Volatility Dynamics in the ASEAN– China Free Trade Agreement

Abstract

This study used three multivariate general autoregressive conditional heteroskedasticity models to analyze the volatility dynamics in the ASEAN–China Free Trade Agreement. Results indicated the presence of long-run persistence, wherein shocks in China’s stock market affect other ASEAN stock indices in the long term. Further tests revealed the presence of time-varying correlations, suggesting dynamic models, such as the dynamic conditional correlations model, are appropriate. The Baba, Engle, Kraft, and Kroner model determined that the conditional covariances of the Chinese and ASEAN indices are functions of their lagged covariances, further proving that China’s stock volatilities impact the volatilities of ASEAN counterparts.

JEL Classification: C58, G15

Keywords

ASEAN–China stock returns and volatility ACFTA bilateral relationship CCC DCC and diagonal BEKK models

1. Introduction

The Association of Southeast Asian Nations (ASEAN) and China play key roles in the rapidly changing international trade dynamics in Asia, particularly in East Asia. These economic developments were initiated in the ASEAN–China Summit in November 2001, during which China proposed to strengthen the sense of regionalism by establishing a free trade area with the ASEAN. The formal agreement was signed in November 2002, and the ASEAN–China Free Trade Agreement (ACFTA) was established. Since then, the ASEAN and China have signed several trade agreements, including economic cooperation pacts, trade agreements regarding goods and services, and investments. At present, the ACFTA is the world’s third-largest free trade agreement in terms of volume (after the European Union and North American Free Trade Areas).

This trade agreement is perceived as a necessary stage in the further development of economic activities and investment opportunities between China and ASEAN member countries. By entering a diversified market, the ASEAN will benefit from China’s aggressive expansion and investment potential; at the same time, China will benefit from an expanded market of natural resources and raw materials. The increasing GDPs of the ASEAN and China suggest their continuing economic growth. In 2013, the combined nominal GDP per capita of the ASEAN was US$2.40 trillion, whereas that of China was US$9.47 trillion. Moreover, the flow of investments from China to the ASEAN reached US$8.64 billion, whereas that from the ASEAN to China totalled US$5.46 billion. The ASEAN is China’s fourth-largest trading partner, and China is the ASEAN’s second-largest trading partner. The ACFTA is expected to promote a deeper sense of regionalism, which will strengthen the integration of intra-regional trade and investments.

The recent wave of regionalisation of economic activities and financial markets sparked the interest of scholars and practitioners. They seek to understand how the volatility in certain markets affects the volatility of other markets. In particular, this article determines how the volatility of a particular asset spills over to another asset directly through its conditional variance or indirectly through its conditional covariances. Karolyi (1995) and Zhu (2009) proved that the volatilities of financial markets tended to move across other markets without any consideration for physical boundaries. Fleming, Kirby, and Ostdiek (1998) and Du, Yu, and Hayes (2011) discovered that the volatility of financial asset returns was transmitted; they also found that covariances and correlations changed over time with persistent dynamics.

The ACFTA is no exception to the potential volatility relationships between the ASEAN and Chinese economies. No empirical study has analysed the volatility dynamics in the ACFTA. The correlation in the financial markets of China and ASEAN member countries has a strong economic significance. By identifying volatility co-movements, investors can become less exposed to unwanted risks and consequently invest in another ASEAN country with less correlation with the Chinese economy. This study captures the volatility and co-volatility relations in the ACFTA by applying three multivariate generalised autoregressive conditional heteroscedasticity (MGARCH) models, which were designed to estimate individual volatilities and co-volatilities of time-series data returns. This study determines the volatility dynamics of the Shanghai Stock Exchange index (SSE; total market capitalisation in 2013: US$1.8 trillion) and its linkage with the individual stock markets of ASEAN member countries, including the Jakarta Stock Exchange index (JKSE), the Kuala Lumpur Stock Exchange index (KLSE), the Philippine Stock Exchange index (PSE), the Straits Times Stock index (STS), the Bangkok Stock Exchange index (BKSE) and the Ho Chi Minh Stock Exchange index (HSE). These financial markets have a combined market capitalisation of US$1.5 trillion.

The first MGARCH model applied in this study was the constant conditional correlation (CCC) model, which was first developed by Bollerslev (1990). This model utilises a non-parametric approach and an adaptive methodology to improve the estimation of volatility. The second MGARCH model was the synthesised Baba, Engle, Kraft and Kroner (BEKK) model proposed by Engle and Kroner (1995); this model allows for the determination of the cross-relations of conditional covariances. The third MGARCH model was the dynamic conditional correlation (DCC) model developed by Engle (2002); this model was an extension of the CCC model that allows a constrained dynamism in the correlations. According to Bauwens, Laurent, and Rombouts (2006), the use of a multivariate framework to model volatility can result in more relevant empirical models than working with separate univariate models.

This article is motivated by the lack of studies on the volatility dynamics in the Asian region. The objectives of this study are as follows:

Identify the presence of long-run and short-run persistence in the relationship between China’s SSE returns and the individual returns of six ASEAN stock markets.

Determine if the volatility of the stock returns is transmitted through their conditional variances or conditional covariances.

Examine if the volatility relationships between China and the ASEAN member countries are constant or changing over time.

Identify which multivariate model can best determine the relationship between China’s SSE and the six ASEAN stock market returns.

This study is relevant because China continues to emerge as an economic superpower and the economies in the ASEAN region have been highly productive in recent decades. The MGARCH models, which captures covariance relationships and time-varying volatility correlations, can quantify the synchronisation of financial markets and identify the volatility clustering of data time-series. Such results cannot be achieved by univariate GARCH and vector autoregression (VAR) models.

This article is organised as follows. Section 2 describes the data and the methodology of the CCC, DCC and diagonal BEKK models. Section 3 interprets the empirical findings. Section 4 presents the conclusion and limitations.

2. Data and Methodology

To examine the volatility dynamics between China and major ASEAN countries, daily closing prices of their major stock indices were collected from the Taiwan Economic Database. The data began from 3 January 2001, except for the co-volatility data of China and Vietnam, which began on 9 October 2006. The article arranged the data, such that each ASEAN trading partner of China has a consistent number of observations for establishing return and volatility relationships. The data were limited to six major ASEAN countries because they have the greatest trading arrangements with China.

The following section explains the three MGARCH models, namely the CCC, DCC and BEKK models, which were adopted from the discussions of Chang, McAleer, and Tansuchat (2011).

2.1. Conditional Constant Correlations Model

The CCC model of Bollerslev (1990) utilises non-parametric models and has a more adaptive model for the constant conditional correlation. The CCC model is illustrated as follows:

y_{t} = E (y_{t} | F_{t - 1}) + ε_{t}, ε_{t} = D_{t} η_{t} ​,

(1)

var(ε_t|F_t_–1) = D_tΓD_t,

where

y_t = (y_1t,…,y_mt)',η_t = (η_1t,…, η_mt)' is a series of independently and identically distributed (iid) random vectors;

F_t_–1 is the available information in the past at particular time t;

$D_{t} = d i a g (h_{1}^{1 / 2}, \dots h_{m}^{1 / 2}) $ is a representation where m captures the number of returns; and t = 1,…, n.

From Equation (1), the constant conditional correlation matrix of the unconditional shocks, η_t, is the same as the constant conditional covariance matrix of the conditional shocks, ε_t (Bauwens et al., 2006; McAleer, 2005). Note that, $ε_{t} {ε^{'}}_{t} = D_{t} η_{t} {η^{'}}_{t} D_{t}, D_{t} = {(d i a g Q_{t})}^{1 / 2} $ and $E (ε_{t} {ε^{'}}_{t} | F_{t - 1}) = Q_{t} = D_{t} Γ D_{t} $ , with $Γ = E (η_{t} {η^{'}}_{t} | F_{t - 1}) = E (η_{t} η^{'}) $ , where Γ = {ρ_ij} for i, j = 1, …, m. Q_t denotes the conditional covariance matrix, which is a positive definite if all the conditional variances are positive and Γ is positive.

A constant conditional variance for each return is assumed and, h_it, i = 1,…, m, is a univariate GARCH process and calculated as:

h_{i t} = ω_{i} + \sum_{j = 1}^{r} α_{i j} ε_{i, t - j}^{2} + \sum_{j = 1}^{s} β_{i j} h_{i, t - j}^{2} ​,

(2)

where

α_ij is the ARCH effect, or the short run persistence of shocks to return i,

β_θj is the GARCH effect and

$\sum_{j = 1}^{r} α_{i j} + \sum_{j = 1}^{s} β_{i j} $ is the long-run persistence.

2.2. Dynamic Conditional Correlation Models

The DCC model of Engle (2002) provides an unconstant and time-dependent conditional correlation matrix. The DCC model is illustrated as follows:

y_{t} | F_{t - 1} + ε_{t}, ε_{t} = D_{t} η_{t} ~ N (0, Q_{t}), t = 1, 2, ... n ​,

(3)

Q_{t} = D_{t} Γ D_{t} ​,

(4)

where

$D_{t} = d i a g (h_{1}^{1 / 2}, \dots h_{m}^{1 / 2}) $ is a diagonal matrix of conditional variances and

F_t is the information set at time t.

The conditional variance, h_it, is a univariate GARCH model and computed as:

h_{i t} = ω_{i} + \sum_{k = 1}^{p} α_{i k} ε_{i, t - k}^{2} + \sum_{l = 1}^{q} β_{i j} h_{i, t - l}^{2} ​,

(5)

From Equation (4), η_t is a vector of iid random variables, with zero mean and unit variance, and Q_t is the conditional covariance matrix (after standardisation, $η_{i t} = y_{i t} / \sqrt{h_{i t}}) $ . The η_it is used to estimate the DCC as follows:

Γ_{t} = {d i a g {(Q_{t})}^{- 1 / 2}} Q_{t} {d i a g {(Q_{t})}^{- 1 / 2}} ​,

(6)

where the k × k symmetric positive definite matrix Q_t is given as

Q_{t} = (1 - θ_{1} - θ_{2}) \overset{__}{Q} + θ_{1} η_{t - 1} {η^{'}}_{t - 1} + θ_{2} Q_{t - 1} ​,

(7)

where θ₁ and θ₂ are the scalar parameters that denote the effects of previous shocks and past dynamic conditional correlations on the present dynamic conditional correlation. They are non-negative scalar parameters with the condition θ₁ + θ₂ < 1 or can be expressed as Q_t > 0.

In Equation (7), Q_t is a conditional covariance matrix, given θ₁ = θ₂ = 0, and ${\overset{__}{Q}}_{} $ is the k × k unconditional variance matrix of η_t.

The DCC model is non-linear, but according to Caporin and McAleer (2009), it may be estimated by using a two-step method: (a) through a sequence of univariate GARCH estimates and (b) through adapting a correlation estimates, which are all based on the likelihood function.

2.3. Baba, Engle, Kraft and Kroner Model

The BEKK model of Engle and Kroner (1995) also represents a dynamic conditional correlation. The model assumes that the conditional covariance matrices are positive definite. The BEKK model is illustrated as follows:

H_{t} = C C^{'} + A^{'} ε_{t - 1} {ε^{'}}_{t - 1} A + B H_{t - 1} B ​,

(12)

The matrices C, A and B’s individual elements are illustrated further as:

A = [\begin{matrix} a_{11} a_{12} \\ a_{21} a_{22} \end{matrix}], B = [\begin{matrix} b_{11} b_{12} \\ b_{21} b_{22} \end{matrix}], C = [\begin{matrix} c_{11} & 0 \\ c_{21} & c_{22} \end{matrix}] ​ .

(13)

From Silvennoinen and Terasvirta (2008) and Chang et al. (2011), the conditional variances are functions of their past values and lagged squared returns shocks, while the conditional covariances are functions of the previous covariances and lagged cross-products of the corresponding returns shocks from the diagonal formulation. This representation assures H_t to be positive definite for all t.

For the BEKK (1,1) model gives N(5N + 1)/2 parameters, and gives the equation B = AD, where D is a diagonal matrix, the number of estimated parameters is minimised and earlier equation will be transformed to

H_{t} = C C^{'} + A^{'} ε_{t - 1} {ε^{'}}_{t - 1} A + D E^{'} [A^{'} ε_{t - 1} {ε^{'}}_{t - 1} A] D ​,

(14)

where $α_{i i}^{2} + b_{i i}^{2} \leq 1 $ , i = 1, 2 is a stationary sequence, and the parameters of the covariance equation (h_ij,t,i ! j) will be products of the subsequent parameters of the two variance equations (h_ij,t).

3. Empirical Results

Table 1 shows that the JKSE posted the highest average positive returns of 3.7 per cent, whereas the same time-series for the SSE had 0.2 per cent gains. The HSE posted the lowest average negative returns of 0.3 per cent, whereas the SSE gained 0.1 per cent. The co-volatility time-series of the SSE and the HSE posted the highest standard deviations with 79.80 per cent and 76.80 per cent, respectively. These results can be attributed to the shorter dataset, which was considerably affected by the high volatility period of the sub-prime mortgage crisis. The case of the HSE is consistent with the Modern Portfolio Theory of Markowitz (1952) that a greater dispersion of returns corresponds to a higher risk of an investment, which in turn may lead to higher gains or higher losses. Most of the samples were negatively skewed, except for the PSE. The Jarque–Bera statistic for residual normality shows that the China–ASEAN returns followed a non-normal distribution assumption.

Table 1.
Sample Size and Summary Statistics of China and ASEAN Stock Indices

ETNs and Futures Start of Data Obs. Mean Std Dev. Skew. Kurt. Jarque–Bera

1. China—Shanghai Stock Exchange index (SSE)
Indonesia—Jakarta Stock Exchange index (JKSE) 3 January 2001 2,940 0.002
0.037 0.700
0.639 –0.096
–0.668 7.400
9.780 2,375.743*
5,849.364*

2. China—Shanghai Stock Exchange index (SSE)
Malaysia—Kuala Lumpur Stock Exchange index (KLSE) 3 January 2001 2,983 0.001
0.012 0.698
0.364 –0.066
–1.029 7.317
14.762 2,318.864*
17,721.09*

3. China—Shanghai Stock Exchange index (SSE)
Philippines—Philippine Stock Exchange index (PSE) 3 January 2001 2,974 –0.001
0.021 0.698
0.586 –0.079
0.053 7.341
15.922 2,338.201*
20,691.23*

4. China—Shanghai Stock Exchange index (SSE)
Singapore—Straits Times Stock index (STS) 3 January 2001 3,041 –0.001
0.008 0.698
0.530 –0.088
–0.189 4.301
8.470 2,347.900*
3,809.675*

5. China—Shanghai Stock Exchange index (SSE)
Thailand—Bangkok Stock Exchange index (BKSE) 3 January 2001 2,956 –0.003
0.026 0.698
0.593 –0.163
–0.489 4.117
4.938 2,100.700*
3,120.509*

6. China—Shanghai Stock Exchange index (SSE)
Vietnam—Ho Chi Minh Stock Exchange index (HSE) 9 October 2006 1,569 0.001
–0.003 0.798
0.768 –0.400
–0.089 5.946
3.268 609.2347*
6.791

ETNs and Futures	Start of Data	Obs.	Mean	Std Dev.	Skew.	Kurt.	Jarque–Bera
1. China—Shanghai Stock Exchange index (SSE) Indonesia—Jakarta Stock Exchange index (JKSE)	3 January 2001	2,940	0.002 0.037	0.700 0.639	–0.096 –0.668	7.400 9.780	2,375.743* 5,849.364*
2. China—Shanghai Stock Exchange index (SSE) Malaysia—Kuala Lumpur Stock Exchange index (KLSE)	3 January 2001	2,983	0.001 0.012	0.698 0.364	–0.066 –1.029	7.317 14.762	2,318.864* 17,721.09*
3. China—Shanghai Stock Exchange index (SSE) Philippines—Philippine Stock Exchange index (PSE)	3 January 2001	2,974	–0.001 0.021	0.698 0.586	–0.079 0.053	7.341 15.922	2,338.201* 20,691.23*
4. China—Shanghai Stock Exchange index (SSE) Singapore—Straits Times Stock index (STS)	3 January 2001	3,041	–0.001 0.008	0.698 0.530	–0.088 –0.189	4.301 8.470	2,347.900* 3,809.675*
5. China—Shanghai Stock Exchange index (SSE) Thailand—Bangkok Stock Exchange index (BKSE)	3 January 2001	2,956	–0.003 0.026	0.698 0.593	–0.163 –0.489	4.117 4.938	2,100.700* 3,120.509*
6. China—Shanghai Stock Exchange index (SSE) Vietnam—Ho Chi Minh Stock Exchange index (HSE)	9 October 2006	1,569	0.001 –0.003	0.798 0.768	–0.400 –0.089	5.946 3.268	609.2347* 6.791

Source: Taiwan Economic Database—various dates until 29 March 2013.

Note: ** and *** are significance at 5 and 1% levels, respectively.

Table 2 illustrates the initial filtering of the univariate data. The Augmented Dickey–Fuller (ADF) unit-root test revealed that the alternative (i.e., no unit roots) was accepted in all stock returns. The minimum value of the Akaike Information Criterion was applied to determine the orders of the ARMA and GARCH models. Enders (2004) explained that the AIC was more effective in small sample sizes. The Breush–Godfrey LM test indicated that the null hypothesis (i.e., no serial correlation) cannot be rejected for all time-series. The Lagrange Multiplier (ARCH–LM) Test by Engle (1982) was used to test the ARCH effects. The relevant statistics of the ARMA model with the null hypothesis of no ARCH effect for all samples were rejected. The filtering also showed that all the univariate samples of the Chinese and ASEAN stock returns had no autoregressive conditional heteroscedasticity.

Table 2.

Summary Statistics of Unit Root, LM and ARMA-LM Tests of China and ASEAN Stock Indices

ETNs and Futures	ADF	ARMA	AIC	LM–test	ARCH–LM	GARCH	AIC	ARCH–LM
1. SSE JKSE	–55.104* –48.930*	(2,2) (1,0)	2.123 1.932	0.041 1.450	76.860* 244.803*	(1,1) (2,2)	1.918 1.723	0.660 0.613
2. SSE KLSE	–25.732* –28.613*	(2,2) (1,2)	2.113 0.793	0.577 3.680	74.253* 170.313*	(1,1) (1,1)	1.911 0.498	0.065 1.912
3. SSE PSE	–25.886* –25.995*	(2,2) (1,2)	2.116 1.754	1.805 4.315	74.840* 86.692*	(1,1) (1,2)	1.908 1.535	0.016 0.285
4. SSE STS	–25.853* –54.480*	(2,2) (1,1)	2.116 1.565	0.036 1.138	85.692* 366.126*	(2,2) (1,2)	1.909 1.197	0.361 0.133
5. SSE BKSE	–25.773* –35.395*	(1,1) (2,2)	2.117 1.787	3.876 1.131	86.204* 444.633*	(2,2) (2,2)	1.909 1.568	0.471 1.857
6. SSE HSE	–18.309* –16.319*	(2,2) (1,2)	2.380 2.221	0.096 2.670	44.444* 167.301*	(2,1) (1,1)	2.179 2.038	0.087 0.822

Source: The author.

Notes: *** is significance at the 1% level.

3.1. Constant Conditional Correlation Model Results

Table 3 provides the estimates of the CCC model. The tests proposed by Tse (2000) and Engle and Sheppard (2001) were used to validate the presence of multivariate ARCH effects for constant correlations. This MGARCH was found applicable to most samples, except for the SSE and the KLSE. Most ARCH (α) estimates as well as nearly all of the GARCH (β) estimates for both the Chinese and ASEAN stock returns were significant. Thus, a long-run persistence is present, wherein changes and shocks in the volatility series of China’s stock returns impact their corresponding ASEAN stock markets in the long term. Such a relationship is expected because the ACFTA is expected to strengthen relationships between China and the six ASEAN economies. The results of α + β < 1 satisfies the second moment and log moment requisites, which are sufficient conditions for the Quasi Maximum Likelihood Estimator (QMLE) to be consistent and asymptotically normal (McAleer, Chan, & Marinova, 2007). These necessary conditions are also applied in the study of Chang et al. (2011) on crude oil spot and futures returns.

Table 3.
Conditional Constant Correlation Estimates

China and ASEAN Model AIC Multivariate ARCH Test
α β a + b CCC Log Likelihood

Tse (2000) E & S (2001)

1. SSE
JKSE (2,2) 3.446 11.983*
(0.001) 16.209*
(0.013) α ₂
α ₁
α ₂
α ₁ 0.087*
(0.000)
0.048*
(0.005)
0.178*
(0.000)
–0.150*
(0.001) β ₂
β ₁
β ₂
β ₁ 0.767***
(0.000)
0.048
(0.316)
–0.572*
(0.055)
1.534*
(0.000) 0.976
0.990 0.177*
(0.000) –5,047.852

2. SSE
KLSE (1,1) 2.375 0.527
(0.468) 6.854
(0.335) α ₁
α ₁ 0.070*
(0.000)
0.135*
(0.000) β ₁
β ₁ 0.919*
(0.000)
0.847
(0.000) 0.988
0.982 0.187*
(0.000) –3,525.144

3. SSE
PSE (2,1) 3.428 1.182
(0.278) 11.527*
(0.073) α ₁
α ₁ 0.076*
(0.006)
0.148*
(0.000) β ₂
β ₁
β ₂
β ₁ –0.014
(0.968)
0.923
(0.014)
–0.223
(0.027)
1.032*
(0.000) 0.985
0.957 0.133*
(0.000) –5,078.806

4. SSE
STS (1,2) 3.062 1.362
(0.243) 20.305*
(0.002) α ₂
α ₁
α ₂
α ₁ 0.066
(0.029)
0.009
(0.780)
–0.038*
(0.081)
0.082
(0.011) β ₁
β ₁ 0.911*
(0.000)
0.876*
(0.000) 0.986
0.995 0.224*
(0.000) –4,636.820

5. SSE
BKSE (2,2) 3.445 1.433
(0.231) 17.697*
(0.007) α ₂
α ₁
α ₂
α ₁ –0.090*
(0.000)
–0.046*
(0.003)
0.098*
(0.002)
–0.072*
(0.000) β ₂
β ₁
β ₂
β ₁ 0.833*
(0.000)
0.007
(0.861)
–0.407*
(0.000)
0.393*
(0.000) 0.976
0.970 0.182*
(0.000) –5,070.135

6. SSE
HSE (1,1) 4.200 6.263
(0.012) 8.650
(0.194) α ₁
α ₁ 0.037
(0.025)
–0.174*
(0.000) β ₁
β ₁ 0.958*
(0.000)
0.776*
(0.000) 0.996
0.950 0.080***
(0.000) –3,277.486

China and ASEAN	Model	AIC	Multivariate ARCH Test	α	β	a + b	CCC	Log Likelihood
1. SSE JKSE	(2,2)	3.446	11.983*** (0.001)	16.209*** (0.013)	α ₂ α ₁ α ₂ α ₁	0.087* (0.000) 0.048* (0.005) 0.178* (0.000) –0.150* (0.001)	β ₂ β ₁ β ₂ β ₁	0.767*** (0.000) 0.048 (0.316) –0.572* (0.055) 1.534*** (0.000)	0.976 0.990	0.177*** (0.000)	–5,047.852
2. SSE KLSE	(1,1)	2.375	0.527 (0.468)	6.854 (0.335)	α ₁ α ₁	0.070* (0.000) 0.135* (0.000)	β ₁ β ₁	0.919*** (0.000) 0.847 (0.000)	0.988 0.982	0.187*** (0.000)	–3,525.144
3. SSE PSE	(2,1)	3.428	1.182 (0.278)	11.527* (0.073)	α ₁ α ₁	0.076* (0.006) 0.148* (0.000)	β ₂ β ₁ β ₂ β ₁	–0.014 (0.968) 0.923 (0.014) –0.223 (0.027) 1.032*** (0.000)	0.985 0.957	0.133*** (0.000)	–5,078.806
4. SSE STS	(1,2)	3.062	1.362 (0.243)	20.305*** (0.002)	α ₂ α ₁ α ₂ α ₁	0.066** (0.029) 0.009 (0.780) –0.038* (0.081) 0.082** (0.011)	β ₁ β ₁	0.911* (0.000) 0.876* (0.000)	0.986 0.995	0.224*** (0.000)	–4,636.820
5. SSE BKSE	(2,2)	3.445	1.433 (0.231)	17.697*** (0.007)	α ₂ α ₁ α ₂ α ₁	–0.090* (0.000) –0.046* (0.003) 0.098* (0.002) –0.072* (0.000)	β ₂ β ₁ β ₂ β ₁	0.833* (0.000) 0.007 (0.861) –0.407* (0.000) 0.393*** (0.000)	0.976 0.970	0.182*** (0.000)	–5,070.135
6. SSE HSE	(1,1)	4.200	6.263** (0.012)	8.650 (0.194)	α ₁ α ₁	0.037 (0.025) –0.174* (0.000)	β ₁ β ₁	0.958* (0.000) 0.776* (0.000)	0.996 0.950	0.080*** (0.000)	–3,277.486

Source: The author.

Notes: *, ** and *** are significance at 10%, 5% and 1% levels, respectively; p-values are in parentheses.

The CCC model estimated a significant volatility between the Chinese and ASEAN stock index returns, confirming that the China and ASEAN stock returns have a constant return volatility relationship that may remain unchanged over time. The highest CCC estimate was 0.224 (between the SSE and the STS), and the lowest was 0.080 (between the SSE and the HSE). The strong financial market relationship between China and Singapore is a product of bilateral trade relations between the two economies, which increased by approximately 440 per cent in the last decade. Among the ASEAN economies, Singapore is China’s top trading partner. The behaviour of a constant conditional volatility is consistent with the findings of Malliaropulos (1997), in which MGARCH models were used to discover that the seven major currencies behaved uniformly over time against the US dollar.

3.2. Dynamic Conditional Correlation Model Results

Table 4 shows the results of the DCC model. The tests proposed by Hosking (1980) and Li and McLeod (1981) were utilised to determine the presence of multivariate ARCH effects, and this MGARCH model was similarly found applicable to most data samples, except the for SSE and the BKSE. The test results for the SSE and the KLSE were significant at the 10.09 per cent level and were thus deemed necessary to be included in the study. In line with previous findings, this article observed that most ARCH (α) estimates for both the Chinese and ASEAN stock returns were significant and normally close to 0.1; nearly all GARCH (β) estimates were also significant. These results imply that a long-run persistence is evident in the stock returns time-series of China and the ASEAN countries. Among the DCC estimates, only the SSE and the KLSE supported a short-run persistence of shocks for the 1st DCC parameter of 0.024. The 2nd DCC parameter confirmed the presence of a long-run persistence of shocks among the significant conditional correlations. The highest DCC estimate was 0.997 (between the SSE and the JKSE), and the lowest estimate was 0.869 (between the SSE and the HSE); these findings are consistent with the CCC estimates recorder earlier. A higher financial market relationship between China and Indonesia can be traced from the growing trade relations between the two countries, which grew approximately 10 times in the last decade. China is the second-largest importer of Indonesia, second to Japan.

Table 4.
Dynamic Conditional Correlation Estimates

China and ASEAN Model AIC Multivariate ARCH Test
α β a + b DCC_E1 DCC_E2 Log Likelihood

Hosking (1980) L & M (1981)

1. SSE
JKSE (2,2) 3.434 27.032*
(0.078) 27.025*
(0.079) α ₂
α ₁
α ₂
α ₁ 0.087*
(0.000)
0.048
(0.005)
–0.150*
(0.001)
0.178*
(0.000) β ₂
β ₁
β ₂
β ₁
0.797*
(0.000)
0.044)
(0.316)
–0.572*
(0.055)
1.534*
(0.000) 0.976
0.990 0.003
(0.134) 0.997*
(0.000) –5,027.590

2. SSE
KLSE (1,1) 2.369 23.516*
(0.101) 23.513*
(0.101) α ₁
α ₁ 0.070*
(0.000)
0.135*
(0.000) β ₁
β ₁ 0.919*
(0.000)
0.847*
(0.000) 0.988
0.982 0.024*
(0.005) 0.938*
(0.000) –3,514.342

3. SSE
PSE (1,2) 3.423 57.087*
(0.000) 30.263
(0.017) α ₂
α ₁
α ₂
α ₁ 0.087*
(0.001)
0.075
(0.017)
0.096*
(0.080)
0.121*
(0.000) β ₁
β ₁ 0.907*
(0.000)
0.718*
(0.000) 0.985
0.935 0.033
(0.275) 0.996*
(0.000) –5,068.308

4. SSE
STS (1,2) 3.042 33.715*
(0.006) 33.698*
(0.006) α ₂
α ₁
α ₂
α ₁ 0.009
(0.780)
0.066
(0.029)
0.096***
(0.080)
0.038*
(0.081) β ₁
β ₁ 0.910*
(0.000)
0.876*
(0.000) 0.986
0.995 0.004
(0.279) 0.996*
(0.000) –4,604.604

5. SSE
BKSE (1,1) 3.442 16.938
(0.389) 16.943
(0.389) α ₁
α ₁ 0.070*
(0.000)
0.104
(0.000) β ₁
β ₁ 0.918*
(0.000)
0.876*
(0.000) 0.988
0.980 0.004
(0.204) 0.996*
(0.000) –5,068.081

6. SSE
HSE (1,1) 4.198 30.137
(0.025) 30.122
(0.025) α ₁
α ₁ 0.037
(0.025)
0.174*
(0.000) β ₁
β ₁ 0.958*
(0.000)
0.775*
(0.000) 0.996
0.950 0.016
(0.228) 0.869***
(0.000) –3,276.754

China and ASEAN	Model	AIC	Multivariate ARCH Test	α	β	a + b	DCC_E1	DCC_E2	Log Likelihood
1. SSE JKSE	(2,2)	3.434	27.032* (0.078)	27.025* (0.079)	α ₂ α ₁ α ₂ α ₁	0.087* (0.000) 0.048 (0.005) –0.150* (0.001) 0.178* (0.000)	β ₂ β ₁ β ₂ β ₁	0.797* (0.000) 0.044) (0.316) –0.572* (0.055) 1.534*** (0.000)	0.976 0.990	0.003 (0.134)	0.997*** (0.000)	–5,027.590
2. SSE KLSE	(1,1)	2.369	23.516* (0.101)	23.513* (0.101)	α ₁ α ₁	0.070* (0.000) 0.135* (0.000)	β ₁ β ₁	0.919* (0.000) 0.847* (0.000)	0.988 0.982	0.024*** (0.005)	0.938*** (0.000)	–3,514.342
3. SSE PSE	(1,2)	3.423	57.087*** (0.000)	30.263** (0.017)	α ₂ α ₁ α ₂ α ₁	0.087* (0.001) 0.075 (0.017) 0.096* (0.080) 0.121* (0.000)	β ₁ β ₁	0.907* (0.000) 0.718* (0.000)	0.985 0.935	0.033 (0.275)	0.996*** (0.000)	–5,068.308
4. SSE STS	(1,2)	3.042	33.715*** (0.006)	33.698*** (0.006)	α ₂ α ₁ α ₂ α ₁	0.009 (0.780) 0.066 (0.029) 0.096* (0.080) 0.038* (0.081)	β ₁ β ₁	0.910* (0.000) 0.876* (0.000)	0.986 0.995	0.004 (0.279)	0.996*** (0.000)	–4,604.604
5. SSE BKSE	(1,1)	3.442	16.938 (0.389)	16.943 (0.389)	α ₁ α ₁	0.070* (0.000) 0.104 (0.000)	β ₁ β ₁	0.918* (0.000) 0.876* (0.000)	0.988 0.980	0.004 (0.204)	0.996*** (0.000)	–5,068.081
6. SSE HSE	(1,1)	4.198	30.137** (0.025)	30.122** (0.025)	α ₁ α ₁	0.037 (0.025) 0.174* (0.000)	β ₁ β ₁	0.958* (0.000) 0.775* (0.000)	0.996 0.950	0.016 (0.228)	0.869*** (0.000)	–3,276.754

Source: The author.

Notes: *, ** and *** are significance at 10%, 5% and 1% levels, respectively; p-values are in parentheses.

The results of the DCC parameters were statistically significant for most cases, suggesting that a constant conditional correlation cannot be assumed for all shocks in the dataset. The time-varying conditional correlations were further proven when the higher values of log-likelihood indicated that the DCC model was better than the CCC model. Ho et al. (2009), Zhu (2009) and Chang et al. (2011) observed dynamic correlations among investment instruments when they examined US business cycles, Chinese stock returns and crude oil spot and futures returns, respectively.

3.3. Baba, Engle, Kraft and Kroner Model Results

Table 5 provides the results of the diagonal BEKK model. Similarly, the tests proposed by Hosking (1980) and Li and McLeod (1981) were utilised to determine if multivariate ARCH effects were present. All data samples showed that this MGARCH model can be applied for the time-series, and most of them presented statistically significant elements of the parameter matrices A and B of the diagonal BEKK model. In other words, for the values of α (A matrix), conditional variances depended only on their own lags, wherein the return volatilities can be determined by their lagged values; however, this notion cannot be ascertained between the SSE and the PSE, between the SSE and the STS, and between the SSE and the HSE. For the values of β (B matrix), the conditional covariances of China and ASEAN’s stock returns were also a function of their lagged covariances or the lagged cross-products of the shocks. That is, the volatilities were determined not solely by their lagged values, and cross-volatility spillovers were present for the entire dataset. The significant results of the C matrix also showed that the diagonal BEKK model proved that the volatilities of China’s stock returns impact major ASEAN stock indices under study. This volatility relationship is similarly expected because of the increased regional linkages caused by the ACFTA, which is expected to strengthen relationships between China and the six ASEAN economies.

Table 5.
Diagonal BEKK Estimates

China and ASEAN Model AIC Multivariate ARCH Test
c₁₁ c₁₂ c₂₂ a₁₁ a₂₂ β₁₁ β₂₂ Log Likelihood

Hosking (1980) L & M (1981)

1. SSE
JKSE (1,2) 3.443 33.613*
(0.009) 33.603*
(0.009) 0.088*
(0.000) 0.049*
(0.000) 0.133*
(0.000) 0.143*
(0.000) 0.354*
(0.000) 0.957*
(0.000) 0.911*
(0.000) –5,043.122

2. SSE
KLSE (1,2) 2.246 33.082*
(0.007) 33.075*
(0.007) 0.076*
(0.000) 0.017*
(0.008) 0.049*
(0.000) 0.233*
(0.000) 0.938*
(0.000) 0.967*
(0.000) 0.938*
(0.000) –3,329.767

3. SSE
PSE (1,2) 3.313 36.006*
(0.003) 35.998*
(0.003) 0.091*
(0.000) 0.040
(0.022) 0.152*
(0.000) 0.000
(1.00) –0.360*
(0.000) 0.955*
(0.000) 0.885*
(0.000) –4,907.085

4. SSE
STS (1,2) 2.947 37.659*
(0.002) 37.638*
(0.002) 0.081*
(0.000) 0.022*
(0.000) 0.045*
(0.000) 0.206*
(0.000) 0.034
(0.771) 0.960*
(0.000) 0.951*
(0.000) –4,460.664

5. SSE
BKSE (1,2) 3.355 48.083*
(0.086) 48.065*
(0.086) 2.080*
(0.000) 0.036*
(0.000) 0.088*
(0.000) 0.210*
(0.000) 0.285*
(0.000) 0.962*
(0.000) 0.931*
(0.000) –4,938.492

6. SSE
HSE (1,2) 4.202 24.352*
(0.082) 24.351*
(0.082) 0.046**
(0.032) 0.067*
(0.084) 0.144*
(0.000) 0.050
(0.534) –0.380*
(0.000) 0.980*
(0.000) 0.881*
(0.000) –3,276.769

China and ASEAN	Model	AIC	Multivariate ARCH Test	c₁₁	c₁₂	c₂₂	a₁₁	a₂₂	β₁₁	β₂₂	Log Likelihood
1. SSE JKSE	(1,2)	3.443	33.613*** (0.009)	33.603*** (0.009)	0.088*** (0.000)	0.049*** (0.000)	0.133*** (0.000)	0.143*** (0.000)	0.354*** (0.000)	0.957*** (0.000)	0.911*** (0.000)	–5,043.122
2. SSE KLSE	(1,2)	2.246	33.082*** (0.007)	33.075*** (0.007)	0.076*** (0.000)	0.017*** (0.008)	0.049*** (0.000)	0.233*** (0.000)	0.938*** (0.000)	0.967*** (0.000)	0.938*** (0.000)	–3,329.767
3. SSE PSE	(1,2)	3.313	36.006*** (0.003)	35.998*** (0.003)	0.091*** (0.000)	0.040** (0.022)	0.152*** (0.000)	0.000 (1.00)	–0.360*** (0.000)	0.955*** (0.000)	0.885*** (0.000)	–4,907.085
4. SSE STS	(1,2)	2.947	37.659*** (0.002)	37.638*** (0.002)	0.081*** (0.000)	0.022*** (0.000)	0.045*** (0.000)	0.206*** (0.000)	0.034 (0.771)	0.960*** (0.000)	0.951*** (0.000)	–4,460.664
5. SSE BKSE	(1,2)	3.355	48.083* (0.086)	48.065*** (0.086)	2.080*** (0.000)	0.036*** (0.000)	0.088*** (0.000)	0.210*** (0.000)	0.285*** (0.000)	0.962*** (0.000)	0.931*** (0.000)	–4,938.492
6. SSE HSE	(1,2)	4.202	24.352* (0.082)	24.351* (0.082)	0.046** (0.032)	0.067* (0.084)	0.144*** (0.000)	0.050 (0.534)	–0.380*** (0.000)	0.980*** (0.000)	0.881*** (0.000)	–3,276.769

Source: The author.

Notes: *, ** and *** are significance at 10%, 5% and 1% levels, respectively; p-values are in parentheses.

c₁₁, c₁₂, c₂₂, a₁₁, a₂₂, β₁₁ and β₂₂ are the coefficient matrices.

The log-likelihood values suggest that the diagonal BEKK model is the best among the three MGARCH models applied, except for the relationships between the SSE and the JKSE as well as between the SSE and the HSE, which were best modelled by the DCC. The findings of this study as regards the power of the diagonal BEKK model are consistent with those obtained by Worthington, Kay-Spratley, and Higgs (2005) and Chang et al. (2011) in their study of Australian spot electricity prices and Brent and WTI crude oil spot and futures returns, respectively.

4. Conclusions and Limitations

This study examined the capability of three MGARCH volatility models, namely the CCC, the DCC proposed Engle (2002) and the diagonal BEKK, to model the volatility relationships between China’s SSE and the top six ASEAN stock markets (i.e., Indonesia’s JKSE, Malaysia’s KLSE, Philippines’ PSE, Singapore’s STS, Thailand’s BKSE and Vietnam’s HSE). The results showed that the CCC model identified constant return volatility relationships between the Chinese and ASEAN stock returns, suggesting the presence of a steady volatility linkage over time. The highest CCC estimate was 0.224 (between the SSE and the STS), which resulted from the strong financial market relationship between China and Singapore through a higher volume of bilateral trade relations. Among the DCC estimates, only China’s SSE and Malaysia’s KLSE have short-run persistence of shocks, whereas the 2nd DCC parameter confirmed the presence of a long-run persistence of shocks between the Chinese and the six ASEAN stock returns. The highest DCC estimate was between the SSE and the JKSE because of the growing trade relations between these two countries, which grew by approximately by 10 times in the last decade. The diagonal BEKK model indicated that the conditional covariances of the Chinese and six ASEAN economies’ stock market returns were functions of the lagged covariances and the lagged cross-products of the shocks. This finding further proved that the volatilities of China’s SSE returns impact the stock return of the six ASEAN countries because of the growing trade relations among the economies. Log-likelihood values revealed that the diagonal BEKK is the best model among the three MGARCH models applied, except for the relationship between the SSE and the JKSE as well as between the SSE and the HSE, which were best modelled by the DCC model.

These results are of economic significance to the investing community, particularly hedgers and speculators, as a possible basis for investing strategies in emerging markets. The knowledge of stronger (or weaker) volatility linkages determines which among the six ASEAN economies will be positively (or negatively) affected by fluctuations in China’s economy, particularly its main stock index, the SSE. The general public and even the government can have a working knowledge of the volatility behaviour in the ACFTA and assist them in making informed choices based on their risk preferences. At the same time, the academic community can gain new insights into the volatility transmission tendencies in the stock markets of the ACFTA.

This study acknowledges a number of possible limitations. First, the study could have had a stronger impact if it correlated its findings with previous works on different MGARCH methodologies, such as the generalised orthogonal types of the GARCH models (i.e., OGARCH and GOGARCH). However, the relatively new applications of the MGARCH models limited the study from having an expanded network of related literature. Second, given that the data span a full decade starting 2001, the recent sub-prime mortgage crisis should have been considered for possible structural break tests for possible changes in volatility linkages before and after the crisis. Finally, other econometric methods, such as univariate models (i.e., GARCH, Exponential GARCH and Asymmetric Power GARCH), can be applied to study the return and volatility relations in the ACFTA or in any other bilateral trade agreements. Despite these limitations, the current study still has its own merits and has considerable contributions to the expanding literature on MGARCH models, particularly in identifying changes in volatility relations among financial instruments.

Declaration of Conflicting Interests

The author certifies that he has no affiliations or involvement in any organization or entity with any financial interest, or non-financial interest in the subject matter or materials discussed in this manuscript.

Funding

The author received no financial support for the research, authorship and/or publication of this article.

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