# 1. Introduction

The study of the relationship of the stock market is a very interesting topic because stock markets are the source of capital that allows businesses to raise funds for their business operations and investors can do investment and make profits from the markets. The stock market is one of the factors that contribute directly and indirectly to the economic development of a country.

Throughout the last several decades, Asian countries have continued to develop their stock markets. This corresponds to the fact that many emerging countries have had rapid economic growth, particularly in the last ten years. In addition, the convenience of international investment has increased from the past and has reduced in limitations in terms of both legal and transactional issues.

Foreign Direct Investment (FDI) of developed countries/economies in Asia such as Japan, Hong Kong, South Korea, and Singapore, as well as political superpowers such as China and the U.S., are also big investors in the world (UNCTAD, 2020).

Investors’ investment and return are usually consistent with the return on investment in the countries/economies, companies, etc., where the investors have invested. From a global supply chain perspective, advanced economies tend to distribute some jobs to countries with lower levels of development, especially activities that use low-wage labor. This allows investors, who are mostly investors from developed countries, to receive higher returns on their investments. This shows the connection between trade and investment between different countries.

The most important source comes from Intra-ASEAN investment with a value of 22 billion US dollars (18.4% of total value) in 2015 (ASEAN, 2016). Next, the investment from the European Union, Japan, and the United States are ranked as 2^{nd}, 3^{rd}, and 4^{th}, and the total value of the four sources accounted for 60 percent of the total. However, there are economies in the Asian region other than ASEAN countries in the top ten of the highest investment inflows, namely Japan, China, South Korea, Hong Kong, and Taiwan. These accounted for nearly one-third of the total (32.2 percent), reflecting the importance of developed economies’ investment in ASEAN countries. This is an obvious linkage between the countries in Asia.

The preceding example illustrates the relationship between increasingly integrated ASEAN financial markets and the processes of change that should be explored in academic studies on this topic. This study, therefore, selects the US stock market return data to study the co-movement with Asia’s stocks. Moreover, in various economies in the Asia-Pacific region and India, the stock exchanges of the regions are relatively high in value of the stock market (see Indexmundi, 2021). The United States ranked No. 1 in the world (not shown in the table), China ranks 2^{nd} in the globe and ranks 1^{st} in Asia, and Vietnam ranks 38^{th} in the world or 17^{th} in Asia. India is one of the most appealing countries due to its strong economic growth rates and stock market value; its stock exchange is the sixth-largest in the world and the fourth largest in Asia, with a high correlation with other securities in the region and the United States. As a result of its large stock market capitalization, India is an important alternative for investors.

Bitcoin is a multi-currency cryptocurrency that has become popular among investors in recent years. It had grown in value rapidly during the coronavirus pandemic, and it reached a market capitalization of 682 billion US dollars on June 30, 2021and had a market capitalization of more than USD 1 trillion. However, the price of Bitcoin has changed noticeably, which means that Bitcoin is quite volatile, and it may not be a good medium for payments.

At present, all countries around the world are facing an epidemic of coronavirus which has caused a remarkable recession in the economy. Therefore, various industries in economies are affected in one way or another. However, it is unclear when the epidemic will subside and people will be able to resume routine activities. To deal with the situation, many central governments continued to spend stimulus money to compensate for the losses in both living costs and employment support. The events are inextricably linked to financial industry investments. Investors’ expected returns in various industries are likely to fluctuate when economic activities are halted or stimulated.

Uncertainty of the price of any securities may affect income or the stability of the country in terms of finance. Therefore, understanding the nature of volatility allows policymakers to better plan hedging risks to the financial system or financial-related activities.

The volatility or uncertainty of returns depends on many factors. The selection of the univariate GARCH model to the data does not accurately explain the volatility without depending on other factors. In this work, a multivariate GARCH model is utilized to predict volatility to get a more accurate estimate of the co-movement. This was connected to the volatility of the returns of the various securities employed in the study.

However, the correlation model used in this study should be a model that considers changes in the context of time as the nature and convenience of investment have changed, for example, the technology of placing orders has made trading easier, and trading regulations for foreign investors have been less complicated. Moreover, the presence/absence of economic crisis events can change the course of the co- movement, which makes dynamic correlation models more useful in estimating correlations than the static models which do not consider any changes.

The dynamic conditional correlation (DCC) model was first invented by Engle (2002) and has been popular for over a decade. It has a more flexible assumption and yields better results than static models proposed by Bollerslev (1990), namely the constant conditional correlation (CCC) model, which is the prototype of the DCC model. The DCC model is a parametric model in which it is assumed that the previously estimated volatility has a normal distribution. The DCC model has the advantage of relying on a small but enough number of coefficients (Engle, 2002). The correlation is estimated from the normal distribution or student’s t distribution, which the latter distribution is more suitable for stock price study. This study finds the correlation between stock/commodity yields in the context of dynamic correlation during the more integration of financial institutions/markets and the spread of the coronavirus. In this study, the DCC-GARCH model, a type of Multivariate GARCH model, is used to estimate returns’ volatility and the correlation between returns.

The research objectives include 1) to understand the characteristic of correlation among Asian stocks’ returns, the U.S. stock’s return, and Bitcoin during the COVID-19 pandemic and 2) to understand the risk which is related to the financial sector during the COVID-19 pandemic.

This paper is organized as follows: section 2 describes the literature review; section 3 presents shows data and methodology; section 4 shows the results; the summary is presented in the last section.

# 2. Literature Review

## 2.1. GARCH Model

The GARCH model is popular for studying volatility and risk. The studies that are related to the coronavirus pandemic generally discussed the increase in stock index/ price volatility during the pandemic, such as the study of Chaudhary et al. (2020) that compared the volatility between the non-crisis and during the crisis of the top ten countries with the highest GDP in the world. The existence of increased security return volatility was also discovered in the research by Yousef (2020) of the G7 stock markets, and the study by Shehzad et al(2020) of the US, Germany, Italy, Japan, and China stock exchanges. Moreover, the GARCH model can help find a risk-return relationship. Hongsakulvasu and Liammukda employed GARCH-in-mean to find the risk-return relationship in crude Oil markets during the pandemic. This study found a positive risk-return relationship during the period of the pandemic and 2020 oil price war between the European oil market and Brent market, West Texas Intermediate (WTI) and North America oil market, Middle East oil market and Dubai, and South East Asia oil market and Singapore Exchange (SGX). Furthermore, the study proposed by Bora and Basistha (2021) found that the volatility of the Bombay Stock Exchange had increased during the pandemic. All of this represents a change and non-constant nature of the volatility. The dynamic conditional volatility is likely to cause a correlation between the returns of securities in different countries, and the correlation should not be considered as a constant correlation. Moreover, a huge drop in the U.S. stock indexes would lead the volatility to be higher mathematically.

## 2.2. DCC-GARCH Model

The DCC-GARCH model was selected for this study because it is sufficiently appropriate for correlation estimates. It has the advantage of being able to estimate the correlation of multiple securities and it also takes advantage of a small number of parameters (Engel, 2002). However, there are various techniques to studying the linkage of Asian stock indexes to the United States that are not based on the DCC- GARCH model. These models are useful for understanding the nature of correlation and these studies can benefit our study in the term of knowledge.

Samarakoon (2011) employed the VAR model to explore the correlation of various stock exchanges in emerging markets, marginal stock markets, and the US stock market. This study pointed out that the sudden changes are often caused by the US stock markets during the non-crisis period. However, the abrupt changes in the stock markets of developing countries tend to affect the US stock markets in the period of crisis. Khabwang (2018) employed the gravity model to study the correlation between the yields of six securities indices in ASEAN, including Indonesia, Malaysia, Philippines, Singapore, and Thailand. The time span is the daily data during 2013–2016. The gravity model is based on economic and distance factors. The study found that the distance between Thailand and each ASEAN 5 country was statistically significant, and the longer distance leads to a lower correlation. Younis et al. (2020) conducted research with a wavelet-based approach to study the relationship between the MSCI (Morgan Stanley capital international) indices of China, India, Pakistan, Malaysia, Singapore, and Indonesia. The results showed that stock indexes were highly correlated during the economic crisis of 1997, 2008, and 2015. All indices exhibited a high correlation with Chinese stock indexes, which had increased over the last two decades. Kamaludin et al. (2021) used a wavelet method to study the relationship between US stock exchanges and ASEAN-5, which includes Malaysia, Indonesia, Singapore, the Philippines, and Thailand. This study confirmed that the correlation between each stock index to the U.S. stock had increased during March – April 2020, which was the time of the severe outbreak of the virus in the U.S.

The correlation study between Asian stock indices is not yet estimated based on variables that include US stock markets, stock exchanges of developed and developing countries in east and southeast Asia, India, Bitcoin.

Wang and Lee (2016) studied the dynamic correlations between the stock exchange and exchange markets of China, Singapore, South Korea, and Taiwan. It was found that China-Singapore had a negative correlation (−0.019), while China-South Korea and China-Taiwan had a positive correlation (0.115 and 0.074). Robiyanto (2018) relied on the DCC-GARCH model to explore the correlation between global oil prices and ASEAN securities indices, including Indonesia, Singapore, Malaysia, the Philippines, and Thailand. The results showed that the relationship between global oil price returns and the returns on the stock exchanges of the five ASEAN countries is dynamic, however, the characteristic of each pair is unique and based on the characteristics of each stock exchange. In the non-crisis period, the correlations had values that fluctuate in a narrow range. However, the correlations tend to fluctuate greatly during the economic crisis. The correlations changes from positive to negative in some correlation pairs. Chitkasame and Tansuchat (2019) employed a Markov-Switching DCC-GARCH model, and the study found that both volati lity and contagion effect was high in/between the stock returns of eight Southeast Asian countries. Hongsakulvasu et al. (2020) employed a bivariate DCC-GARCH-in-mean model to study the linkage between Singapore and Thai stock indexes. The study relied on 11 industry sector indexes, with daily data from October 2016 to October 2019. In the pre-coronavirus outbreak, it was found that the returns of the Singapore oil market and the securities of Thailand were correlated in the same direction, consisting of resources, industries, petrochemicals and chemicals, and energy and utility sectors. However, it appears that consumer goods and industries in those countries are moving in opposite directions. For the period of the COVID-19 pandemic (since November 2019), Singapore oil market returns have had a negative effect on Thai securities yields in the sector of financial, consumer goods, agriculture and food, industries, real estate, and construction, and services. The dynamic correlation analysis showed that the correlations between Singapore’s oil market returns, and various industry indexes of Thailand fluctuated over time and became more volatile during the COVID-19 pandemic. Corbet et al. (2020) studied the dynamic correlations between Bitcoin and two Chinese stock exchanges, the Shanghai Stock Exchange, and the Shenzhen Stock Exchange. The results showed that correlations among securities have increased during the 2019 pandemic. Rusmita et al. (2020) studied the relationship between Islamic and conventional stock markets in Southeast Asia, including Malaysia and Indonesia, by using daily data of FTSE Bursa Malaysia Index Series, Jakarta Islamic Index (JII), Jakarta Stock Exchange Composite Index (JCI), and FTSE Bursa Malaysia Hijrah Shariah (Hijrah). This study employed DCC with t distribution and found that the co-movement between those conventional stock markets with Islamic stock indexes is low, indicating no benefit for portfolio diversification between the four indexes. Le and Tran (2021) studied the correlation between the US stock market index, Vietnam, and the Philippines during the global financial crises (GFC) and the Coronavirus pandemic. This study found that the US securities yields had a contagion effect on Vietnamese securities yields during the GFC but there was no such effect between the US stock exchange and the Philippines. However, the US financial outbreak had affected Vietnam and the Philippines during the COVID-19 pandemic, and the Philippines had been affected more than Vietnam.

# 3. Data and Methodology

In this research methodology, we will discuss the research processes which it leads to the research results, showing in the next chapter. The research methodology consists of two important parts: data used in the study and research Methodology.

## 3.1. Data

The variables used in this study include the returns of the United States Dow Jones Index (DJI), Japan Nikkei Securities Index (N225), South Korean Stock Exchange Composite Index KOSPI (KS11), Hong Kong Hang Seng Index (HSI), Shanghai Composite Index (SSE), Singapore Straits Times Index (STI), FTSE Index Bursa Malaysia (KLSE) Jakarta Indonesia Stock Market Composite Index (JKSE), Thailand Stock Market Index (SET), Ho Chi Minh (VNI), India BSE Sensex 30 (BSESN), and Bitcoin (BTC) - all indices representing the stock indexes level. Most of the observations are collected and available on YahooFinance. com, except SET and VNI which can be accessed from Investing.com. All observations are based on daily data from January 4, 2015, to May 28, 2021, (1116 observations). Securities’ returns are calculated based on log returns, r_{t} = log (P_{t} / P_{t−1}), r_{t} is the return of security or index at time t, P_{t} is the price of security or index at time t, and P_{t−1} is the price of security or index at time t−1.

## 3.2. Methodology

This study relies on three GARCH-type models, including simple GARCH (sGARCH), GJR-GARCH, and EGARCH. We employ the GJR-GARCH and EGARCH models which consider the asymmetric effect of both positive and negative shocks on volatility. This assumption is closer to the reality which negative news affects volatility more than positive news. While the sGARCH model did not consider the asymmetric effect. We will select the best explain the model and apply the estimated result of conditional volatility to further step of the dynamic conditional correlation.

### 3.2.1. GARCH Model

The GARCH-type models used in this work are sGARCH and GJR-GARCH and EGARCH. sGARCH does not incorporate the leverage effect, however, the other two GARCH-type models do, namely GJR-GARCH and EGARCH.

To estimate the GARCH model that was first proposed by Engle (1982), it is necessary to construct the mean equation, and use the residuals to apply into the conditional variance equation to find the conditional volatility.

The residuals for each yield data are estimated by the mean equation in equation 1, where i is the return on security i at time t, r_{i, t} is the mean of the return, and ε_{i, t} is the residual which is independent and identically distributed.

\(r_{i, t}=\mu_{i}+\varepsilon_{i, t} \quad i=(\mathrm{DJIA}, N 225, \mathrm{KS} 11, \ldots, \mathrm{BTC})\) (1)

then, we can then estimate volatility using the three GARCH models mentioned above. The standardized residual and square root of conditional volatility can be composed to be the error term.

\(\varepsilon_{i, t}=\sqrt{h_{i, t}} z_{i, t} \text{,}\) (2)

h_{i, t} is the conditional volatility of the return on security i at time t, while z_{i, t }is the standardized residual. The residual term has zero mean and a standard deviation of one. If we move the standardized residual in equation 2 to the left-hand side of the equation, we can find the value of h_{i, t} which has a mean equal to zero and volatility equal to σ^{2}. The conditional volatility was estimated using the sGARCH(1, 1), GJR-GARCH(1, 1), and EGARCH(1, 1) models, which are presented in the following subsections.

#### 3.2.1.1. Simple GARCH(1, 1) Model

The conditional volatility estimated by the simple GARCH(1, 1) model can be represented as follows;

\(h_{i, t}=\omega_{i}+\sum_{q=1}^{Q} \alpha_{i, q} \varepsilon_{i, t-q}^{2}+\sum_{p=1}^{P} \beta_{i, p} h_{i, t-p} \text{,}\) (3)

where ω_{i}, α_{i}, β_{i} > 0. ω_{i} is a constant term, The parameter α captures the ARCH effect, β captures the GARCH effect, and α + β shows the volatility persistence.

#### 3.2.1.2. GJR-GARCH(1, 1) Model

The GJR-GARCH model, proposed by Glosten, Jagannathan, and Runkle (1993), differs from the simple GARCH model in that it has a leverage term. The leverage term demonstrates the asymmetric effect of volatility.

\(h_{i, t}=\omega_{i}+\sum_{q=1}^{Q}\left(\alpha_{i, q}+\gamma_{i, q} I_{i, t-q}\right) \varepsilon_{i, t-q}^{2}+\sum_{p=1}^{P} \beta_{i, p} h_{i, t-p} \text{,}\) (4)

and the indicator function can be shown as

\(I_{i, t-1}=\left\{\begin{array}{l} 1 \text { if } \varepsilon_{i, t-1}<0 \\ 0 \text { if } \varepsilon_{i, t-1} \geq 0 \end{array}\right. \text{,}\)(5)

#### 3.2.1.3. EGARCH(1, 1) Model

Nelson (1991) invented EGARCH that has the ability to handle asymmetric effects between positive and negative effects on the volatility. The volatility estimation using EGARCH(1, 1) model can be illustrated as follows:

\(\begin{aligned} \ln \left(h_{i, t}\right)=& \omega_{i}+\beta \ln \left(h_{i, t-1}\right)+\alpha_{i}\left(\left|\frac{\varepsilon_{i, t-1}}{\sigma_{i, t-1}}\right|-E\left|\varepsilon_{i, t}\right|\right) \\ &+\gamma_{i}\left(\frac{\varepsilon_{i, t-1}}{\sigma_{i, t-1}}\right) \end{aligned}\) (6)

γ_{i} represents the ARCH effect and α_{i} represents the asymmetric effect of positive and negative shocks.

However, all parameters, except β EGARCH, can have both positive and negative values, causing EGARCH to lack volatility persistence and the capacity to explain why volatility is stationary, as other GARCH-type models do. The value of the parameter β is positive and less than unity.

### 3.2.2. DCC-GARCH Model

The dynamic correlation can be obtained from the DCC model, which is a model that studies the relationship between volatilities. The variance data used in the model was obtained from the GARCH process described previously. The conditional covariance equation can be as follows:

H_{t} = D_{t}R_{t}D_{t}, (7)

H_{t} is a conditional covariance matrix, size n × n, and \(H_{t}=E\left[r_{t} r_{t}^{\prime} \mid \psi_{t-1}\right]\). This represents that the volatility is conditional on the information in time t−1. \(r_{t}=\left(r_{\mathrm{DJI}, t}, r_{N 225, t}, r_{\mathrm{HSI}, t}, \ldots, r_{\mathrm{BTC}, t}\right)^{\prime}\) and \(r_{t} \mid \psi_{t-1} \sim N\left(0, H_{t}\right)\). H_{t} comprises two main parts, including the diagonal matrix of conditional standard deviation (D_{t}):

\(D_{t}=\left[\begin{array}{ccccc} \sqrt{h_{\text {DJIA}, t}} & 0 & 0 & \cdots & 0 \\ 0 & \sqrt{h_{N 225, t}} & 0 & \cdots & 0 \\ 0 & 0 & \sqrt{h_{H S I, t}} & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & \sqrt{h_{\text {BTC}, t}} \end{array}\right] \text {, }\) (8)

R_{t} is a matrix that represents the correlations between asset’s returns, which has size 12 × 12, while \(r_{t}=H_{t}^{1 / 2} z_{t}\) and \(z_{t}=D_{t}^{-1} r_{t} \sim N\left(0, R_{t}\right)\) . This shows that the standardized residual’s variance is equal to the correlation between asset’s indices. \(z_{t}=\left(z_{\mathrm{DJI}, t}, z_{N 225, t}, z_{\mathrm{HSI}, t}, \ldots, z_{\mathrm{BTC}, t}\right)^{\prime}\) R_{t} can be computed from:

\(R_{t}=Q_{t}^{*-1} Q_{t} Q_{t}^{*-1}\) (9)

D_{t }is transformed into \(Q_{t}^{*}\):

\(Q_{t}^{*}=\left[\begin{array}{ccccc} \sqrt{q_{\mathrm{DJI}, t}^{*}} & 0 & 0 & \ldots & 0 \\ 0 & \sqrt{q_{N 225, t}^{*}} & 0 & \ldots & 0 \\ 0 & 0 & \sqrt{q_{\mathrm{HSI}, t}^{*}} & \ldots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \ldots & \sqrt{q_{\mathrm{BTC}, t}^{*}} \end{array}\right]\) (10)

the Log-Likelihood can be computed by using 2-step estimation proposed by Engel (2002)

\(L(\Theta)=-\frac{1}{2} \sum_{t=1}^{T}\left(\begin{array}{l} n \log (2 \pi)+\log \left|D_{t}\right| \\ +\log \left|R_{t}\right|+z_{t}^{\prime} R_{t}^{-1} z_{t} \end{array}\right)\) (13)

Θ is a set of parameters.

# 4. Results

In this chapter, there are four main sections to discuss, including descriptive statistics, the goodness of fit result, the result of DCC-EGARCH, the result of mean difference test between pre- and during- COVID-19 pandemic.

## 4.1. Descriptive Statistics

The key descriptive statistics and test statistics are shown in Table 1. Initially, Bitcoin returns have the highest volatility. While Malaysian stock index returns have the lowest volatility. Most of the price yields have skewed distribution to the left, especially in the case of Malaysian securities. The only exception is Indian stock indexes that are skewed to the right. High kurtosis occurred in the yields of the US, Malaysia, and Thailand securities. The skewness and highness results might indicate that the yield data is not normally distributed. We employ the Jarque-Bera test for normality test, and the result shows that the return data is not normally distributed. This is a characteristic that often occurs with the yield data of securities with a heavy-tailed distribution. However, this does not affect our volatility and Q_{t}, the conditional volatility matrix can be computed from DCC(1, 1) process:

\(Q_{t}=(1-a-b) \bar{Q}+a z_{t-1} z_{t-1}^{\prime}+b Q_{t-1}\) (11)

the lying above equation shows the persistence of correlation via a + b, the higher value, the more persistence. If a + b is equal to 0, the correlation will be constant over time and equal to the conventional correlation, \(\bar{Q}=\frac{1}{T} \sum_{t=1}^{T} z_{t} z_{t}^{\prime} \cdot Q_{t}\) can be constructed as follow:

\(Q_{t}=(1-a-b)\left[\begin{array}{ccccc} 1 & \rho_{\mathrm{DJI}, N 225} & \rho_{\mathrm{DJI}, \mathrm{HSI}} & \cdots & \rho_{\mathrm{DJI}, \mathrm{BTC}} \\ \rho_{N 225, \mathrm{DJI}} & 1 & \rho_{N 225, \mathrm{HSI}} & \cdots & \rho_{N 225, \mathrm{BTC}} \\ \rho_{\mathrm{HSI}, \mathrm{DJI}} & \rho_{\mathrm{HSI}, N 225} & 1 & \cdots & \rho_{\mathrm{HSI}, \mathrm{BTC}} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ \rho_{\mathrm{BTC}, \mathrm{DJI}} & \rho_{\mathrm{BTC}, N 225} & \rho_{\mathrm{BTC}, \mathrm{HSI}} & \cdots & 1 \end{array}\right]+a\left[\begin{array}{c} Z_{\mathrm{DJIA1}, t-1} \\ Z_{N 225, t-1} \\ Z_{\mathrm{HSI}, t-1} \\ \vdots \\ Z_{\mathrm{BTC}, t-1} \end{array}\right]\left[\begin{array}{c} Z_{\mathrm{DJIA}, t-1} \\ Z_{N 225, t-1} \\ Z_{\mathrm{HSI}, t-1} \\ \vdots \\ Z_{\mathrm{BTC}, t-1} \end{array}\right]+b Q_{t-1},\)(12)

analysis since only the residuals from the mean equation are used in the GARCH model. In summary, the data of each security is stable at the I(0) level. Therefore, all yield data can be used to study volatility and correlation.

**Table 1: Descriptive Statistics of Securities’ Returns**

**Note: *Represents that the test statistic rejects the null hypothesis at strong to very strong evidence using the Minimum Bayes Factor (MBF) of Goodman (1999).**

## 4.2. The Goodness of Fit Result

The result of the goodness of fit (Table 2) shows that DCC(1, 1) with t-distribution based on EGARCH(1, 1) with normal distribution has the best goodness of fit values compared to other candidates (we include normal, student’s t(t), skewed normal, the skew student’s in GARCH-type models; Multivariate normal and Multivariate t in the DCC model). The EGARCH(1, 1) model has the lowest AIC value, suggesting that it is the best characterized model of historical data when compared to other models, as well as the lowest BIC value, indicating that it has the best forecasting performance to predict the correlation by comparison. Because the information from the preceding period is required to characterize the covariance of the later period, the DCC model necessitates a model capable of predicting covariance measures. Therefore, this study used DCC(1, 1)-EGARCH(1, 1) model in the DCC estimation.

**Table 2: Goodness of Fit**

## 4.3. The Result of DCC-EGARCH

The result from DCC(1, 1)-EGARCH(1, 1) indicates that the volatility of each variable has a relatively high correlation to volatility in the past (time t−1) (Table 3). Most of the variables have parameter β_{i} values greater than 0.9 and are statistically significant (in the GARCH part). However, BTC has a very low value of the parameter (0.3148). It shows that the volatility of BTC cannot be explained well by its own past volatility.

**Table 3: The Result of DCC(1,1)-Multivariate EGARCH(1,1)**

**Note: This study avoids p-value but uses the calibrated p-value via Bayes Factor of Goodman (1999) the evidence supports including *weak, **moderate, ***moderate to strong, and ****strong to very strong evidence**

The result from the EGARCH model shows that negative news on prices generates a higher effect on volatility than positive news due to the negative value of α_{i} which this occurs in most of the cases, except SSE and BTC.

Moreover, in the EGARCH(1, 1) model part, which relates to the parameter γ_{i}. Most of the cases have a positive value γ_{i} and are statistically significant. Except for BTC, which has a negative value, the normalized standard deviation at time t−1 has a positive effect on the volatility at time t.

The conditional volatility values generated from the multivariate EGARCH(1, 1) model (Figure 1) show a marked increase in volatility. The increase in volatility occurred around March 2020 or after the spread of the coronavirus disease 2019 which reached every region of the world. The stock exchanges in the United States, which could be the origin of stock index changes, as well as other stock indexes, had seen a significant drop during the month. Because of their correlation in investments, where investors may simply move their investments from one source to another and the ease of making investments, changes in the US stock markets tend to affect other stock exchanges across the world.

**Figure 1: Conditional Variance of Stock Indexes using GARCH(1, 1)**

The DCC(1, 1) model demonstrated that the correlation of all securities/commodities returns is extremely persistent with correlation in the preceding period (t−1), with a and b values of 0.0059 and 0.9228, respectively. When the two values are added together, the result is greater than 0.93, indicating that the ability to describe correlations based on previous time correlations is declining and that the correlation is not constant but changes over time. The statistically significant test for parameters a and b shows that the estimates of dynamic conditional correlations are reliable. The dynamic conditional correlation graphs between the US stock, Asian stocks indexes, and Bitcoin are shown in Figure 2 as an example.

**Figure 2: DJI Index Value and Dynamic Conditional Correlation Between DJI with Other Securities**

The median value of the correlation of the periods is shown in Table 4 without showing the correlation of the full sample. Except for HSI-DJIA (Hong Kong and US stock indexes) and KLSE-JKSE (Malaysia and Indonesia stock indexes), the results show that most correlation pairs have positively changed since the coronavirus outbreak was announced on December 31, 2019, with the exception of HSI-DJIA (Hong Kong and US stock indexes) and KLSE- JKSE (Malaysia and Indonesia stock indexes), where there is a decrease in the size of the correlation (as shown by t-test).

**Table 4: Median of Conditional Correlation in Pre- and During- COVID-19 Pandemic**

**Note: Normal typing numbers are pre-COVID-19 correlation, while numbers in [ ] are the correlation during COVID-19 pandemic, and *represents that the test statistic rejects the null hypothesis (that the mean value of correlations in pre- and during COVID-19 are the same) at weak to very strong evidence using Minimum Bayes Factor (MBF) of Goodman (1999)**

Asian stocks indexes are highly correlated with the Hong Kong stock index with the value between 0.46 – 0.61 (HSI- JKSE and HSI-STI) during the pandemic period, while the top 3 correlation pair values between Asian and the US stock index are DJI-STI, DJI-N_{22}5, and DJI-KS11 with the values of 0.3897, 0.3884, and 0.3692, respectively. The DJI-SET has the highest value of correlation compared to DJI- each stock of ASEAN. Moreover, we should note that most Asian stock indexes are highly correlated with the stock indexes of Hong Kong, Singapore, and South Korea, with values 0.6689 (HSI-STI), 0.6125 (HSI-KS11), and 62.68 (KS11-N_{22}5), respectively.

During the pandemic, the stock indexes of developing ASEAN countries such as Indonesia, Malaysia, and Thailand are well-correlated with the stock indexes of South Korea, Hong Kong, and Singapore, with all pairs of the aforementioned countries exceeding 0.4270 (KS11-SET). This indicates that the stock markets of the three ASEAN countries are well-connected with the three Asian tigers more than the stock market of Japan (the highest pair is N_{22}5-KLSE with the value of 0.42).

The stock index of India is well-connected with Asian stock indexes, including BSESN-HIS (0.5030), BSESN- KS11 (0.4543), BSESN-STI (0.4385), and BSESN-SET (0.4356). However, there is an insignificant link between BTC and other major stock indices (lower than 0.10).

# 5. Conclusion

This study aims to explore the correlation of Asian stock indexes, using the DCC model. However, most stock markets are known to be influenced by the US markets. A cryptocurrency like Bitcoin has grown in popularity in recent years and has become a viable investment option. That is why we include the return of United States Dow Jones Index (DJI) and Bitcoin (BTC) into our study, together with the returns of 10 Asian stock indexes, including the Japan Nikkei Securities Index (N_{22}5), South Korean Stock Exchange Composite Index KOSPI (KS11), Hong Kong Hang Seng Index (HSI), Shanghai Composite Index (SSE), Singapore Straits Times Index (STI), FTSE Index Bursa Malaysia (KLSE), Jakarta Indonesia Stock Market Composite Index (JKSE), Thailand Stock Market Index (SET), Ho Chi Minh Stock Market Index (VNI), and India BSE Sensex 30 (BSESN). We employ 1, 116 observations, which are daily data from January 2015 to May 2021.

The result of the unit root test shows that all returns are stationary, then we use the estimated error in the next step, the DCC-GARCH model. From the goodness of fit result, the DCC(1, 1)-EGARCH(1, 1) with multivariate t distribution in the DCC and normal distribution in the EGARCH is the best explaining and forecasting model by AIC and BIC values Most of the returns’ volatilities generated by EGARCH(1, 1) pointed out a very high volatility persistence, except BTC. Moreover, the negative shocks/news have more impact on the volatilities than positive shocks/news in most of the cases, except SSE and BTC. The result of dynamic conditional correlation indicates that the time-varying correlation is more suitable than the constant one. Most of the correlation pairs show higher correlation values during the COVID-19 pandemic compared to the pre-COVID-19, except HSI-DJIA and KLSE- JKSE. The dynamic conditional correlation of stock returns between developed countries in Asia to developing countries in Asia, and each country in ASEAN to other countries in ASEAN, has changed significantly during the COVID-19 pandemic, indicating that the markets in Asia are well connected. Furthermore, the correlation of HSI-DJI, HSI-N_{22}5, and HSI-KS11 in pre- and during-COVID-19 pandemic have no difference, indicating the stable correlation between those pairs of correlation. However, most dynamic conditional correlation pairs rapidly increased in March 2020, before plummeting in April 2020 due to the severe outbreak of COVID-19 in many nations, particularly the United States. However, it took a few months to adjust. The result of correlation also shows the connectedness between Asian stock indexes, which are well-connected within the region, with Korea, Singapore, and Hong Kong especially.

#### References

- ASEAN. (2016). Top ten sources of foreign direct investment inflows in ASEAN. https://asean.org/wp-content/uploads/2015/09/Table-27_oct2016.pdf
- Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Economics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
- Bora, D., & Basistha, D. (2021). The outbreak of COVID-19 pandemic and its impact on stock market volatility: Evidence from a worst-affected economy. Journal of Public Affairs, 36(2), 43-69. https://doi.org/10.1002/pa.2623
- Chaudhary, R., Bakhshi, P., & Gupta, H. (2020). Volatility in international stock markets: An Empirical Study during COVID-19. The Journal of Risk and Financial Management, 13(9), 1-17. https://doi.org/10.3390/jrfm13090208
- Chitkasame, T., & Tansuchat, R. (2019). An analysis of contagion effect on ASEAN stock market using multivariate Markov Switching DCC GARCH. Thai Journal of Mathematics, 56, 135-152. http://thaijmath.in.cmu.ac.th/index.php/thaijmath/article/view/3911
- Corbet, S., Larkin, C., & Lucey, B. (2020). The contagion effects of the COVID-19 pandemic: Evidence from gold and cryptocurrencies. Finance Research Letters, 35, 101554. https://doi.org/10.1016/j.frl.2020.101554
- Engle, R. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. Inflation. Economics, 50, 987-1008. https://doi.org/10.2307/1912773
- Engle, R. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics, 20(3), 339-350. https://www.jstor.org/stable/1392121 https://doi.org/10.1198/073500102288618487
- Glosten, L., Jagannathan, R., & Runkle, D. (1993). Relationship between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48, 1779-1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
- Goodman, S. N. (1999). Toward evidence-based medical statistics. The Bayes factor. Annals of Internal medicine, 130(12), 1005-1013. https://doi.org/10.7326/0003-4819-130-12-199906150-00019
- Hongsakulvasu, N., Khiewngamdee, C., & Liammukda, A. (2020). Does the COVID-19 crisis affect the spillover of the oil market's return and risk on Thailand's sectoral stock return? Evidence from bivariate DCC GARCH-in-mean model. International Energy Journal, 20(4), 647-662. http://www.rericjournal.ait.ac.th/index.php/reric/article/view/2552
- Hongsakulvasu, N., & Liammukda, A. (2020). The risk-return relationship in crude oil markets during COVID-19 pandemic: Evidence from time-varying coefficient GARCH-in-mean model. The Journal of Asian Finance, Economics, and Business, 7(10), 63-71. https://doi.org/10.13106/jafeb.2020.vol7.no10.063
- Indexmundi (2021). The market capitalization of listed domestic companies (current US$) - Country ranking. https://www.indexmundi.com/facts/indicators/CM.MKT.LCAP.CD/rankings
- Kamaludin, K., Sundarasen, S., & Ibrahim, I. (2021). COVID-19, Dow Jones and equity market movement in ASEAN-5 countries: Evidence from wavelet analyses. Heliyon, 7(1), e05851. https://doi.org/10.1016/j.heliyon.2020.e05851
- Khabwang, D. (2018). Analyzing the correlation between Thailand and ASEAN-5: Equity markets returns with the gravity model [Master thesis, Chiang Mai University]. Chiang Mai, Thailand. https://archive.lib.cmu.ac.th/full/T/2018/econ80518dkhab_tpg.pdf
- Le, T. P. T. D., & Tran, H. L. M. (2021). The contagion effect from U.S. stock market to the Vietnamese and the Philippine stock markets: the evidence of DCC - GARCH model. Journal of Asian Finance. Economics and Business, 8(2), 759-770. https://doi.org/10.13106/jafeb.2021.vol8.no2.0759
- Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica - The Econometric Society, 59(2), 347-370. https://doi.org/10.2307/2938260
- Robiyanto, R. (2018) The dynamic correlation between ASEAN-5 stock markets and world oil. Journal of Finance and Banking, 22(2), 198-210. https://doi.org/10.26905/jkdp.v22i2.1688
- Rusmita, S. A., Rani, L. N., Swastika, P., & Zulaikha, S. (2020). Capital market volatility MGARCH analysis: Evidence from Southeast Asia. The Journal of Asian Finance, Economics, and Business, 7(11), 117-126. https://doi.org/10.13106/jafeb.2020.vol7.no11.117
- Samarakoon, L. P. (2011). Stock market interdependence, contagion, and the U.S. financial crisis: The case of emerging and frontier markets. Journal of International Financial Markets Institutions and Money, 21(5), 78-111. https://doi.org/10.2139/ssrn.1784295
- Shehzad, K., Xiaoxing, L., & Kazouz, H. (2020). COVID-19's disasters are perilous than global financial crisis: A rumor or fact? Financial Research Letters, 36, 101669. https://doi.org/10.1016/j.frl.2020.101669
- UNCTAD. (2020). World investment report 2020: International production beyond the pandemic. UNCTAD: United Nations Publication.
- Wang, M. C., & Lee, S. H. (2016). Analysis of the correlation structure between stock and exchange rate markets: An example of China on Asian emerging markets. Accounting and Finance Research, 5(2), 104-114. https://doi.org/10.5430/afr.v5n2p104
- Younis, I., Longsheng, C., Basheer, M. F., & Joyo, A. S. (2020). Stock market comovements among Asian emerging economies: A wavelet-based approach. PLoS One, 15(10), e0240472. https://doi.org/10.1371/journal.pone.0240472
- Yousef, I. (2020). The impact of coronavirus on stock market volatility. International Journal of Psychosocial Rehabilitation, 24(6), 18069-18081.