Khảo sát mối liên hệ giữa các thị trường chứng khoán đông nam á: tiếp cận bằng kiểm định nhân quả granger tính hiệu quả thông tin giữa các thị trường

DALAT UNIVERSITY JOURNAL OF SCIENCE Volume 10, Issue 4, 2020 43-56 
43 
INVESTIGATING THE RELATIONSHIPS BETWEEN 
ASEAN STOCK MARKETS: AN APPROACH USING 
THE GRANGER CAUSALITY TEST OF 
TIME-VARYING INFORMATION EFFICIENCY 
Tran Thi Tuan Anha* 
aUniversity of Economics Ho Chi Minh City, Ho Chi Minh City, Vietnam 
*Corresponding author: Email: anhttt@ueh.edu.vn 
Article history 
Received: November 4th, 2019 
Received in revised form: December 19th, 2019 | Accepted: January 6th, 2020 
Abstract 
The information efficiency and the relationships between ASEAN stock markets are two of 
the issues that are of great research interest. However, these two issues were often 
investigated separately in previous studies. Therefore, this paper combines these two issues 
in the same analysis. Data on the daily closing index of six ASEAN stock markets, including 
Indonesia, Malaysia, the Philippines, Singapore, Thailand, and Vietnam are used to 
calculate Shannon entropy to measure the stock market information efficiency. In addition, 
this paper conducts the Granger causality test to reveal the relationships between the ASEAN 
stock markets. The results show that all six stock markets are not in the state of information 
efficiency, which means the stock indices, stock returns, and volatility are not purely random, 
but patterned. In addition, the Granger test results show that the ASEAN stock markets are 
logically correlated. The two markets that are more integrated than the others are Indonesia 
and Malaysia. Vietnam participates in regional economics in a passive way, while the 
Philippines is more proactive. The Singapore stock market is also less integrated with the 
other ASEAN markets, although it is a mature stock market that outperforms the rest. 
Keywords: ASEAN stock markets; Efficient market hypothesis; Granger causality test; 
Rolling window method; Shannon entropy. 
DOI:  
Article type: (peer-reviewed) Full-length research article 
Copyright © 2020 The author(s). 
Licensing: This article is licensed under a CC BY-NC 4.0 
DALAT UNIVERSITY JOURNAL OF SCIENCE [ECONOMICS AND MANAGEMENT] 
44 
KHẢO SÁT MỐI LIÊN HỆ GIỮA CÁC THỊ TRƯỜNG 
CHỨNG KHOÁN ĐÔNG NAM Á: TIẾP CẬN BẰNG KIỂM ĐỊNH 
NHÂN QUẢ GRANGER TÍNH HIỆU QUẢ THÔNG TIN GIỮA 
CÁC THỊ TRƯỜNG 
Trần Thị Tuấn Anha* 
aTrường Đại học Kinh tế TP. Hồ Chí Minh, TP. Hồ Chí Minh, Việt Nam 
*Tác giả liên hệ: Email: anhttt@ueh.edu.vn 
Lịch sử bài báo 
Nhận ngày 04 tháng 11 năm 2019 
Chỉnh sửa ngày 19 tháng 12 năm 2019 | Chấp nhận đăng ngày 06 tháng 01 năm 2020 
Tóm tắt 
Tính hiệu quả thông tin trên thị trường chứng khoán và mối liên hệ giữa các thị trường chứng 
khoán của các quốc gia Đông Nam Á là hai trong số những vấn đề rất được quan tâm nghiên 
cứu. Tuy nhiên, hai vấn đề này thường được tách biệt trong nghiên cứu riêng trong các 
nghiên cứu trước. Do vậy, bài viết này kết hợp nghiên cứu hai vấn đề này trong cùng một 
phân tích. Dữ liệu về chỉ số chứng khoán đóng cửa hàng ngày của sáu thị trường chứng 
khoán Đông Nam Á, bao gồm Indonesia, Malaysia, Philippines, Singapore, Thái Lan, và Việt 
Nam được sử dụng để tính toán Shannon entropy nhằm đo lường tính hiệu quả của thị trường. 
Bên cạnh đó, bài viết cũng đồng thời áp dụng kiểm định nhân quả Granger để khảo sát mối 
liên hệ giữa thị trường chứng khoán các quốc gia Đông Nam Á. Kết quả nghiên cứu cho thấy 
cả sáu thị trường chứng khoán đều không đạt trạng thái hiệu quả thông tin, điều đó có nghĩa 
là biến động chỉ số chứng khoán và tỷ suất sinh lợi trên thị trường chưa phải hoàn toàn ngẫu 
nhiên. Ngoài ra, kết quả kiểm định Granger cho thấy rằng các thị trường chứng khoán ở các 
quốc gia Đông Nam Á có mối liên hệ hợp lý với nhau. Hai thị trường hội nhập tốt với khu 
vực bao gồm Indonesia và Malaysia. Việt Nam tham gia vào các mối liên hệ trong kinh tế 
khu vực với vai trò thụ động hơn các quốc gia khác, còn Philippines, mặc dù có khuynh 
hướng suy giảm trong suốt thời gian dữ liệu được thu thập, nhưng lại đóng vai trò chủ động 
trong khu vực. Thị trường chứng khoán Singapore cũng ít hội nhập với khu vực mặc dù đây 
là thị trường chứng khoán phát triển và trưởng thành vượt trội hơn các quốc gia còn lại. 
Từ khóa: Kiểm định nhân quả Granger; Phương pháp cửa sổ cuộn; Shannon entropy; Thị 
trường chứng khoán các nước Đông Nam Á; Thị trường hiệu quả thông tin. 
DOI:  
Loại bài báo: Bài báo nghiên cứu gốc có bình duyệt 
Bản quyền © 2020 (Các) Tác giả. 
Cấp phép: Bài báo này được cấp phép theo CC BY-NC 4.0 
Tran Thi Tuan Anh 
45 
1. INTRODUCTION 
The information efficiency in the stock market and the relationship among 
ASEAN’s stock markets are issues of great concern to researchers. The information 
efficiency of stock markets originates as a concept from the efficient market hypothesis 
(EMH) of Fama (1970). According to the EMH, stock prices in an efficient market always 
reflect all relevant information. As a result, an efficient market cannot be beaten because 
it incorporates all important determining information into current share prices. Therefore, 
stocks trade at a fair value and cannot be purchased undervalued or sold overvalued. It is 
not possible to employ technical analysis, fundamental analysis, or find a pattern to 
forecast stock prices to obtain outstanding returns. Many methods have been proposed to 
test market efficiency, such as testing for random walk, Monday effect, January effect, 
turn-of-the-month effect, holiday effect, variance ratio test, and other statistical 
techniques. In addition to these traditional statistical tools, after the Shannon entropy 
concept was borrowed from thermodynamics and applied to finance, many financial 
researchers have been interested in using entropy to measure the efficiency of stock 
markets. Some representative studies that can be mentioned include Mensi (2012), Risso 
(2009), and Zunino, Massimiliano, Tabak, Pérez, and Rosso (2009). These studies have 
achieved many interesting results. However, measuring the stock market’s efficiency and 
measuring the relationship between stock markets have often been performed in separate 
studies. Now, researchers have started to combine these issues together. In line with this 
research trend, this article aims to provide more empirical evidence on information 
efficiency as well as the relationship among ASEAN stock markets. Along with the above 
objectives, the following sections of this article are organized as follows: Section 2 
summarizes some relevant previous studies; Section 3 introduces data and methodology; 
Section 4 represents the data analysis and discusses the results; and Section 5 concludes 
the main results of the article and proposes some implications. 
2. LITERATURE REVIEW 
The efficient market hypothesis was proposed by Fama (1970) with the idea that 
the stock market will reach a state of information efficiency when stock prices reflect all 
available information on the market. The efficiency of markets is considered in three 
forms: weak, semi-strong, and strong efficient markets. If all past prices, historical values, 
and trends have been reflected in prices, then the market reaches the weak form efficiency 
state. The semi-strong form efficiency theory states that all public information is used in 
the calculation of a stock's current price, so investors cannot utilize either technical or 
fundamental analysis to gain abnormal returns in the market. And for the market to 
achieve a state of strong efficiency, stock prices must reflect not only the information 
available to the public but also any information not publicly known. The strong and semi-
strong forms of efficiency are difficult for markets to achieve in practice, so most research 
on market efficiency focuses on testing the weak form of efficiency. In the sense that, 
when the market is weakly efficient, investors cannot predict future stock prices with only 
the information of past stock prices. This implies that historical data of stock prices do 
not help to predict future prices; there is no opportunity to discern patterns in stock time 
series. Consequently, a common way to perform weak efficiency tests is to try to find the 
DALAT UNIVERSITY JOURNAL OF SCIENCE [ECONOMICS AND MANAGEMENT] 
46 
paradigm or pattern of the historical time series of a stock’s prices or returns. If there 
exists any pattern in the historical data, it means that investors can also exploit past 
information to predict future stock prices to gain abnormal profits. This is evidence 
against the efficiency of the market. A variety of statistical tools are used to find empirical 
patterns, such as the calendar effect, seasonal effect, weekend effect, and others. Most of 
these approaches are performed through statistical tests or regression techniques. As 
opposed to traditional statistical approaches, the Shannon entropy approach is based on 
the randomness of the stock market time series. The more efficient the market, the more 
random the stock price movement is, and all possible outcomes of stock prices or returns 
are equally probable. This property is the basis for using entropy to measure the efficiency 
of the market. In the early studies of entropy, Shannon (1948) used entropy to measure 
the chaotic nature of a physical system. When applying Shannon entropy in economics, 
researchers also considered the randomness of stock fluctuations to be similar to the 
disorder of a physical system, and thus it is reasonable to employ entropy to measure this 
randomness. An efficient market implies that it is impossible to predict whether the next 
day’s stock return will be higher or lower than the mean. So, the probability p for a stock 
return to be higher or lower than the mean is 0.5 for both outcomes. Then Shannon entropy 
reaches its maximum value of 1. Based on this feature, there can be evidence for market 
inefficiency when the Shannon entropy of the stock series is less than 1. The larger the 
calculated Shannon entropy, the more efficient the market is, and vice versa. 
Among studies that apply Shannon entropy and extended forms of entropy in 
quantitative finance, some particularly relevant studies include Risso (2009), Zunino et 
al. (2009), and Mensi (2012). Risso (2009) applied a symbolic technique to transform a 
continuous return time series into a discrete form and then computed Shannon entropy to 
measure the efficiency of 20 stock markets. His data were the daily stock indices from 
July 1997 to December 2007 of some developed countries, such as Japan and Singapore, 
and some emerging economies. The results show that Taiwan (R.O.C), Japan, and 
Singapore had the highest levels of stock market efficiency, and that developed stock 
markets often had lower market efficiency levels than those of emerging stock markets. 
Different from Risso (2009), Zunino et al. (2009) proposed an extension of the Shannon 
entropy method, named permutation entropy, to quantify the degree of market 
inefficiency. The common feature of both types of entropy is that prices are random for 
an efficient market. If there is a pattern that dominates the frequencies, the market is no 
longer random. The results show that emerging markets, such as Greece, Hong Kong 
(P.R.C), Singapore, Taiwan (R.O.C), and Turkey, became more efficient over time from 
1995 to 2007. Mensi (2012) evaluated the time-varying efficiency of crude oil markets 
by using Shannon entropy and symbolic time series analysis (STSA). Mensi used daily 
price data from May 20th, 1987, to March 6th, 2012, for two worldwide crude oil 
benchmarks, West Texas Intermediate (WTI) and European Brent. His work revealed that 
the weak market efficiency of both oil markets improved over time. However, the WTI 
market appears to be less efficient than the European Brent market. These results have 
many implications for market investors and policymakers of the countries concerned. 
Lahmiri, Bekiros, and Avdoulas (2018) used daily data of stock markets in Asia, America, 
Europe, and Oceania to measure market information efficiency. Their paper used 
Shannon entropy, the Hurst exponent, and the Lempel-Ziv index to conduct calculations. 
Tran Thi Tuan Anh 
47 
The authors also used the Granger causality test to investigate the information flow among 
these markets. The research results showed that the randomness and efficiency of 
information in these markets are transmitted to each other. The Granger causality effect 
is bidirectional between all pairs of stock markets except Oceania and Europe. In general, 
these transmissions depend on the geographical locations of the markets. Several studies 
in Vietnam by Tran (2018a, 2018b, 2019) have used entropy to verify the information 
efficiency of the stock market, but these studies only deal with time-invariant Shannon 
entropy. They do not test information transmission between markets by the Granger 
causality test on time-varying Shannon entropy series. 
3. DATA AND METHODOLOGY 
3.1. Data 
This paper uses daily closing prices collected from the website Investing.com for 
ASEAN-6 stock markets from March 2012 to October 2019. The six stock markets 
included in the sample are Vietnam, the Philippines, Malaysia, Indonesia, Thailand, and 
Singapore. These six countries have jointly launched the ASEAN Trading Link, a 
gateway for securities brokers to offer investors easier access to connected exchanges. 
This ASEAN exchange aims to promote growth in the ASEAN capital market and bring 
more investment opportunities for investors in ASEAN. The stock indices used in this 
article are listed in Table 1. 
Table 1. List of stock market index of ASEAN countries 
Order Country Stock index Stock exchange 
1 Vietnam VNI Vietnam Stock Index 
2 Philippines PSEI Philippines Stock Exchange Index 
3 Malaysia KLCI FTSE Bursa Malaysia KLCI Index 
4 Indonesia JCI Jakarta Stock Exchange Composite Index 
5 Thailand SET Stock Exchange of Thailand SET Index 
6 Singapore STI FTSE Straits Times Index 
From the daily closing prices, the stock returns are calculated by a logarithmic 
formula as follows: 
, 1
100 ln itit
i t
P
r
P −
= (1) 
where rit is the stock return of market i at day t, Pit is the closing price of market i 
at day t, and Pi,t-1 is the closing price of market i at day t-1. 
DALAT UNIVERSITY JOURNAL OF SCIENCE [ECONOMICS AND MANAGEMENT] 
48 
Figure 1. Daily closing price and return series of ASEAN-6 stock markets 
from 2012 to 2019 
Tran Thi Tuan Anh 
49 
The daily returns along with daily closing prices of stock indices are plotted in 
Figure 1. The plots on the left side of Figure 1 show the trend of stock indices, while those 
on the right show the return series of the ASEAN-6 markets, including Indonesia, 
Malaysia, Philippines, Singapore, Thailand, and Vietnam, respectively. Each stock index 
has its own up and down movements, but their overall trends are increasing, except f ...  formula for the symbolized binary series is 
1
0
( ) log ( )i it it
i
H p S i p S i
=
= − = = (6) 
The maximum value of Shannon entropy of the symbolized binary series is 1, 
which occurs when the two nondecreasing and decreasing states of the return series have 
equal probabilities, and the minimum value is 0, when the stock return is always at the 
same state. The closer the calculated Shannon entropy value is to 1, the more purely 
random and less patterned the stock returns are, and the more difficult to predict because 
of the high complexity. Therefore, the market is more efficient. Conversely, the further 
Shannon entropy is from 1, the more the series has more patterns because there will be 
one state that has a higher probability than the others. It can be said that the market has 
not reached the state of information efficiency. 
In this paper, the calculation of Shannon entropy will be performed by the rolling 
window technique with window length W = 250. After finishing the windowing process, 
we will have a time-varying Shannon entropy series that shows changes in the 
randomness level of the stock index and changes in the efficiency level of the stock 
market. The length of the rolling window is 250, corresponding to the average of 250 
trading days per year on these stock markets. Data samples for six stock index series will 
be symbolized and then Shannon entropy series will be computed. The Shannon entropy 
series of each market is used to examine market-to-market linkages through the Granger 
causality test. 
3.2.2. Granger causality test 
The Granger causality test is used to test the empirical relationship between two 
time series, Xt and Yt. The Xt series has a Granger effect on Yt if past values of X contain 
information useful to explain or predict the current and future value of Y. This test is 
performed through the regression function 
0
1 1
p p
t j t j j t j t
j j
Y Y X  − −
= =
= + + +  (7) 
where α0 is the intercept, βj is the slope of Yt-j, αj is the slope of Xt-j, and εt is the 
error. 
Tran Thi Tuan Anh 
51 
If the hypothesis 0 1: ... 0pH = = = 
is rejected, there is sufficient statistical 
evidence to conclude that Xt has a Granger effect on Yt at lag p. To ensure that the Granger 
causality test results do not suffer from spurious regression, this article conducts a 
stationarity test for time-varying Shannon entropy series of all markets. Calculations are 
performed by using Python software. 
4. RESULTS AND DISCUSSION 
4.1. Descriptive statistics 
Table 2 presents descriptive statistics of the daily closing prices of ASEAN-6 
stock markets. This table shows the mean, standard deviation, maximum and minimum 
value of stock indices and does not reveal significant information about the efficiency of 
these stock markets. 
Table 2. Descriptive statistics of ASEAN stock indices 
Country No. of obs. Mean Std. dev. Min. Max. 
Indonesia 1,562 5,215.67 734.30 3,717.88 6,680.62 
Malaysia 1,619 1,723.36 86.02 1,532.14 1,895.18 
Philippines 1,619 269.73 53.80 169.00 423.33 
Singapore 1,619 316.48 22.77 251.98 373.81 
Thailand 1,619 1,507.90 157.08 1,099.15 1,837.49 
Vietnam 1,619 680.45 203.78 375.79 1,198.12 
Table 3 shows descriptive statistics of the daily returns of ASEAN-6 stock indices. 
Among these, the Philippines stock market has a negative average return over the period 
of 2012-2019. This is quite reasonable because of the general declining trend of the 
Philippines market, as seen in Figure 1. The Philippines is also the market with the largest 
standard deviation while Vietnam is the market with the highest average return, Malaysia 
is the market with the lowest standard deviation and lowest range of return. 
Table 3. Descriptive statistics of ASEAN stock returns 
Countries No. of obs. Mean Std. Dev. Min. Max. 
Indonesia 1,562 0.0004 0.0094 -0.0401 0.0465 
Malaysia 1,619 0.0001 0.0055 -0.0318 0.0225 
Philippines 1,619 -0.0003 0.0131 -0.0605 0.1369 
Singapore 1,619 0.0001 0.0073 -0.0422 0.0276 
Thailand 1,619 0.0002 0.0086 -0.0523 0.0459 
Vietnam 1,619 0.0006 0.0104 -0.0587 0.0385 
DALAT UNIVERSITY JOURNAL OF SCIENCE [ECONOMICS AND MANAGEMENT] 
52 
4.2. Shannon entropy results 
The article applies the symbolizing technique to the stock return series of the 
ASEAN-6 markets according to Equation (5) and the rolling window method with a 
window size of 250 transaction days. In each window frame, the Shannon entropy of the 
symbolized data series is calculated using Equation (6). Figure 2 shows a graph of the 
time-varying Shannon entropy series for each market, and Table 4 gives their stationarity 
test results. 
Figure 2. Time-varying Shannon entropy series for ASEAN-6 stock markets 
The Shannon entropy series of the six markets shown in Figure 2 are all quite far 
from the maximum possible value of Shannon entropy. This represents quantitative 
evidence of market inefficiency. Therefore, all six ASEAN-6 stock markets do not 
achieve information efficiency. This result is consistent with Tran (2018a); that study also 
concludes that the ASEAN-6 stock markets are inefficient, using data from 2010 to 2016. 
However, Tran (2018a) applied Shannon entropy for the whole sample, which treats 
Shannon entropy as time-invariant. This paper, using the rolling window technique, 
shows the variation in inefficiency over time with the visualization in Figure 2. 
4.3. Granger causality results 
Table 4 gives the stationary test results of the Shannon entropy series representing 
the six markets. Among them, the entropy series of Vietnam and the Philippines are not 
Tran Thi Tuan Anh 
53 
stationary at the level but stationary at the first difference. To avoid spurious results for 
the Granger causality test, the Shannon entropy series of Vietnam and the Philippines 
were taken at the first difference. The Shannon entropy series for Indonesia, Malaysia, 
Singapore, and Thailand were considered at the level. 
Table 4. Unit root test for time-varying Shannon entropy series of ASEAN-6 stock 
markets 
Country 
 Augmented Dickey-Fuller Test 
Level First difference 
Indonesia -3.4810*** 
Malaysia -3.1407** 
Philippines -2.1837 -7.4275*** 
Singapore -3.1660 
Thailand -3.3024** 
Vietnam -1.4110 -17.2040*** 
Notes: *, **, *** correspond to significance levels of 10%, 5%, and 1%, respectively. 
Table 5 shows the results of the Granger causality test of the Shannon entropy 
series among the ASEAN-6 stock markets. The series included in the Granger causality 
test are all stationary after taking the first difference for entropy series of Vietnam and 
the Philippines. However, the difference symbols are not shown in Table 5 of the Granger 
causality test. Table 5 shows the results of the Granger causality test between the Shannon 
entropy series ASEAN-6 stock markets. Since the Granger causality test results may 
depend on the chosen lag, we perform the Granger causality test with lags from 1 to 5 to 
account for weekly seasonal trends in the data. The stock markets are not trading on 
weekends, so the lag of 5 represents the one-week cycle in the stock market. The results 
are summarized in Table 5 and shown in Figure 3, where the statistically significant 
Granger relationships are represented by arrows connecting the countries' names. 
Figure 3. Relationships among ASEAN-6 stock markets by Granger causality test 
Indonesia 
Vietnam 
Thailand Singapore 
Philippines 
Malaysia 
DALAT UNIVERSITY JOURNAL OF SCIENCE [ECONOMICS AND MANAGEMENT] 
54 
Table 5. Granger causality test–sorted by causal market 
Causal market 
Response 
market 
F-statistic 
Lag 1 Lag 2 Lag 3 Lag 4 Lag 5 
Indonesia => Malaysia 0.130 1.510 3.610** 2.800** 2.340** 
Indonesia => Philippines 0.690 0.440 0.650 1.300 1.170 
Indonesia => Singapore 0.330 1.050 1.220 1.060 1.010 
Indonesia => Thailand 1.010 2.730* 2.940** 2.410** 2.050* 
Indonesia => Vietnam 3.610* 2.150 3.390** 4.460*** 3.760*** 
Malaysia => Indonesia 0.940 2.160 3.180** 4.530*** 0.954*** 
Malaysia => Philippines 0.000 0.330 0.390 0.290 0.170 
Malaysia => Singapore 0.000 0.780 0.660 0.560 0.870 
Malaysia => Thailand 3.470* 1.850 1.580 1.250 0.980 
Malaysia => Vietnam 6.960*** 5.040*** 5.910*** 5.280*** 4.220*** 
Philippines => Indonesia 2.490 1.160 1.930 1.380 3.700*** 
Philippines => Malaysia 0.100 1.430 1.480 1.320 2.690** 
Philippines => Singapore 4.180** 2.330* 1.520 1.120 1.870* 
Philippines => Thailand 0.290 2.890* 2.720* 2.590** 2.620** 
Philippines => Vietnam 0.910 0.710 0.860 0.760 1.800 
Singapore => Indonesia 0.100 0.370 0.370 1.510 1.350 
Singapore => Malaysia 0.080 0.310 0.550 0.540 0.440 
Singapore => Philippines 1.860 2.000 2.200* 1.840 3.030** 
Singapore => Thailand 0.150 0.600 0.770 0.570 0.710 
Singapore => Vietnam 2.220 1.250 0.810 0.610 0.500 
Thailand => Indonesia 0.790 0.720 0.590 0.700 0.680 
Thailand => Malaysia 0.830 1.200 0.970 0.640 0.700 
Thailand => Philippines 0.150 1.150 0.640 0.440 0.300 
Thailand => Singapore 1.200 0.620 0.490 0.450 0.370 
Thailand => Vietnam 2.500 2.030 1.780 5.210*** 4.230*** 
Vietnam => Indonesia 0.050 1.510 1.160 0.990 1.190 
Vietnam => Malaysia 0.410 0.240 0.300 0.280 0.530 
Vietnam => Philippines 0.000 0.890 1.280 1.830 1.450 
Vietnam => Singapore 2.880* 2.350* 1.960 1.640 1.350 
Vietnam => Thailand 0.090 0.710 0.450 0.520 1.060 
Notes: *, **, *** correspond to significance levels of 10%, 5%, and 1%, respectively. 
It can be seen from Figure 3 that each of these six markets is linked to at least 
three other markets and that there is no isolated market. There are some markets which 
Tran Thi Tuan Anh 
55 
are more integrated than the others. The most well-integrated markets, as shown in Figure 
3, are Indonesia and Malaysia, with connections occurring with most other countries, 
except Singapore. The results also show that the role of Vietnam is very different from 
that of the Philippines in these relationships. Vietnam suffers impacts from other markets 
but has less impact on them; whereas the statistical evidence shows that the Philippines 
has a useful role in providing information to predict stock market movements of many 
other countries. The results of this study are consistent with some previous studies on the 
stock market linkages of ASEAN countries. Jiang, Niea, and Monginsidi (2017), using 
the variational mode decomposition and copula methods, also show a close relationship 
between the Indonesian and Malaysian stock markets, as well as a weak relationship 
between Vietnam and other markets in the region. Similarly, another study by Gabriella, 
Suryanarayana, and Esady (2016) also found evidence of a strong short-term spillover 
effect among these ASEAN-6 countries. 
5. CONCLUSION AND IMPLICATIONS 
This article uses data on daily closing prices of ASEAN-6 stock markets, 
including Indonesia, Malaysia, the Philippines, Singapore, Thailand, and Vietnam. The 
daily returns are also calculated and used to construct a symbolized series. The rolling 
window technique was applied in combination with the Shannon entropy for each market 
to compute the time-varying entropy series. The Shannon entropy series of all ASEAN-6 
stock markets do not attain the maximum value of 1, so this is evidence for information 
inefficiencies in all six markets. This result also implies that the stock index and return 
fluctuations on these markets are not completely random. They have potential patterns 
inside the series. Investors can use fundamental analysis or technical analysis tools to 
discover opportunities for outstanding profit. 
In addition, the paper also applies the Granger causality test with many different 
lags on the Shannon entropy series to find statistical evidence of the relationships between 
the ASEAN-6 stock markets. The Granger causality test reveals whether it is possible to 
use information from past markets to predict current and future information for other 
markets. According to the Granger causality test results, the ASEAN-6 stock markets 
have significant relationships with each other. Indonesia and Malaysia are two markets 
that are particularly well-integrated with the other markets. Vietnam plays a passive role 
in the relationships with other ASEAN stock markets because Vietnam receives more 
information from other markets than it transfers to them. Another interesting finding is 
that Philippines plays an active role in the region, more than Vietnam and other countries, 
despite the overall decreasing trend during the study period. Singapore’s stock market is 
also less integrated with the region, possibly because the Singapore market is quite mature 
and developed, so it has more links with other developed stock markets around the world, 
such as the US, EU, China, and Japan than with ASEAN’s developing markets. 
REFERENCES 
Gabriella, L. G., Suryanarayana, R., & Esady, V. (2016). Financial integration in 
ASEAN-5. Economics and Finance in Indonesia, 62(1), 44-58. 
DALAT UNIVERSITY JOURNAL OF SCIENCE [ECONOMICS AND MANAGEMENT] 
56 
Jianga, Y., Niea, H., & Monginsidi, J. Y. (2017). Co-movement of ASEAN stock markets: 
New evidence from wavelet and VMD-based copula tests. Economic Modelling, 
64, 384-398. 
Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The 
Journal of Finance, 25(2), 383-417. 
Lahmiri, S., Bekiros, S., & Avdoulas, C. (2018). Time-dependent complexity 
measurement of causality in international equity markets: A spatial approach. 
Chaos, Solitons, & Fractals, 116, 215-219. 
Mensi, W. (2012). Ranking efficiency for twenty-six emerging stock markets and 
financial crisis: Evidence from the Shannon entropy approach. International 
Journal of Management Science and Engineering Management, 7(1), 53-63. 
Risso, W. A. (2009). The informational efficiency: The emerging markets versus the 
developed markets. Applied Economics Letters, 16(5), 485-487. 
Shannon, C. E. (1948). A mathematical theory of communication. The Bell System 
Technical Journal, 27(3), 379-423. 
Tran, T. T. A. (2018a). Đo lường mức độ hiệu quả thông tin trên thị trường chứng khoán 
các nước Đông Nam Á bằng Shannon entropy. Tạp chí Kinh tế và Phát triển, 
(252), 22-29. 
Tran, T. T. A. (2018b). Đo lường tính hiệu quả của thị trường chứng khoán Việt Nam 
bằng Shannon entropy và mối liên hệ với khả năng sụt giảm của chỉ số thị trường. 
Tạp chí Công nghệ Ngân hàng, (151), 7-17. 
Tran, T. T. A. (2019). Đo lường độ phức tạp trong chuỗi thời gian của các cổ phiếu trong 
danh mục VN30: Tiếp cận bằng entropy hoán vị. Tạp chí Khoa học Đại học Mở 
TP. Hồ Chí Minh, 14(1), 18-28. 
Zunino, L., Massimiliano, Z., Tabak, B. M., Pérez, D. G., & Rosso, O. A. (2009). 
Forbidden patterns, permutation entropy, and stock market inefficiency. Physica 
A, 388, 2854-2864.