, for JKSE and KLSE during Covid-19, there is asymmetric volatility where good news increases volatility more that bad news.Furthermore, for JKSE and STI during Covid-19, there is asymmetric volatility where good news increases volatility more than bad news.Lastly, for STI and KLSE during Covid-19, there is asymmetric volatility where good news increases volatility more than bad news.
a) Calculating stock returns using equation (1) and conducting stationarity tests.b) Creating an ARMA( ) model based on equation (4).c) Creating an EGARCH( ) model according to equation (5).d) Analyzing the values of the gamma parameter.

Table 1 :
ADF test results of the ASEAN stock index returns

Table 2 :
Box-CoxTransformation results of the ASEAN stock index returns

Table 3 :
ARMA model of the stock index ASEANAfter obtaining the ARMA model, the residuals from that model are used to form the EGARCH model.The EGARCH models for each dataset are presented in Table4.

Table 4 :
EGARCH model of the stock index ASEAN

Table 5 :
Gamma values of EGARCH model