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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 ent[r]
(1)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: http://dx.doi.org/10.37569/DalatUniversity.10.4.614(2020) Article type: (peer-reviewed) Full-length research article Copyright © 2020 The author(s)
(2)KHẢO SÁT MỐI LIÊN HỆ GIỮA CÁC THỊ TRƯỜNG
CHỨNG KHỐN ĐƠNG NAM Á: TIẾP CẬN BẰNG KIỂM ĐỊNH NHÂN QUẢ GRANGER TÍNH HIỆU QUẢ THƠNG 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 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 thơng tin thị trường chứng khoán mối liên hệ thị trường chứng khốn quốc gia Đơng Nam Á hai số vấn đề quan tâm nghiên cứu Tuy nhiên, hai vấn đề thường tách biệt nghiên cứu riêng nghiên cứu trước Do vậy, viết kết hợp nghiên cứu hai vấn đề phân tích Dữ liệu số chứng khốn đóng cửa hàng ngày sáu thị trường chứng khốn Đơng Nam Á, bao gồm Indonesia, Malaysia, Philippines, Singapore, Thái Lan, Việt Nam sử dụng để tính tốn Shannon entropy nhằm đo lường tính hiệu thị trường Bên cạnh đó, viết đồng thời áp dụng kiểm định nhân Granger để khảo sát mối liên hệ thị trường chứng khốn quốc gia Đơng Nam Á Kết nghiên cứu cho thấy cả sáu thị trường chứng khoán không đạt trạng thái hiệu thông tin, điều có nghĩa là biến động số chứng khoán tỷ suất sinh lợi thị trường chưa phải hoàn toàn ngẫu nhiên Ngoài ra, kết kiểm định Granger cho thấy thị trường chứng khốn quốc gia Đơng Nam Á có mối liên hệ hợp lý với Hai thị trường hội nhập tốt với khu vực bao gồm Indonesia Malaysia Việt Nam tham gia vào mối liên hệ kinh tế khu vực với vai trò thụ động quốc gia khác, Philippines, có khuynh hướng suy giảm suốt thời gian liệu thu thập, lại đóng vai trò chủ động trong khu vực Thị trường chứng khốn Singapore hội nhập với khu vực là thị trường chứng khoán phát triển trưởng thành vượt trội quốc gia lại
Từ khóa: Kiểm định nhân Granger; Phương pháp cửa sổ cuộn; Shannon entropy; Thị trường chứng khốn nước Đơng Nam Á; Thị trường hiệu thông tin
DOI: http://dx.doi.org/10.37569/DalatUniversity.10.4.614(2020) Loại báo: Bài báo nghiên cứu gốc có bình duyệt
Bản quyền © 2020 (Các) Tác giả
(3)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 summarizes some relevant previous studies; Section introduces data and methodology; Section represents the data analysis and discusses the results; and Section concludes the main results of the article and proposes some implications
2 LITERATURE REVIEW
(4)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 Based on this feature, there can be evidence for market inefficiency when the Shannon entropy of the stock series is less than 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
(5)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 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
Table List of stock market index of ASEAN countries
Order Country Stock index Stock exchange Vietnam VNI Vietnam Stock Index
2 Philippines PSEI Philippines Stock Exchange Index Malaysia KLCI FTSE Bursa Malaysia KLCI Index Indonesia JCI Jakarta Stock Exchange Composite Index Thailand SET Stock Exchange of Thailand SET Index Singapore STI FTSE Straits Times Index
From the daily closing prices, the stock returns are calculated by a logarithmic formula as follows:
,
100 ln it it
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
(6)(7)The daily returns along with daily closing prices of stock indices are plotted in Figure The plots on the left side of Figure 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 for the Philippine stock market which declined over time The graphs of the return series also show unequal variations over time of these six stock markets
3.2 Methodology
3.2.1 Shannon entropy
Shannon entropy was firstly introduced by Shannon (1948) as a quantity used to measure the level of randomness or complexity in a signal sequence The Shannon entropy concept was later used extensively in financial studies, especially to measure the randomness in financial time series Suppose we consider a time series Xt, t=1,2,3,…
representing fluctuations in financial asset prices, Xt can take discrete values x1, x2,…, xn
with probabilities p(x1), p(x2),…, p(xn)which satisfy the condition
1
( ) n i i p x = =
Shannon
entropy, H, is then calculated using Equation (2)
1
( ) log ( ) n
i i
i
H p x p x
=
= − (2)
Shannon entropy takes the minimum value of if there is a certain value xi that
will inevitably occur in all cases, meaning that the probability that Xt equals xi is
Otherwise, Shannon entropy will be maximized when all possible values of xi have the
same probability of occuring That is, all possible outcomes are equally likely to happen, so the series is completely random
In the case that Xt is a continuous random variable, the calculation of Shannon
entropy becomes more difficult than when Xt is a discrete variable One of the simplest
ways to calculate Shannon entropy for continuous random variables is to symbolize them into a discrete binary series and then compute the entropy The symbolization process is performed as follows:
1 1 t t t t t if X X S
if X X − − = (3)
That is, assume Xt is the daily closing price Pit of the ith stock index; it can be
easily interpreted that St will receive value if the stock index stays the same or goes up,
and St will receive value if the stock price falls The symbolization rules for the ith stock
index will be:
, ,
1
it i t it
it i t if P P S
(8)Equivalently, the stock price stays the same or increases ( Pit Pi t,−1 ) corresponding to a zero or positive rate of return, while a stock price decrease (Pit Pi t,−1 )
corresponds to a negative rate of return Thus, the binary series can also be made by using returns instead of prices:
1 0 it it it if r S if r = (5)
and the Shannon entropy 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
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
(9)If the hypothesis H0:1= = p =0 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 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 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 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 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 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 Descriptive statistics of ASEAN stock returns
(10)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 shows a graph of the time-varying Shannon entropy series for each market, and Table gives their stationarity test results
Figure Time-varying Shannon entropy series for ASEAN-6 stock markets The Shannon entropy series of the six markets shown in Figure 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 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
4.3 Granger causality results
(11)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 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 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 of the Granger causality test Table 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 to to account for weekly seasonal trends in the data The stock markets are not trading on weekends, so the lag of represents the one-week cycle in the stock market The results are summarized in Table and shown in Figure 3, where the statistically significant Granger relationships are represented by arrows connecting the countries' names
Figure Relationships among ASEAN-6 stock markets by Granger causality test Indonesia
Vietnam
Thailand Singapore
(12)Table Granger causality test–sorted by causal market
Causal market Response market
F-statistic
Lag Lag Lag Lag Lag 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
(13)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 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
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: http://dx.doi.org/10.37569/DalatUniversity.10.4.614(2020) CC BY-NC 4.0