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RESEARCH ARTICLE
Risk and causality Co-movement of Malaysia’s
stock market with its emerging and OECD
trading partners. Evidence from the wavelet
approach
Xiaoyang Wang
1,2
*, Hui Guo
1
, Muhammad WarisID
3
*, Badariah Haji Din
3
1Innovation College, North Chiang Mai University, Nong Kaew, Hong Dong, Chiang Mai, Thailand,
2Xuchang Industrall & Commerclal Administration School No.3, Jian’an District, Xuchang City, Henan
Province, China, 3Ghazali Shafie Graduate School of Government, University Uttara Malaysia, Malaysia,
Malaysia
*g646501006@northcm.ac.th (XW); Warisraobzu051@gmail.com (MW)
Abstract
The growing trend of interdependence between the international stock markets indicated
the amalgamation of risk across borders that plays a significant role in portfolio diversifica-
tion by selecting different assets from the financial markets and is also helpful for making
extensive economic policy for the economies. By applying different methodologies, this
study undertakes the volatility analysis of the emerging and OECD economies and analyzes
the co-movement pattern between them. Moreover, with that motive, using the wavelet
approach, we provide strong evidence of the short and long-run risk transfer over different
time domains from Malaysia to its trading partners. Our findings show that during the Asian
financial crisis (1997–98), Malaysia had short- and long-term relationships with China, Ger-
many, Japan, Singapore, the UK, and Indonesia due to both high and low-frequency
domains. Meanwhile, after the Global financial crisis (2008–09), it is being observed that
Malaysia has long-term and short-term synchronization with emerging (China, India, Indo-
nesia), OECD (Germany, France, USA, UK, Japan, Singapore) stock markets but Pakistan
has the low level of co-movement with Malaysian stock market during the global financial cri-
sis (2008–09). Moreover, it is being seen that Malaysia has short-term at both high and low-
frequency co-movement with all the emerging and OECD economies except Japan, Singa-
pore, and Indonesia during the COVID-19 period (2020–21). Japan, Singapore, and Indone-
sia have long-term synchronization relationships with the Malaysian stock market at high
and low frequencies during COVID-19. While in a leading-lagging relationship, Malaysia’s
stock market risk has both leading and lagging behavior with its trading partners’ stock mar-
ket risk in the selected period; this behavior changes based on the different trade and invest-
ment flow factors. Moreover, DCC-GARCH findings shows that Malaysian market has both
short term and long-term synchronization with trading partners except USA. Conspicuously,
the integration pattern seems that the cooperation development between stock markets
matters rather than the regional proximity in driving the cointegration. The study findings
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OPEN ACCESS
Citation: Wang X, Guo H, Waris M, Din BH (2024)
Risk and causality Co-movement of Malaysia’s
stock market with its emerging and OECD trading
partners. Evidence from the wavelet approach.
PLoS ONE 19(1): e0296712. https://doi.org/
10.1371/journal.pone.0296712
Editor: Fiza Qureshi, University of Southampton -
Malaysia Campus, MALAYSIA
Received: May 6, 2023
Accepted: December 17, 2023
Published: January 25, 2024
Peer Review History: PLOS recognizes the
benefits of transparency in the peer review
process; therefore, we enable the publication of
all of the content of peer review and author
responses alongside final, published articles. The
editorial history of this article is available here:
https://doi.org/10.1371/journal.pone.0296712
Copyright: ©2024 Wang et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: Data is available in
support information file in attachment.
Funding: The author(s) received no specific
funding for this work.
have significant implications for investors, governments, and policymakers around the
globe.
1. Introduction
The stock market is an integral part of each economy that leads to economic growth and
industrial development within the nation. Stock markets fulfill the financial needs of the cor-
porate sector and may open different opportunities for investors to earn profit from trading in
the stock market. Many aspects, such as crises, pandemics, and environmental changes, affect
the stock market. The fluctuation in the stock market prices creates a risk for investors. Still,
due to globalization, the risk transfer from one economy to another makes this task worse for
the investors of the international portfolio. Globalization has strengthened the linkage between
international stock markets. Through globalization, cross-border trade is boosted by eliminat-
ing the barriers to stock market integration [1,2]. Therefore, with the stock market fluctuation,
the risk and causality transmission create another problem for the investors.
Similarly, the stock market of Malaysia shows different patterns in pre- and post-crisis.
However, the crisis and the pandemic affected the pattern of the Malaysian stock market, cre-
ating different economic challenges. The Asian Financial Crisis 1997 98 is considered one of
Malaysia’s most crucial economic crises. This crisis created the deregulation of the capital
accounts and the financial sector, which caused a decline in the GDP growth of 6.7% or 7.7%
before the crisis period. This crisis on the first day decreased the Kula lumper stock exchange
to 44.9%. The value of the currency ringgit also fell in January 1998. There is enormous pres-
sure on both the currency and financial markets due to the crisis. In the financial crisis of
2008–9, there was a decline in the total GDP to 1.7% in 2009 and had some other negative
consequences.
Moreover, due to COVID-19, all financial activities have dropped in the world, including
the downsizing in the stock market prices. Like the other economy, Malaysia was also affected
by the country’s lockdown. According to [3], Malaysia’s stock market indices have dropped
and are highly correlated with the pandemic.
Moreover, the crisis in one economy affects the other stock market because a correlation
exists between them due to globalization that creates another issue. Similarly, When the
Malaysian market is affected by the crashes, it may impact the trading partners in different
world regions. When the Stock market of Malaysia (Kula Lumpur Stock Exchange) declined
due to the crisis in 2008, it also decreased in the Japanese stock exchange due to the significant
foreign direct investment made by Japan in Malaysia. The Chinese stock market crash of 2015
affected the Malaysian stock market due to the interdependence among the stock markets. At
that time, the oil prices also hit Malaysia to its lowest in six years. Gold was considered the safe
market during the crisis, but gold prices decreased in China and impacted the Malaysian econ-
omy. Moreover, emerging and the OECD economies also effected in the crisis period that are
highly independent. Hence, this study mainly investigated the pattern and cointegration
between Malaysia, OECD, and emerging countries pre- and post-crisis.
The increased capital flow between countries due to globalization through the rapid devel-
opment of technology is the cause of the economic integration between different markets and
has played an essential role over the last two decades. Every financial institution and portfolio
management needs to understand the extent and nature of the linkage between financial mar-
kets [4]. The nexus of interdependence between these markets can be analyzed by finding
return and volatility transfer between these different financial markets. Risk and causality
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Competing interests: The authors have declared
that no competing interests exist.
transmission is crucial for designing hedge strategies and making optimal portfolios. [5] find
the emerging markets are severely affected by the different crises in history, and these effects
are transmitted to other countries. However, cointegration between the stock market has
excellent indicators showing the risk and causality that may transfer from Malaysia to its trad-
ing partners in the two regions. Therefore, the main reason behind that factor is the increase
in the capital flow among these countries and the rapid development of the technology
enhancement between the market that is observed in globalization.
Moreover, the trade volume of Malaysia between emerging and OECD countries grew at
different rates in the last 20 years. Therefore, when trade volume between different markets,
regions, and countries changes, it also changes the market volatility transmission. Moreover,
Malaysian trade with OECD and emerging economies. However, it is essential to investigate
the risk and causality transfer from the Malaysian market to its trading partners because of the
increasing trend of the trade volume existence that created the interdependence between them
over the last two decades. Moreover, each crisis has a different intensity and has different
behavior of transfer from one economy to another, such as leading and lagging behavior
between markets due to the type of trade and foreign direct investment. Therefore, this study
examines the risk and causality transmission between different markets during the major
financial crisis (financial crisis in 1997–98, 2008–09, and the period of the pandemic 2020–21).
Various studies have been conducted on the stock market cointegration by focusing on the
major economic crisis in the world [6]. In addition to these studies, the International Mone-
tary Fund, Banks for International Settlements, Financial Stability Board (FSB), and other reg-
ulatory bodies have examined the connection between global stock markets and systemic risks
that were typically undervalued before the crises. These investigations again identified the frag-
mented local markets as the primary cause of the crises, which led to excessive market volatility
and links between the stock market [7]. Most previous research had found substantial levels of
linkage among developed markets with few opportunities for diversification. Nevertheless,
research on the emerging market is growing to find opportunities for diversification [8]. More-
over, limited studies on the risk transformation in the period of crisis and pandemics, espe-
cially in emerging economies such as Malaysia, create an exciting gap for the investigation.
Accordingly, our study aims to investigate the stock market risk co-movement between
Malaysia and its trading partners in different time and frequency domains. We aim to answer
our research questions about Transferring the risk and causality from the Malaysian stock
market to its trading partners pre- and post-crisis. Some motivation points behind our
research include it is exciting to focus on Malaysia with its trading partners belonging to
emerging and OECD countries as Malaysia is a rapidly growing emerging market with increas-
ing market capitalization and trade partnership with attracting foreign direct investment
inwards from different emerging and OECD economies. Malaysia has had a significant role
and has become one part of the main engine of the world economy in the last two decades.
Malaysia has a substantial role in neighboring countries’ economies and also in all Asian
economies.
Similarly, we contributed to the literature in the current study through theoretical, variable,
and methodological contributions. First, it contributes fresh evidence of the stock market inte-
gration with its emerging and OECD trading partners at different time intervals. Also, it con-
tributes to the literature on co-movement and covariance by exploring the capital markets
related to two different regions, including Emerging and OECD countries, that have gained lit-
tle attention in previous studies. Second, it contributes to the existing theory information that
trade agreements and other financial contracts between the economies can provide a hedge
and safe opportunity for the investors following the co-integration patterns. Still, the previous
theory states that investment in some developed economies like the USA and the UK provides
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investors with a safe, even opportunity. Third, this research used the stock market indices and
employed the three-dimensional wavelet methodology that simultaneously measures the co-
movement based on the multiple investment horizons over time.
Moreover, to the best of my knowledge, this research is the first to use the complete wavelet
methodology and wavelet based DCC-GARCH for calculating the co-movement of Malaysia
with its trading partners belonging to two different regions in both time and frequency
domains. In addition, another aspect of this research is the use of wavelet coherency, which is
helpful for the investigation. The use of wavelet coherency in this research to examine whether
economic and financial considerations justify coherence in co-movement at different time fre-
quencies is also a great feature of the methodology. Fourth, this study contributes to the grow-
ing body of literature on the impact of crisis and pandemic by presenting the new data
calculated with the help of DCC-GARCH variance to check the influence of the global finan-
cial crisis of 1997–98, 2008–9 and the COVID-19 stress on emerging and OECD stock mar-
kets. Moreover, this research adds to the literature on the interdependence between Malaysia
and the emerging OECD stock market at different investment horizons; there is still little evi-
dence from previous studies on that subset. This research adds to the previous literature by
investigating the global stock market uncertainty during the crisis that caused the cointegra-
tion fluctuation between the stock markets and also a contribution focused on the financial cri-
sis of 1997–98, 2008–9, and COVID-19 on the short- and long-term dynamic linkage of
emerging and OECD capital markets.
The remaining paper is organized as section 2, which discusses the literature review, includ-
ing the theoretical and empirical literature. The methodology with the data description is
included in section 3, and estimated models are explained. The results and their discussion are
illustrated in section 4, and the conclusion recommendations with policy implications and
limitations are discussed in section 5. Moreover, the future research suggestions are also dis-
cussed in section 5.
2. Literature review and hypothesis development
The cointegration of the stock markets means the correlation or co-movement between differ-
ent stock market prices [9–11]. Stock market co-movements have restructured global invest-
ment markets, making it a leading research topic. Following groundbreaking work by [6,12],
stock market co-movements have attracted significant research attention by presenting
numerous theoretical models that attempt to elucidate the issue further. There is an increasing
trend in research on the co-integration of the stock markets due to the effect of the financial
crisis. There is an increase in portfolio shock due to the strong integration between the stock
markets of different economies, which is a response to the increased integration of the mar-
kets. The contagion effect could be felt worldwide, in both emerging and developed markets.
This was a direct result of the financial crisis, which resulted in a significant credit crunch due
to the collapse of financial markets. Among the events covered in the literature review section
are the stock market movements during the devaluation of the Mexican peso in 1994, the East
Asian financial crisis in 1997, the global financial crisis in 2009, the Chinese devaluation in
2015, and the period of the pandemic, such events have been the subject of numerous studies,
some of which are presented in the literature review section of this study [6,13]. Apart from
such studies, the International Monetary Fund (IMF), the top global economic financial insti-
tutions, Banks for International Settlements, the Financial Stability Board (FSB), and other reg-
ulatory bodies have examined the relationship between international stock markets and the
systemic risks which went generally undervalued before the crises. These investigations consis-
tently pointed to disordered local markets as the initial source of the crises, which resulted in
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surplus market interconnections and stock market interconnections as a result of interconnec-
tions [14,15]. Previous studies have discovered high levels of interconnection among devel-
oped markets, with few opportunities for diversification in most cases. Nonetheless, studies on
emerging markets are becoming increasingly popular as investors look for opportunities to
diversify their portfolios.
A high degree of interconnection between developed markets has been investigated in most
previous studies, with little prospect for diversification. On the other hand, studies on the
emerging market are becoming increasingly popular as investors seek diversification opportu-
nities. Various theoretical explanations for stock market linkages have emerged from the
growth economies of knowledge on the subject, including the law of one price and theories of
stock market movement and stock market interdependence derived from Modern portfolio
theory, which all serve to justify stock market linkages [16,17]. Theories underline portfolio
diversification in global markets [18–20]. Prospect theory asserts that investors’ similar expec-
tations about their investments serve as accurate indicators of the performance of their invest-
ments. The arbitrage pricing theory, Capital asset pricing theory, assesses the risk principles. It
is supported by the principle of interconnectedness of international markets and that asset
pricing theory and arbitrage pricing theories depend on a commodity with the same unit price
in all international markets.
Similarly, according to the stock market efficiency theory, stock price information flows
between international stock markets create a connection between them. According to behav-
ioral finance theory, investor preferences are based on subjective factors that cause herd effects,
which cause stock markets to become more correlated. The information spillover effect is anal-
ogous to the stock market efficiency theory, which holds that stock market information is the
most critical factor in determining the level of correlation between stock markets. It is also
assumed that disseminating stock information across countries, regions, and time zones con-
tributes to the correlation between stock information and the performance of international
stock markets. Equity market consensus measures are widely regarded as a gold standard for
evaluating the benefits of portfolio diversification for investors and the real economy regarding
economic growth and global market connectivity, among other things.
[20] state that Malaysia’s stock market indices have dropped and are highly correlated with
the pandemic. The global economic crisis is the leading cause of the rise in oil prices, another
main economic problem.
[21] explained the different equity markets and found the interconnectedness of the US,
UK, and EU markets that played a critical role in strengthening their respective currencies and
exchange rates, distinguishing them from other economies. These three markets’ interconnec-
tedness and coordination have fostered their strong financial positions.
Many researchers have studied the past impact of stock market volatility on economic
development, but their conclusions have conflicted. Nigeria’s stock market volatility was stud-
ied from 1986 to 2010 by [22]. [23] evaluated the relationship between Malaysian stock market
volatility and macroeconomic indicators. They found only consumer price index and interest
rate volatility Granger substantially affect volatility in stock market returns. Macroeconomic
conditions don’t affect the stock market’s performance. Only the money supply volatility has a
meaningful link with stock market volatility as per their regression studies.
A considerable study has been undertaken on the impact of domestic stock market cointe-
gration with the global stock market, concentrating on stock market links, integration, and
interdependence on an integrated stock market in which marketplaces are linked. After the
global financial crisis of 2007–2009, [24] examined six East Asian stock markets and found
that the market was less tolerant to shocks from US stock market movements. [25] deeply ana-
lyze India’s stock and growing markets.
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By applying the different classification systems [26,27], study the relationship between the
ASEAN-5 countries’ stock markets (Indonesia, Singapore, Malaysia, Thailand, and the Philip-
pines) and the world’s developed stock markets (the United States stock market and the Asian
stock market such as Japanese Stock Market) and concluded that cointegration between
ASEAN-5 stock prices, US stock prices, and Japanese stock prices persists through time, with a
stronger cointegration during crisis period. Consequently, emerging stock markets are espe-
cially vulnerable to changes in the stock markets of developed countries, particularly in the
United States of America (USA). The stock markets of the ASEAN-5 countries are closely
linked to those of the United States and Japan, and this linkage was solid before the financial
crisis. Their findings also show that emerging stock markets are highly vulnerable to the vola-
tility of stock markets in developed countries, particularly the United States. As a result of [28]
research on four international stock exchanges (the U.S., the ASEAN block, Asia, and the
world), the national and international stock exchanges have a variety of channel connections.
However, there was a clear link between domestic and international markets regarding inte-
gration. [29] examined Asian capital market cointegration and found opportunities for diversi-
fication to potential investors in Pakistan, India, Bangladesh, and China, respectively.
More research has been conducted to investigate the reasons for stock market volatility,
including macroeconomic factors. [28]) conducts a series of tests based on long-term monthly
data for the United States to discover the macroeconomic factors for stock market fluctuations.
[30–33] provide additional data on the macroeconomic determinants of market volatility. As a
result of the interdependence of markets, there are three possible paths: shared shocks, trade
ties with competitive devaluations, and financial links. There is a wide range of market connec-
tions that have contributed to the establishment of these channels. As an example [34], cite sig-
nificant increases in global or US interest rates [35], lists changes in commodity prices as well
as recessions in major industrial countries, and [36] includes slowdowns in US or global indus-
trial production as well as changes in the ratings of developed countries.
Moreover [37], argue that the developed market of the United States has a more significant
effect on the Australian stock market than other countries in the region, but this is not true for
the other Pacific Basin countries. This study examined the relationship between the stock mar-
kets of Pacific Basin nations from 1988 to 1996. Moreover [38], investigated the region of Scan-
dinavian countries and the United States of America during the same period to see whether
US stock transactions had an impact on the countries and found the high co-integration
between these economies.
[39] found little correlation between eleven growing Asian stock exchanges and developed
markets. Similarly [40], argue that Asian markets were uniform and dominated by a strong
market force and found no relationship between Asian markets and developed economies.
Similarly [41], concluded the long and short-term relationship between the equities markets of
11 Asia-Pacific nations, including the Malaysian stock market and other important trading
partners like Japan and the United States. Data was analyzed from July 1, 1996, to June 30,
1998, and found the short term and long term co-movement between them. [42] evaluated the
interconnectedness of the stock markets of Australia, Hong-Kong, Japan, Korea, the U.K., and
the U.S. based on the Co-integration tests and also of high intensity of the risk co-movement
pattern between them at different time intervals.
[43] investigated the relationship of the stock markets of developed and emerging econo-
mies in the context of long-term relationships and found both short-term and long-term co-
movement between these selected markets, such as India market has long-term co-movement
with mature markets. A recent study by [44] looked at the correlation between the US and
Argentina, Brazil, China, India, and Russia stock markets and found a strong cointegration
between the selected markets due to the trade interdependence. [45] found the
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interrelationships between the markets of GCE countries. In that study, there was a period
between June 2, 2005, and April 2, 2008, and high cointegration between the selected econo-
mies was found during the respective period. Moreover, they concluded that the cointegration
between the stock markets varies due to the volume of the trade agreements, trade volume,
and foreign direct investment.
[46] investigated the long-term relationship between the German and Central and Eastern
European stock markets. This study also looked into the impact of various stock market char-
acteristics, including size and volatility, as well as interest rate and inflation differentials, on
integrating these markets into the global economy. [47] examined the South African stock
market and found strong co-integration with the major global stock markets. Moreover, India,
Singapore, and Malaysia’s equity markets are compared using stock prices from July 1997 to
February 2005 to assess the long-term and short-term linkages. To see the co-integration [45],
studied India and two other developed economies, Japan and the USA. They found a signifi-
cant relationship between them due to the trade agreements. [48] conducted a study on the
cointegration between Malaysia, Hong Kong, Taiwan, and South Korea. They found a solid
linear cointegration between the stock markets of the selected economies due to the trade alli-
ances prevailing in those days. On the ground of previous literature, we developed the follow-
ing hypothesis,
H1. The Global Financial crisis significantly negatively impacted Malaysia’s stock market
and trading partners pre- and post-crisis.
H2. The risk in the Malaysian stock market has significant positive co-movement with its
trading partners pre- and post-crisis.
H3.Malaysian stock market has significant positive causation with trading partner’s stock
markets pre- and post-crisis.
3. Material and estimated methods
3.1 Data description and sample
We use the daily stock market indices data from 1
st
January 1993 to 31
st
December 2021 with
7565 observations for each country’s stock market. The stock market taken as a sample
includes Malaysia, China, India, Indonesia, Pakistan, Singapore, the United States of America
(USA), Germany, France, and the United Kingdom (UK). The selection of the stock markets is
based on the trade flow and volume between these countries, like exports and imports.
According to [49] that explained the price and the volatility linkage through the trade flow and
trade volume. These selected countries are the most significant trading partners of Malaysia.
The trade flow between Malaysia and the selected trading partners increased from 1993 to
2021. China is its biggest trading partner, with a trade volume of $423 Billion in 2019 and an
export volume of $336 Billion. Malaysia’s second-largest trading partner is Singapore, with an
export trade volume of $ 330 Billion and an Import trade volume of $261 Billion, which has
been increasing since 1992.
Pakistan is also a trading partner of Malaysia, with an import trade volume of $2.5 Billion
and an export of $ 1.1 Billion. It has an increasing trend in the trade volume. India has a trade
volume of exports with Malaysia of $9.0 Billion and imports of $5.8 billion. The United King-
dom is a trading partner of Malaysia, with an import trade volume of $1.7 Billion and an
export volume of $2.19 Billion. The United States is Malaysia’s third biggest trading partner,
with a trade volume of imports of $165 Billion and a trade volume of exports of $231 Billion.
Japan is Malaysia’s fourth most significant trading partner based on trade volume, with the pri-
mary export of all products with a volume of $157 Billion and imports of $153 Billion, an
increasing trend compared to the previous years. Germany is a trading partner of Malaysia
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with a rising trend in trade volume, with the export of all products at $6.2 Billion and imports
at $6.4 Billion. France is also a trading partner of Malaysia, with a trade volume of $1.5 Billion
and import of $2.6 Billion with the increasing trend. Indonesia is also a trading partner of
Malaysia, with a trade volume of exports of $7.4 Billion and imports of $9.3 Billion, with an
increasing trend compared to the previous years.
Malaysia was selected as the base economy on the ground of different reasons. First, it has
been a growing economy since 1986 but was affected in 1997–98. Secondly, Malaysia is
selected on the grounds of regional proximity; Malaysia has not been influenced by other polit-
ical factors such as war and border conflicts, etc. Data of indices (MSCI) is extracted for each
stock market from the DataStream database using the University Utara, Malaysia Library
access. The long-term time horizon is selected to investigate critical events in the world econ-
omy with more significant change. The selected period also includes the period of 1993 to
2021, which describes the increasing trend of oil prices globally, Mexican currency crisis
(1994–95), Asian economic crisis (1997–98), Russian default (1998), major economic crisis
(2007–09) and also the period of COVID 19. Nowadays, the period of COVID-19 is also a hot
topic due to the lockdown of business activities globally, which has negative consequences on
the global economy.
3.2 Estimated models
This study used different estimated models to obtain our study objectives. To attain our objec-
tives, we used the complete wavelet approach. However, our applied approach is very suitable
for three key reasons. First, this study covers OECD and emerging stock markets, which helps
compare the emerging economy across other regions. Second, this is supported by the reason-
ably large sample size; other approaches are useless due to the large sample or manipulating
the results on a large sample. However, our study approach is very suitable for large sampling
sizes, especially in the time series. Third, by fulfilling the necessities of the research, the risk
co-movement transfer from Malaysia to its trading partners.
3.2.1 Time-varying volatility. As per the GARCH modeling, volatility clustering is one of
the specific characteristics of the stock market return. Before the volatility analysis through
GARCH Modeling, we should fulfill the GARCH assumption of the volatility clustering exist-
ing in the stock market return. Therefore, we use the GARCH (1,1) model to estimate the
time-varying volatility for r
t
, a country’s stock market return:
rt¼aþbrt1þtwhere; tjItNð0;s2
tÞ ð1Þ
s2
t¼o0þo12
t1þo2s2
t1:ð2Þ
Eq (1) indicates the average model equation, while Eq (2) indicates the conditional uncer-
tainty that tracks transient fluctuations of the stock market, capturing the conditional volatility
that encapsulates the time-variable uncertainties in the financial markets of our study. Our
goal is to analyses both co-movement and volatility. To do this, we split our sample into the
OECD and emerging economies to learn more about how risks are distributed across the two
regions [50]. We investigate how Malaysia’s stock markets move in tandem with its trading
partners in Asia and other regions. The lag selection is based on the VAR (vector autoregres-
sive) model. We select the lag value that is 1, and that’s why our GARCH estimation is (1,1).
According to [50], the lag selection should be based on SC and HQ when both parameters are
significant at the same point, and less lag is suitable for an accurate result.
3.2.2 Wavelet analysis. The wavelet method is a modern and advanced tool for analyzing
time-series behavior in the time-frequency domain. The analysis of wavelet helps academics
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and practitioners to decompose a time-series (ψu, (t)) into several components that allow
deducing information over time. In line with earlier works like [51,52], a wavelet, ψ()2L
2
(R),
a real-valued or a complex-valued function defined over the real axis is expressed in the follow-
ing:
ctð Þ ¼ 1ffiffis
pctu
s
ð3Þ
in which 1=ffiffis
prepresents the factor of normalization ensuring that kψ
u,s
k
2
= 1, where you rep-
resent the position of the respective wavelet and s represents the parameter for scale dilation.
The wavelet specified by Morlet is defined as:
cM
0tð Þ ¼ p1=4eio0tet2
2ð4Þ
where ω
0
represents the wavelet’s central frequency that must be chosen appropriately to sat-
isfy a good balance between time and frequency localization [53,54].
3.2.3 Continuous wavelets. The continuous wavelet transform defined in [53,54]
(CWT), W
x
(u,s) through a ψ(.) projection on the time-series as:
Wxu;sð Þ ¼ Z1
1
xðtÞ1ffiffis
pctu
s
dt ð5Þ
where ψ(.) denotes the specific wavelet. The CWT could combine the function x(t)2L
2
(R)
such that
x tð Þ ¼ 1
ccZ1
0Z1
1
Wxðu;sÞcu;sðtÞdu
ds
S2;s>0:ð6Þ
The variance for the power spectrum can be specified as follows:
x tð Þ ¼ 1
ccZ1
0Z1
1 jWxðu;sÞ2jdu
ds
S2:ð7Þ
3.2.4 Cross-wavelet transform, wavelet coherence, and phase differences. This paper
employs the Cross-Wavelet Power (hereafter, XWP) to locate the high market price-co-move-
ment regions in the time-frequency domain. The two-signal cross-wavelet can be defined
through the spectrum of cross-wavelet (WXY
nðsÞ) as:
WXY
nðsÞ ¼ WX
nðsÞWY∗
nðsÞ;ð8Þ
where WY∗
nðsÞrepresents the complex conjugate of WX
nðsÞ.WXY
nðsÞ. The theoretical distribution
of the cross-wavelet power of two signals with power spectra PX
kand PY
kis given in the follow-
ing form:
DjWX
nðsÞWY∗
nðsÞj
sXsY<p
¼ZvðpÞ
vffiffiffiffiffiffiffiffiffiffiffi
PX
KPY
K
p;ð9Þ
where
σ
Xand
σ
Ydenote the standard deviations of xand y,Z
v
(p) represents the confidence
interval with p to be the probability density function following a χ
2
Distribution. The wavelet
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coherence is computed as:
R2u;sð Þ ¼ jSðs1Wxyðu;sÞÞj2
Sðs1jWxðu;sÞj2Þ:Sðs1jWyðu;sÞj2Þ;ð10Þ
In the above equation, the smoothing parameter is denoted by S. The coefficient of squared
wavelet-coherence (CSWC) satisfies the inequality condition of 0R
2
(u,s)1. R
2
(u,s)
approaching one (zero) implies a high (weak) correlation. Due to the above reasons, the wave-
let-coherence approach is considered the most appropriate method to inspect a variable in
time and frequency domains. In addition, the two time-series phase-difference variables, that
is, ϕ
x,y
. It can be used to distinguish between the phase-relationship. The phase difference
defined below determines the positions in the pseudo-cycle:
x;y¼tan1TfWxy
ng
RfWxy
ng
with x;y2 p;p½ :ð11Þ
As shown in Table 1, Arrows are designed to describe the phase and lead-lag relationships.
Right (Left) pointing arrows indicate that the two variables correlate positively (negatively).
Besides, an arrow’s right and up or left and down direction indicates that x(t) leads to y(t).
Similarly, the left and up or right and down arrow movement indicates y(t) leads x(t).
3.2.5 Wavelet-based granger causality. Even though economic theory is built on two-
time scales, examining the different periods is crucial since they have different causal links.
Time series commonly contain high- and low-frequency components. This study uses a non-
parametric method to assess the Granger causality in spectral density matrices produced via
wavelet modification. Wilson-Burg spectral factorization and non-linear variance decomposi-
tion are employed [55]. The spectral matrix elements obtained by a wavelet transformation of
a time series are measured using Sab ¼ ½WXaðt;fÞWXb ðt;fÞ∗where a = 1, 2; b = 1.2. Here
W
Xa
(t,f) represent the continuous mother wavelet transformation employing the mother
wavelet function, C(η), which is articulated as:
W t;sð Þ ¼ jSj0:5Z1
1
xðZÞC∗ðZ1
sÞdZð12Þ
*specifies a complex conjugate. The data’s time-frequency representation is obtained by
varying the scale parameter s and decoding over time t, yielding the wavelet function’s loca-
tion. This study chose the Morlet wavelet, which is a plane wave modulated by a Gaussian
envelope, CðZÞ ¼ p1=4expðioZÞexpð Z2=2ÞWith ω6 as the wavelet function. The Gaussian
envelop, exp(−η
2
/2) commendably confines the wavelet in time, and ωcontrols the time/fre-
quency determination. The terms frequency and scale are used interchangeably (sf). The
time-frequency domain resolution is inversely related, as shown by the fact that a more signifi-
cant value improves frequency resolution but reduces time resolution [56]. Among wavelet
types, the Morlet wavelet provides the best data time-frequency distribution. The cycle analysis
process commonly makes use of it. The Morlet wavelet is a type of wavelet analysis that bene-
fits from the varying periods of non-stationary data. It can detect high-frequency or short-
term changes [57]. To factorize the spectral density matrix S into a collection of unique lowest
phase (thus, stable inverse) functions, use the Wilson-Burg matrix factorization theorem [58].
S¼cc∗ð13Þ
where *denotes the matrix adjoint, and ψdenotes the minimum-phase spectral density matrix
factor, with cðexpðif ÞÞ ¼ P1
k¼0Axexp expðikf Þ. Here, A
k
equals 1
2p
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Table 1. Descriptive statistics.
Panel D 1993–2021
Description MALAYSIA CHINA FRANCE GERMANY INDIA INDONESIA JAPAN PAKISTAN SINGAPORE UK USA
Mean 0.011 -0.002 0.021 0.021 0.040 0.037 0.006 0.013 0.009 0.012 0.032
Median 0.000 0.000 0.027 0.055 0.000 0.000 0.000 0.000 0.000 0.014 0.036
Maximum 23.263 14.036 10.363 11.125 16.423 16.829 13.062 14.199 10.974 9.265 11.043
Minimum -24.159 -14.457 -13.150 -13.341 -13.740 -19.145 -10.435 -15.733 -9.833 -11.503 -12.922
Std. Dev. 1.263 1.792 1.318 1.367 1.458 1.764 1.291 1.651 1.191 1.095 1.147
Skewness 0.766 0.014 -0.245 -0.264 -0.287 -0.129 -0.203 -0.430 -0.036 -0.342 -0.456
Kurtosis 59.940 9.200 9.438 9.187 11.182 14.370 9.231 10.152 10.385 11.220 14.910
Jarque-Bera 1022683 12116 13139 12153 21207 40767 12291 16355 17193 21445 44972
Probability 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Sum 84.781 -18.284 155.987 159.689 301.383 281.454 46.827 96.150 68.118 90.403 242.493
Sum Sq. Dev. 12063 24290 13133 14125 16088 23530 12599 20622 10727 9066 9959
Observations 7565 7565 7565 7565 7565 7565 7565 7565 7565 7565 7565
Panel C 1997–98
Description MALAYSIA CHINA GERMANY FRANCE INDIA INDONESIA JAPAN PAKISTAN SINGAPORE UK USA
Mean -0.356 -0.314 0.027 0.011 -0.092 -0.358 -0.118 -0.165 -0.197 0.011 0.035
Median -0.575 -0.388 0.160 0.015 0.000 -0.207 -0.118 0.000 -0.124 0.046 0.078
Maximum 23.263 12.725 5.594 6.076 7.288 16.829 6.814 14.199 10.974 3.493 4.859
Minimum -24.159 -14.457 -7.532 -4.991 -5.590 -19.145 -5.099 -15.733 -8.999 -3.610 -6.967
Std. Dev. 3.904 3.325 1.655 1.443 1.597 3.729 1.427 2.837 2.056 1.122 1.256
Skewness 0.888 0.117 -0.749 -0.304 0.137 -0.205 0.248 -0.647 0.577 -0.248 -0.824
Kurtosis 14.395 5.533 5.099 4.790 4.428 7.336 5.228 9.237 8.848 3.707 9.330
Jarque-Bera 1812.04 88.16 90.64 48.70 28.80 258.52 71.02 552.76 484.10 10.17 582.93
Probability 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.006 0.000
Sum -116.322 -102.614 8.750 3.580 -30.131 -117.124 -38.679 -53.894 -64.553 3.621 11.283
Sum Sq. Dev. 4968 3603 893 678 831 4533 664 2624 1379 410 514
Observations 327 327 327 327 327 327 327 327 327 327 327
Panel B 2008–09
Description MALAYSIA CHINA FRANCE GERMANY INDIA INDONESIA JAPAN PAKISTAN SINGAPORE UK USA
Mean -0.099 -0.097 -0.120 -0.110 -0.047 -0.037 -0.149 -0.149 -0.124 -0.090 -0.081
Median -0.009 0.000 -0.083 0.000 0.000 0.016 -0.030 0.000 -0.086 -0.032 0.006
Maximum 4.326 12.853 8.501 5.733 7.073 8.973 5.006 9.330 6.099 8.489 5.227
Minimum -10.242 -10.813 -6.888 -7.386 -9.494 -8.008 -5.992 -5.122 -6.492 -5.549 -9.160
Std. Dev. 1.288 2.757 1.569 1.365 2.207 2.155 1.712 1.888 1.618 1.561 1.491
Skewness -1.406 0.188 0.252 -0.291 -0.228 -0.174 -0.212 0.062 0.145 0.308 -0.666
Kurtosis 14.862 5.233 6.597 6.937 4.554 5.196 3.756 5.458 4.609 6.078 7.630
Jarque-Bera 2024.880 69.856 179.736 215.799 35.749 67.335 10.225 82.544 36.411 134.267 316.282
Probability 0.000 0.000 0.000 0.000 0.000 0.000 0.006 0.000 0.000 0.000 0.000
Sum -32.360 -31.714 -39.217 -35.922 -15.211 -11.951 -48.748 -48.709 -40.467 -29.302 -26.543
Sum Sq. Dev. 540.848 2477.562 802.829 607.244 1587.950 1513.658 955.360 1161.785 853.852 793.945 724.436
Observations 327 327 327 327 327 327 327 327 327 327 327
Panel A 2020–21
Description MALAYSIA CHINA FRANCE GERMANY INDIA INDONESIA JAPAN PAKISTAN SINGAPORE UK USA
Mean -0.017 0.078 0.008 0.027 0.066 -0.046 0.044 -0.089 -0.010 -0.041 0.073
Median 0.000 0.100 0.052 0.056 0.194 0.000 0.000 0.000 0.000 0.023 0.166
Maximum 6.794 4.870 8.058 9.900 8.459 14.444 7.056 4.931 6.504 8.494 8.983
Minimum -5.523 -6.172 -13.150 -13.341 -13.740 -8.430 -5.691 -7.791 -7.411 -11.503 -12.922
(Continued)
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Rp
pcðexpðif ÞÞexpð ikf Þdf ;where ψ(0) = A
0
, which is a real upper triangular matrix with con-
structive diagonal components. After an assessment of Eqs (4) and (6), we write the error
covariance matrix as:
S¼A0AT
0ð14Þ
Likewise, by rewriting Eq (6) as S¼cA1
0A0AT
0AT
0c∗and comparing Eqs (4) and (7), the
transfer function can be rewritten as:
H¼cA1
0ð15Þ
Here, ψψ*= HSH* * =*, and Tdenotes the matrix transposition. Spectral matrix factoriza-
tion is a vital and novel step to non-parametrically obtain Hand Sfrom spectral analysis. The
Wilson-Burg algorithm is a widely used factorization method that achieves superb numerical
efficiency. It eliminates the effort from O(N
2
) to O(N
3
) operation when carrying out factoriza-
tion. The Wilson-Burg algorithm is a commonly used spectral density matrix factorization
algorithm. The convergence theorem of [56] ensures validity. The noise covariance matrix and
the transfer function in Eqs (14) and (15) produced from Wilson-Burg factorization into the
spectral Granger causality formula in Eqs (14) and (15) are used to estimate non-parametric
wavelet Granger causality.
We use a wavelet approach to determine the synchronization between the selected stock
markets. Wavelets are excellent at capturing the non-stationary behavior and time-varying
trends present in the stock volatility data. In the frequency-time domain, the wavelet can be
used to analyze risk co-movements in OECD and developing stock markets [59,60]. The
cross-wavelet transforms and wavelet coherence are discussed in this study as tools for analyz-
ing the cointegration between two-time series. Additionally, this study demonstrates how the
Granger causality test can confirm causal linkages and evaluate the mechanical model of physi-
cal links between related time series. Red noise backgrounds are used to evaluate the statistical
significance through Monte Carlo simulation techniques. Furthermore, shocks that affect the
interrelationships between time series can be timed more precisely with the help of wavelets.
4. Results and discussions
4.1 Summary statistics
The time series regular stock price and the return graphs describe the changing means and vol-
atility for the sampling period 1993 to 2021 and display the volatility clustering, an assumption
of the research modeling.
Fig 1 above shows that all indices show a simultaneous decline in the stock market in
response to the financial crisis of 1997–98, 2001, 2008, 2012, 2015, and 2020. The decline in
Table 1. (Continued)
Std. Dev. 1.130 1.565 1.841 1.813 1.789 2.056 1.312 1.653 1.411 1.690 1.981
Skewness -0.192 -0.480 -1.273 -1.248 -1.760 0.547 -0.067 -1.149 -0.375 -1.048 -0.988
Kurtosis 9.329 4.199 13.850 15.530 17.810 12.074 7.330 7.974 9.432 12.460 13.507
Jarque-Bera 546.069 32.030 1687.105 2217.145 3147.506 1134.785 254.877 407.743 569.652 1275.350 1552.489
Probability 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Sum -5.547 25.404 2.627 8.829 21.588 -14.998 14.225 -29.121 -3.258 -13.264 23.780
Sum Sq. Dev. 414.771 795.694 1102.100 1067.762 1039.628 1373.342 559.717 887.581 647.300 927.765 1275.483
Observations 326 326 326 326 326 326 326 326 326 326 326
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China’s stock market was also observed in July 2015 due to the Devaluation of the China Stock
market and its impact on China’s trading partners. However, higher trends have been observed
since 2015 in Indonesia, Malaysia, the USA, and India than in other countries like China, Sin-
gapore, and China. The UK, France, Germany, and Pakistan trend pattern shows that the 2015
China currency devaluation has affected the market but does not follow the same pattern. The
disparity in the trend of each stock with other country markets shows the low correlation
between them. We can see the return volatility of each stock market concerning return in the
above figure. Every selected market had volatility clustering during the financial crisis. Still,
Malaysian return volatility was low as compared to the other stock markets during the finan-
cial crisis of 2008–9, but Malaysian return volatility was high during the financial crisis of
1997–98, which means that the global financial crisis of 1997–98 has more effect on Malaysian
economy as compared to the global financial crisis of 2008–9. Some preliminary GARCH and
wavelet assumptions justify this methodology’s selection and make them suitable for the cur-
rent study.
The selected stock market returns’ descriptive statistics in Panel D (1993–2021), the Malay-
sian stock market index has an average return that is positive 0.011207, with a maximum value
of 23.26283 and minimum -24.1591, the second lowest in the selected markets group. The pos-
itive return of Malaysia indicates the positive performance of the Malaysian stock market in
the selected timeframe. China has a negative mean value of -0.00242, with a maximum of
14.03612 and a minimum of -14.4569, the lowest value in the group. It means China’s stock
market performance is low due to the average stock market return in the respective time, indi-
cating the loss in the selected timeframe. France, Germany, Pakistan, Indonesia, UK, and the
Fig 1. Return volatility pattern of all selected markets.
https://doi.org/10.1371/journal.pone.0296712.g001
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USA have positive average returns, meaning these markets perform well due to the market
structure. The Indian Stock market has an average return of 0.039839, the highest average
return in the group during the selected period in panel D, which means that Indian Stock has
approximately 4% average return earned on their investment during that period.
In Panel C, the Malaysian stock market index has an average rerun of -0.35573, which
means that the Malaysian market faced a loss due to the financial crisis of 1997–98, with a min-
imum return of -24.1591 and a maximum of 23.26283 due to the high volatility due to bad
news of the crisis shock. From the given data, we can conclude that in the selected period of
panel C, Malaysian stock market performance is negative due to the financial crisis of 1997–
98. In Panel C, all the selected markets have negative average stock returns except Germany,
France, the UK, and the USA; these markets are developed and a small decline in their average
return due to the financial shock. The crisis impacted all markets, including OECD stock mar-
kets, due to the negative average return on a specific day. Malaysia and Indonesia Stock mar-
kets have the lowest average return in the group, which is -0.35573 and -0.35818, respectively,
which means that the financial shock of 1997–98 hit these economies very critically.
In panel B, the period of 2008–9, every stock market has a negative average stock return
due to the global financial crisis 2008 9. Malaysia has an average stock return of -0.09896,
China has -0.09698, Indonesia has -0.03655, Pakistan has -0.14896, and others have negative.
Japan has a -0.14908 average return, the lowest in the selected group. Indonesia has better than
all selected economies but has negative performance with an average return of -0.03655 during
the 2 08–9 global financial crisis. In panel A, Malaysia has an average return of -0.01701, Indo-
nesia -0.04601, Pakistan -0.08933, Singapore -0.00999, United Kingdom -0.04069, and other
markets China, Japan, USA, France and Germany have a positive average return. It means that
the negative average return stock markets faced the problem of COVID-19 critically by the
lockdown in their business, and that’s why their performance goes to the negative but those
countries that average return in this period is positive, it means that their supply chain is effec-
tive despite the pandemic crisis. In panel A, the country stock market with the highest average
return in the selected group is China, with 0.077928. Pakistan’s lowest average return country
has a negative average return of -0.08933. Due to these factors, China faced the first entry of
COVID-19, but the government of China made innovative measures to promote its economy
through different measures and controls.
The volatility or the fluctuation from its means of the stock prices can be measured through
the calculation of the standard deviation of the sample. If volatility from its means is greater,
there is a high risk in the stock prices. When we look at Panel D, the highest and lowest value
of the standard deviation in the selected markets is 1.792002 and 1.094799, representing China
and the United Kingdom, respectively. In Panel C, the stock price with the highest and lowest
standard deviation values is 3.903887 and 1.122109, representing Malaysia and the UK, respec-
tively, in the period of financial crisis 1997–98. Malaysia faced huge volatility or fluctuation in
the stock prices due to the financial crisis of 1997–98, but the lowest fluctuation is found in the
stock prices of the United Kingdom. In Panel B, China has the highest value of a standard devi-
ation of 2.756789, and Malaysia has the lowest value of 1.288039; it means that during the
Global financial crisis of 2008–9, China’s stock price fluctuated more as compared to the other
economies in the group. Still, Malaysia has the lowest fluctuation, even with a negative average
return of -0.09896. The highest and lowest standard deviation is being observed in Indonesia
and Malaysia, representing 2.055643 and 1.129698, respectively, meaning that Indonesian
Stock prices have greater return volatility than the selected markets. Malaysia has the lowest
volatility due to the strong measures by the central government. All the selected markets,
except the lowest and highest, go to approximately 1.5 value of standard deviation in their
stock return.
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The Skewness describes the normal distribution of data. If the skewness value is zero,
then we can say that the data set is normally distributed. Before the run of the analysis,
some assumptions of the model run should be fulfilled by the researchers. The data normal
distribution is also necessary for the data analysis to minimize errors. A skewness may be a
positive or negative value; if it is a positive skewness, it is suitable for the normal distribu-
tion of data because Skewness is the indicator of the normal distribution of the dataset. The
negative skewness means the values are not suitable. In panel D, all the countries’ stock
return skewness value except Malaysia and China is negative, which indicates the data set is
unsuitable for normal distribution and frequently changes due to crisis. Similarly, Malaysia
and China’s skewness value is positive, indicating a suitable normal distribution markets
dataset.
In panel C, some countries, like Malaysia, China, India, Indonesia, Japan, and Singapore,
have positive Skewness, indicating the suitable normal distribution of the dataset during the
period of the financial crisis of 1997–98. On the other side, in the selected group, Germany,
France, UK, USA, and Pakistan skewness value is negative, indicating a suitable value. Simi-
larly, In panel B, Malaysia, Germany, India, Indonesia, and the USA had negative skewness in
2008–9, while other selected countries had positive skewness that indicated suitability. Same as
in Panel A, all the country’s stock return skewness value is negative, indicating the non-suit-
able normal distribution of the financial market’s dataset in the period of COVID-19 due to
the lockdown of the business activities, and the dataset shows the abnormal changes from the
previous one due to pandemic.
The Kurtosis value in the descriptive statistics measures the probability in the tail of the bell
shape of the normal distribution diagram. The kurtosis value should equal 3, which is helpful
compared to the normal distribution. Our analysis considers that the Kurtosis value should be
greater than 3, meaning the selected dataset is normally distributed.
The goodness of fit of the sample normally distributed data based on the Skewness and Kur-
tosis value is represented by the Jarque-Bera test. The Jarque-Bera test should be far from zero
value. Jarque-Bera is also used to diagnose the normal distribution in datasets for large sample
sizes. The significant value at a 1% level of significant is adjusted to reject the null hypothesis
in our Jarque-Bera test analysis, and compared with the Kurtosis value, its Kurtosis value is
less than three, then we indicate that the data is not normally distributed. There is a necessary
assumption of the Generalized Autoregressive Conditional Heteroscedasticity (GARCH)
Modelling.
Table 2 summarizes the correlation matrix of the sample. If a positive correlation existed
between the two stock markets, then we can say that a common co-movement direction
existed. In our sample countries, stock market correlation ranges from 0.0056 to 0.8523,
respectively. Stock returns are below the value of 0.80, indicating weak co-movement and a
lack of multi-collinearity. In our correlation matrix, the correlation value between France and
the UK is above 0.80, indicating the strong co-movement between these countries’ stock mar-
kets return in panel D; both countries belong to the OECD economies. Same as in the period
of crisis of 1997–98, the correlation value between Germany-France and France-UK is above
0.80, indicating strong cointegration. However, Malaysia- Singapore has greater value in the
emerging economies but less than 0.80.
On the other hand, some stock markets show less value of the correlation between them
that seems more robust across developing countries, while smaller between OECD and emerg-
ing economies. Hence, we can consider these points in the diversification opportunity across
the regions. By keeping these points in mind, we can diversify our portfolio and earn the maxi-
mum expected return on the given investment by minimizing the risk.
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Table 2. Correlation matrix.
Correlation Panel D 1993–2021
Countries MALAYSIA CHINA FRANCE GERMANY INDIA INDONESIA JAPAN PAKISTAN SINGAPORE UK USA
MALAYSIA 1.000
CHINA 0.334 1.000
FRANCE 0.160 0.285 1.000
GERMANY 0.158 0.286 0.856 1.000
INDIA 0.187 0.336 0.286 0.264 1.000
INDONESIA 0.311 0.370 0.204 0.197 0.282 1.000
JAPAN 0.251 0.406 0.284 0.262 0.247 0.278 1.000
PAKISTAN 0.095 0.076 0.053 0.051 0.116 0.080 0.068 1.000
SINGAPORE 0.422 0.539 0.371 0.360 0.377 0.426 0.430 0.104 1.000
UK 0.185 0.297 0.850 0.777 0.283 0.206 0.285 0.048 0.380 1.000
USA 0.041 0.174 0.536 0.549 0.180 0.089 0.130 0.018 0.214 0.518 1.000
Panel C 1997–98
Countries MALAYSIA CHINA GERMANY FRANCE INDIA INDONESIA JAPAN PAKISTAN SINGAPORE UK USA
MALAYSIA 1.000
CHINA 0.377 1.000
GERMANY 0.177 0.258 1.000
FRANCE 0.175 0.177 0.752 1.000
INDIA 0.172 0.233 0.199 0.206 1.000
INDONESIA 0.324 0.327 0.234 0.201 0.209 1.000
JAPAN 0.253 0.299 0.350 0.394 0.109 0.292 1.000
PAKISTAN 0.159 0.170 0.130 0.126 0.049 0.080 0.121 1.000
SINGAPORE 0.467 0.522 0.303 0.280 0.206 0.417 0.322 0.303 1.000
UK 0.272 0.247 0.704 0.764 0.221 0.203 0.377 0.126 0.322 1.000
USA -0.062 0.014 0.401 0.463 0.113 -0.035 0.110 0.011 0.075 0.455 1.000
Panel B 2008–09
Countries MALAYSIA CHINA FRANCE GERMANY INDIA INDONESIA JAPAN PAKISTAN SINGAPORE UK USA
MALAYSIA 1.00
CHINA 0.52 1.00
FRANCE 0.31 0.34 1.00
GERMANY 0.31 0.33 0.95 1.00
INDIA 0.40 0.62 0.40 0.40 1.00
INDONESIA 0.52 0.62 0.28 0.29 0.49 1.00
JAPAN 0.48 0.65 0.34 0.33 0.47 0.43 1.00
PAKISTAN 0.14 0.04 0.07 0.05 0.14 0.08 0.12 1.00
SINGAPORE 0.54 0.75 0.51 0.47 0.62 0.62 0.62 0.09 1.00
UK 0.31 0.37 0.94 0.90 0.41 0.30 0.33 0.05 0.52 1.00
USA 0.02 0.09 0.54 0.50 0.14 0.15 0.05 0.04 0.18 0.52 1.00
Panel A 2020–21
Countries MALAYSIA CHINA FRANCE GERMANY INDIA INDONESIA JAPAN PAKISTAN SINGAPORE UK USA
MALAYSIA 1.00
CHINA 0.44 1.00
FRANCE 0.37 0.49 1.00
GERMANY 0.36 0.50 0.95 1.00
INDIA 0.51 0.52 0.59 0.55 1.00
INDONESIA 0.44 0.35 0.34 0.30 0.51 1.00
JAPAN 0.38 0.42 0.46 0.45 0.34 0.29 1.00
(Continued)
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4.2 Wavelet transformation estimates and discussion
4.2.1 Cross wavelet transformation of emerging and OECD countries. When localized
similarities are present, the typical feature extraction uses the Cross Wavelet Transform
(XWT) approach. This method requires fewer parameters than the other methods for classify-
ing timeframe features into normal and abnormal classifications. Additionally, this method
can produce more precise results because it is compatible with loud surroundings. Due to its
capacity to manage the imaginary portion of the input without employing the absolute func-
tion, it also keeps the information on the phase. Figs 2–5represent the XWT across the coun-
tries’ stock market indices return.
Moreover, we make four panels based on the crisis, considering D, C, B, and A, respectively.
Panel D represents the period from 1993 to 2021. Panel C represents the time domain of the
crisis period of 1997–98, the period of the Asian financial crisis. Moreover, panel B represents
the period of 2008–09, the Global financial crisis. Panel A represents the time domain of the
COVID-19 2020–2021 respectively. It should be emphasized that the arrows represent phase
Table 2. (Continued)
PAKISTAN 0.30 0.22 0.25 0.26 0.39 0.36 0.10 1.00
SINGAPORE 0.59 0.53 0.56 0.55 0.67 0.47 0.57 0.25 1.00
UK 0.29 0.47 0.91 0.88 0.54 0.28 0.46 0.19 0.53 1.00
USA 0.16 0.49 0.66 0.67 0.39 0.31 0.31 0.18 0.36 0.66 1.00
https://doi.org/10.1371/journal.pone.0296712.t002
Fig 2. Cross-wavelet power spectra of selected stock markets (Panel D 1993–2021): Cross- wavelet power spectra are considered significant at 5% under
the red noise prediction defined by Monte Carlo. The two variables have a positive relationship if the arrows are toward the right. Suppose the arrow is
towards the right and up. In that case, the first variable leads, and there is a positive relationship, or if arrows are toward right and downward, the variables first
are lagging and positive. On the other side, if the arrows are toward left and up, the first variable is lagging, and the relationship between variables is negative, or
if the arrows are toward left and down, then the variable is leading, and the correlation is negative.
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information that enables us to comprehend how various global markets interact with Malay-
sian markets.
The in-phase relationship in all selected country pairs is shown in Fig 2, related to Panel D
(1993–2021), indicated by the arrows towards the right, which can be found in the numerous
significant regions. In panel D, the pair Malaysia- India is an in-phase relationship during the
period of the crisis 2008–09, with Malaysia as the leading effect at the low-frequency domain
(32–128), but during the COVID-19 pandemic, both markets are in-phase relationship, and
Malaysia is lagging, and India is leading on the Malaysia stock market, It means that during
the financial crisis 2008–9, the Malaysian stock market drives Indian market but this seen is
opposite in COVID-19 period.
In the pair of Malaysia-China, a high level of covariance is found between two stock market
risks in the period of 1993 to 1999 at both high and low frequency domain, indicating the in-
phase relationship between these two-stock market risks and Malaysia is leading effect, arrows
are right and upward. The same level of covariance was observed in 2008–9 and 2020–21, and
Malaysia is leading the China stock market risk at different frequency domains.
Similarly, a different pattern of market risk behavior is being observed in the two pairs of
Malaysia-France and Malaysia-Germany, where both market risks are in phase, and Malaysia
is lagging from 1993 to 2012 at the high frequency of (1024–2048), indicating the high level of
the covariance between the risk of these selected countries and Malaysia is lagging because
arrows are right and downwards. In 2008–9 and 2020–21, there is also covariance between
these stock markets’ risk at low frequency, with Malaysia’s leading effect during 2020–21.
Fig 3. Cross-wavelet power spectra of selected stock markets during crisis 1997–98 (Panel C): Cross-wavelet power spectra are considered significant at
5% under the red noise prediction defined by Monte Carlo. Two variables have a positive relationship if the arrows are toward the right. Suppose the arrow is
towards the right and up. In that case, the first variable leads, and there is a positive relationship, or if the arrows are towards right and downward, the variables
first are lagging and positive. On the other side, if the arrows are toward left and up, the first variable is lagging, and the relationship between variables is
negative, or if the arrows are toward left and down, then the variable is leading, and the correlation is negative.
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In addition, quite a similar pattern is found for the Malaysia-US pair; the significant in-
phase relationship is shown during 2020–21 only, and Malaysia is the leading effect in that
period. However, the same pattern of risk is found in the pairs of Malaysia-Japan and Malay-
sia-Singapore, indicating the in-phase relationship between risks and Malaysia is leading (lag-
ging) from 1993 to 1994, 1995 to 2016, and 2020–21. High levels of covariance are also shown
in these pairs during the financial crisis period of 1997–98 and 2008–9.
In the pair of Malaysia-Indonesia, we found the covariance during 2008–9 and 2020–21 at a
medium level of the frequency domain, indicating the in-phase relationship with Malaysia is
the leading effect. The arrows are right(upward). In the pair of Malaysia- Pakistan, in-phase
relations are shown between these two stock market risks, indicating the high level of covari-
ance between these two stock market risks; Malaysia is leading to the risk of Pakistan stock
market from 1997 to 2008, 2008–9 and 2020–21 at the high, medium and low-frequency
domain, means the high, medium, low level of covariance between the risk are found between
the pairs.
Similarly, the same Parten is found between the Malaysia-USA stock market risk pair,
where in-phase relationships are found. Still, Malaysia has a lagging effect from 1993 to 1997,
1997–98, and 2008–9 at low, medium, and high-frequency domains. This finding shows that
the positive relationship between the time series USA stock market drives Malaysia. From our
findings of Panel D, we show that Malaysia’s stock market risk is correlated with all trading
partners during the crisis period and also after the crisis period, where Malaysia’s stock market
risk drives the other trading partners stock market risk and sometimes other trading partners
Fig 4. Cross-wavelet power spectra of selected stock markets during crisis 2008–09 (Panel B): Cross-wavelet power spectra are considered significant at
5% under the red noise prediction defined by Monte Carlo. The two variables have a positive relationship if the arrows are toward the right. Suppose the
arrow is towards the right and up. In that case, the first variable leads, and there is a positive relationship, or if arrows are toward right and downward, the
variables first are lagging and positive. On the other side, if the arrows are toward left and up, the first variable is lagging, and the relationship between variables
is negative, or if the arrows are toward left and down, then the variable is leading, and the correlation is negative.
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stock market risk drives the Malaysian stock market risk at different frequency levels and at
different time domains.
Additionally, high levels of covariance are shown in XWT transformation for all emerging
and OECD stock market pairs with Malaysia from 1993 to 2021; we denoted it as panel D in
Fig 2. Our findings are consistent with the findings of [61–63]. We also found the co-move-
ment in risk of some degree between Malaysia and its trading partners at low, medium, and
long horizons in panel D.
In panel C (1997–98), the covariance between Malaysia-India, Malaysia-USA, Malaysia-
France, Malaysia-Germany, Malaysia-Japan, and Malaysia-Pakistan- Malaysia-UK is seen pos-
itive from July to September 1997 in high frequency. We make the three months for finding
the relationship between them according to the quarterly effect. In these pairs, Malaysia is lead-
ing effect, which means that in the crisis period from July to September 1997, the stock markets
of India, USA, France, Germany, Japan, Pakistan, and the UK are driven by Malaysia due to
leading effect, indicating arrows are right (upwards). In the pair Malaysia-China, there is also
positive covariance from July to September 1997, but Malaysia has a lagging effect due to the
arrows being right (downwards). An in-phase (positive) relationship is found only in Malay-
sia-Singapore and Malaysia-Indonesia. During December 1997, all the pairs were in a phase
relationship, showing the positive covariance between them. During September 1998, all the
selected pairs were in an in-phase (positive) relationship. From September to October 1998,
Malaysia-Singapore Malaysia-India pairs, in which Malaysia is lagging effect at a higher fre-
quency due to the trade fluctuation between them. Our results consisted of the findings of
[64], also opposite to those of [65], which shows the negative covariance between selected
Fig 5. Cross-wavelet power spectra of selected stock markets during the pandemic COVID-19 2020–21 (Panel A): Cross- wavelet power spectra are
considered significant at 5% under the red noise prediction Monte Carlo defines. If the arrows are toward the right, two variables have a positive
relationship. Suppose an arrow is towards the right and up. In that case, the first variable is leading, and there is a positive relationship, or if the arrows are
towards right and downward, the variable first is lagging and has a positive relationship. On the other side, the first variable is lagging if the arrows are toward
the left and up. The relationship between variables is negative, or if the arrows are towards the left and down, the variable leads, and the correlation is negative.
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markets in that period. In panel A (for the period 2020–21), in all the selected pairs, risk
covariance is positive between them from March to August 2020, indicating that in the period
of the COVID-19 disease, one economy transferred the financial risk to another economy. All
the pairs show a high level of covariance from March to August 2020, and that’s why co-move-
ment between the stock market is high in that period.
4.2.2 Wavelet coherence transformation of emerging and OECD countries. Figs 6–9
exhibit wavelet coherence results at different intervals. It is shown that overall, the Malaysia
stock market risk moves significantly with its emerging and OECD trading partners. In addi-
tion, a relatively large portion of the wavelet coherence area often turns into the region of core
of influence (COI), which represents the significant, with left to right turns arrows, which indi-
cates that Malaysia is in-phase (Positive covariance) with its all-selected trading partners.
In Panel D (1992–2021), as the emerging trading partners for the couple Malaysia-China,
Malaysia-Pakistan, and Malaysia-Indonesia, the right arrows indicate the positive covariance
between them at a higher frequency domain from 1993 to 2021; in this way, our findings are
consistent with the result of [66] that China, Malaysia, and Indonesia stock market risk are
correlated at high frequency due to the trade agreements between them.
The covariance between emerging and OECD economies is very interesting for both
regions. The risk covariance pattern between the pair Malaysia-Germany, Malaysia-UK, and
Malaysia-France is positive, indicating the arrows are right (downwards) from 1993 to 2021,
showing that Malaysia is lagging the Stock market of Germany, France, and the UK at a higher
frequency. Still, during 2020–21, they had a high-risk covariance level.
Fig 6. Wavelet coherence of selected stock markets during crisis 1993–2021 (Panel D).
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In addition, in the pair of Malaysia-US, there is an in-phase relationship being seen in the
period of 1997–98, 2007, and 2020 for the short run at a low frequency that shows the low level
of the covariance due to the US and China Trade conflicts, China is the trade agreement with
Malaysia already. In this context, our findings are consistent with the findings of [67]) that
Malaysia and China are cointegrated with the USA at low frequency due to the conflicts. High
co-movement was found between Malaysia and Japan at both medium and high-frequency
domains from 1993 to 2021. In the pair of Malaysia-Singapore, positive cointegration is found
between the risk of the stock markets at a low, medium, and high-frequency domain, indicat-
ing that the arrows are right due to the large trading volume between them. The in-phase rela-
tionship between the couple Malaysia-India during 2008–9 and 2020–21 at medium frequency
domain considers the weak relationship in the selected group.
In panel A (2020–21), all the selected couples have an in-phase(positive) significant rela-
tionship, indicating the arrows are right and up(down), showing the leading and lagging risk
of the Malaysia stock market for the time January 2020 to June 2021. Malaysia has to lead in
the couple Malaysia-France and Malaysia-Japan during March 2020 because the arrows are
right and up. Still, Malaysia lags in Malaysia-Indonesia and Malaysia-China pairs because the
arrows are from October to December 2021.
4.3 Robustness: Wavelet-based Granger causality test
To complement our findings of the XWT and WCOH using the robustness test, we applied a
wavelet-based Granger causality test using the four frequency domains (D1, D2, D3, and D4),
and the results are exhibited in Table 3.Fig 10 also shows the directions of the causality
between the selected stock markets. In our findings, most of the selected market has bi-
Fig 7. Wavelet coherence of selected stock markets during Crisis 1997–98 (Panel C).
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directional causalities between Malaysia’s stock market and its trading partners. Still, the fre-
quency domain varies from one pair to another pair or from one region to another. In particu-
lar, we find the bi-directional causation between the Malaysia stock market and the US, UK,
France, Germany, Indonesia, and Singapore in the D1 frequency domain, corresponding to
the short and long horizons. In addition, we find the unidirectional causality transfer from
India and Pakistan, where both countries’ stock markets caused the Malaysia stock market due
to the trading that existed between them. These findings confirm the strong correlation
between them over the D1 frequency domain.
Similarly, we find bi-directional causality in D2 and D3 between the Malaysia-Indonesia
and Malaysia-China. In a similar pattern, there is unidirectional causality between Malaysia,
Japan, and Singapore, and there is also bi-directional causality between Malaysia and the USA,
France, Germany, and China in the D1 frequency domain. In addition, in the D3 frequency
domain, bi-directional causality between Malaysia and Japan, India, Pakistan, China, and Sin-
gapore found, also unidirectional causality find between Malaysia and UK, USA, France, Ger-
many, where these countries stock market causes the Malaysia stock market over the D3
frequency domain. Interestingly, causality results show evidence of only two pairs of bi-direc-
tional causality found between Malaysia-Pakistan and Malaysia-UK in frequency domain D4.
All the other countries except Japan cause Malaysia to be in the D4 frequency domain. In the
original frequency domain from 1993 to 2021, bi-directional causality was found between
Malaysia-Singapore, Malaysia-Indonesia, and Malaysia and China couples; the rest of the
countries had unidirectional causality with Malaysia and caused to Malaysia stock market at
the overall selected time domain.
Fig 8. Wavelet coherence of selected stock markets during crisis 2008–09 (Panel B). Wavelet Coherence is considered significant at 5% under the red noise
prediction defined by Monte Carlo. The two variables have a positive relationship if the arrows are towards the right. Suppose the arrow is towards the right
and up. In that case, the first variable leads, and there is a positive relationship, or if arrows are toward right and downward, the variables first are lagging and
positive. On the other side, if the arrows are toward left and up, then the first variable is lagging, and the relationship between variables is negative, or if the
arrows are toward left and down, then the variable is leading, and the correlation is negative yet.
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The Granger causality test shows evidence of significant bi-directional and unidirectional
causalities transfer from Malaysia to other trading partners and vice versa over all the selected
frequency domains. This is consistent with the idea that there will not be an issue of the leader
position between the Malaysian stock market and its trading partners in the long run, except
for Indonesia, Singapore, and China. Similarly, when we compare the OECD country’s causal-
ity, we find the unidirectional causality transfer from the OECD economy to Malaysia on the
different time horizons.
These findings imply that the temporary shocks of the developed or OECD country’s stock
markets directly impact the Malaysian stock market, extending to the longer scale. At the same
time, proximity does not affect stock market correlation as Malaysia and its trading partners
need longer to absorb each stock market shock and adjust their prices accordingly. To sum up,
our time-frequency domains causality analysis (D1, D2, D3, and D4) sheds light on the time
the Malaysian market requires to interact with its trading partners and the nature of the lead-
lag relationship. This time-frequency is very helpful for investors to decide on the investment
in Malaysian stock market by considering the shock effect and its captured period.
4.4 Robustness: Dynamic conditional correlation GARCH
When one univariate time series has impact on the other univariate time series then we can
say that multivariate analysis existed. Same as, when one stock market effect the other stock
Fig 9. Wavelet coherence of selected stock markets during crisis 2020-2021(Panel A) in panel C (1997–98), there is a high level of co-movement being
found between the pairs Malaysia-China and Malaysia-Singapore; co-movement is high from October 1997 to October 1998 at medium and high-
frequency domain because arrows are right at both frequency domains. In pairs, Malaysia-Pakistan, Malaysia-UK, Malaysia-Japan, Malaysia-France, and
Malaysia-Indonesia in-phase relationships are being observed from June 1997 to August 1997 at frequency domain, indicating the short-run relationship
between the risk of these stock market in the period of financial crisis and findings are similar with [51,68]. The Malaysia-India Pair has high co-movement,
and an in-phase relationship is observed from October 1998 to December 1998.
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Table 3. Granger causality test for emerging and OECD economy at various frequencies.
Frequency
Domain
Independent
Variable
Dependent Variable
D1 COUNTRY MALAYSIA FRANCE GERMANY INDIA INDONESIA JAPAN CHINA PAKISTAN SINGAPORE UK USA
MALAYSIA 28.6557*** 26.7694*** 3.80154 3.02885** 0.60684 1.71034 0.0698 2.88212*33.8582*** 38.4182***
FRANCE 75.9992*** 0.0682 4.51507** 67.8841*** 424.532*** 120.442*** 10.5533*** 85.3534*** 2.29458 53.4729***
GERMANY 70.0670*** 17.3533*** 12.5668*** 50.521*** 387.968*** 115.541*** 7.52839*** 101.457*** 4.06290** 32.0487***
INDIA 14.1105*** 4.86897*** 6.15997*** 11.7796*** 28.273*** 3.041** 2.29766 0.13490 6.26184*** 23.5285***
INDONESIA 9.65302*** 17.1649*** 11.8088*** 2.03964** 1.3804 2.867*0.00179 6.95935*** 23.9739*** 37.4060***
JAPAN 0.43267 104.655*** 112.361*** 13.8025*** 2.28665 4.88667*** 1.40205 14.0055*** 98.4597*** 187.247***
CHINA 0.89978 41.6071*** 49.412*** 10.122*** 5.143*** 10.9336*** 0.32728 18.5211*** 28.4779*** 80.8209***
PAKISTAN 3.10963** 10.1536*** 4.55114** 0.64473 5.18940*** 1.27871 0.15352 1.29909 8.35943*** 9.00903***
SINGAPORE 11.5834*** 23.7754*** 29.0600*** 2.19485 1.95247 32.7822*** 11.8897*** 1.11372 28.5613*** 87.1038***
UK 85.2226*** 8.89413*** 2.40883*7.52932*** 68.0097*** 442.307*** 114.61*** 11.6413*** 105.112*** 65.3502***
USA 134.802*** 213.191*** 141.525*** 39.4526*** 126.872*** 525.209*** 214.422*** 9.66359*** 260.381*** 215.185***
D2 COUNTRY MALAYSIA FRANCE GERMANY INDIA INDONESIA JAPAN CHINA PAKISTAN SINGAPORE UK USA
MALAYSIA 5.71866*** 6.51985*** 0.29738 3.06033** 2.16027 14.7231*** 0.06581 0.95483 6.71971*** 2.62718*
FRANCE 21.3409*** 23.6925*** 24.5467*** 36.1723*** 206.325*** 83.1279*** 0.48017 48.388*** 0.37406 14.8087***
GERMANY 18.6352*** 21.8052*** 13.9922*** 18.8025*** 211.828*** 80.4971*** 0.47477 36.5117*** 9.07076*** 4.71015***
INDIA 1.34287 2.68403*1.35587 3.11801** 25.4501*** 9.60525*** 0.94194 0.09472 3.8866** 0.40824
INDONESIA 19.7424*** 6.71043*** 4.74873*** 0.89180 4.23277** 13.2238*** 0.34392 6.18031*** 4.79488*** 2.54911*
JAPAN 3.18695** 17.5963*** 14.4197*** 6.71078*** 2.11674 1.70311 1.10235 3.44271** 19.9438*** 11.2431***
CHINA 21.5171*** 5.86958*** 11.1162*** 9.6574*** 2.20801 5.42748*** 1.13144 16.1407*** 2.91681*8.28519***
PAKISTAN 0.10424 9.97116*** 5.13841*** 0.55164 0.20960 1.40741 0.49115 0.55134 6.67498*** 6.68089***
SINGAPORE 4.31391** 0.83394 4.08216** 3.18682** 5.75960*** 36.4177*** 24.6301*** 1.12653 2.12085 5.10276***
UK 18.2857*** 4.59388** 6.93552*** 19.4852*** 31.1229*** 166.298*** 57.0599*** 0.73125 41.5295*** 17.8413***
USA 67.3852*** 158.816*** 115.914*** 49.1388*** 82.9117*** 390.367*** 165.877*** 3.35795** 163.698*** 172.341***
Frequency
Domain
Independent
Variable
Dependent Variable
D3 COUNTRY MALAYSIA FRANCE GERMANY INDIA INDONESIA JAPAN CHINA PAKISTAN SINGAPORE UK USA
MALAYSIA 0.67136 0.27848 3.76825** 5.46947*** 2.74132*4.5931** 11.7335*** 3.6397** 0.17766 0.79647
FRANCE 36.3167*** 8.93080*** 19.5716*** 12.1629*** 159.689*** 20.4713*** 1.82804 21.9447*** 11.2791*** 8.3524***
GERMANY 31.6780*** 1.77589 21.5294*** 17.5858*** 144.273*** 11.3062*** 1.06242 27.2522*** 10.3773*** 6.05603***
INDIA 9.41455*** 1.10099 0.30308 5.21466*** 8.79452*** 2.94943*1.7399 0.62155 1.00675 0.49012
INDONESIA 14.7413*** 7.60283*** 8.34136*** 0.52667 8.34424*** 0.99076 4.23202** 0.2548 2.01955 5.26463***
JAPAN 8.07308*** 0.34113 0.26327 2.25932 6.04226*** 5.69743*** 3.26832** 4.94862*** 4.2398** 3.12301**
CHINA 40.9882*** 2.66644*4.34339** 0.28341 1.64833 9.22877*** 8.37448*** 1.69116 1.09767 2.29522
PAKISTAN 12.9557*** 2.25964 3.05106** 9.50798*** 5.80874*** 2.17087 4.27675** 2.35309*2.92891*0.18028
SINGAPORE 20.8068*** 3.15608** 2.99052*2.56655*4.64778*** 30.6046*** 4.08046** 10.197*** 3.42441** 2.55878*
UK 32.8545*** 11.8029*** 14.1045*** 20.4557*** 18.1974*** 154.407*** 37.7490*** 1.3173 21.3149*** 1.10527
USA 88.3633*** 166.451*** 127.675*** 50.6238*** 42.4667*** 283.792*** 105.794*** 3.74623** 133.248*** 151.93***
(Continued)
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Table 3. (Continued)
D4 COUNTRY MALAYSIA FRANCE GERMANY INDIA INDONESIA JAPAN CHINA PAKISTAN SINGAPORE UK USA
MALAYSIA 1.18269 0.90002 1.22322 1.12337 2.22936 7.74383*** 2.85105*0.46287 4.02973** 0.2769
FRANCE 21.1854*** 1.7694 4.15802** 17.6496*** 121.185*** 25.4856*** 17.1764*** 42.8507*** 2.25643 3.48096**
GERMANY 28.5271*** 0.88988 14.4717*** 24.8448*** 123.165*** 40.1521*** 15.9035*** 57.2591*** 3.63715** 9.13691***
INDIA 3.25677** 3.47653** 1.16248 5.16604*** 17.4677*** 3.58501** 10.0019*** 1.72061 2.15458 0.56198**
INDONESIA 17.0644*** 1.82212 4.07687** 0.68922 7.51116*** 0.44116 7.08634*** 1.90852 2.26426 2.4693*
JAPAN 0.85549 7.40225*** 13.3034*** 4.67244*** 3.87664** 6.50018*** 4.13203** 2.93250*14.0712*** 1.17098
CHINA 0.0537 1.00142 3.12835** 0.73845 1.00117 8.60384*** 10.9483*** 0.44276 2.2436 2.19754
PAKISTAN 4.18613** 1.15942 0.31093 0.62048 0.71407 2.64772*0.57068 1.36098 2.33079*1.15827
SINGAPORE 5.17499*** 0.32545 0.37698 1.83741 10.8303*** 13.7522*** 0.76095 9.14092*** 1.37432 0.7737
UK 16.4921*** 3.16723** 1.45144 8.91715*** 14.5824*** 101.330*** 17.9989*** 17.5267*** 47.8071*** 5.87309***
USA 39.7472*** 65.6574*** 45.9539*** 22.5265*** 28.327*** 169.606*** 44.6668*** 24.8038*** 89.6227*** 74.6483***
Frequency
Domain
Independent
Variable
Dependent Variable
Original COUNTRY MALAYSIA FRANCE GERMANY INDIA INDONESIA JAPAN CHINA PAKISTAN SINGAPORE UK USA
MALAYSIA - 4.7307 3.0653 9.8700 50.6917*** 5.6539 18.311*** 8.1884 19.5525*** 6.7328 2.1507
FRANCE 21.6337*** - 22.081*** 26.1415*** 18.4011*24.9588*** 14.0096** 8.2880 13.3823*37.4406*** 12.0193*
GERMANY 17.7834*** 13.5710** - 30.4171*** 33.1515*** 10.2059 15.3847*** 2.4271 12.4512*10.5856 11.6200
INDIA 17.9042*** 6.1672 7.9953 - 12.3027*7.2776 11.9493*22.7252*** 11.8569*14.5220** 12.7171*
INDONESIA 69.8378*** 19.3386*** 12.7047*4.4243 - 6.2905 19.1970*** 8.2145 9.5827 10.6620 12.2390*
JAPAN 20.7662*** 3.1915 12.2572*21.0298 47.3353*** - 71.4622*** 4.4740 54.2252*** 15.6457** 6.71831
CHINA 36.5633*** 9.387 14.6043** 13.0117*17.5991*16.112** - 9.9395 24.2604*** 3.7647 4.6794
PAKISTAN 18.6574*** 17.0594*** 5.7103 6.5377 20.8076*** 3.1609 4.9337 - 5.7345 14.9156** 11.8055*
SINGAPORE 12.5824*7.4685 9.7981 10.2697 20.8210*** 15.5846** 7.5710 7.1126 - 5.0112 8.7894
UK 23.4694*** 26.7443*** 23.3432*** 13.5713*9.4483 32.7390*** 35.5893*** 11.2170 34.9255*** - 15.6891**
USA 248.4180*** 659.2065*** 530.6530*** 178.9931*** 262.8604*** 601.3178*** 402.7803*** 21.6220*** 571.5506*** 787.252*** -
Note. level of significance is 1%, 5%, and 10%, respectively and represented by ***,** and *
https://doi.org/10.1371/journal.pone.0296712.t003
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market in the same or different regions, then we can say that there is multivariate relationship
existed between them. To find the relationship between volatilities and co-volatilities of several
univariate stock markets then we can use the Multivariate GARCH model. DCC GARCH is a
type of the Multivariate GARCH methodology. The motivation of using Multivariate method-
ology is to find the correlation between the volatility between two or more stock markets.
Another motivation is to make the portfolio allocation on the basis of co-integrated markets
and spillover impact. The volatility in one stock market transfers to the other stock market, it
means that these markets are co-integrated. Investors are more critical for making investment
in co-integrated markets. In this study, we used the DCC GARCH model because DCC
GARCH model parametrized the conditional correlation directly. In view to DCC-GARCH,
the one stock market interdependence on the other stock market. The relationship between
two or more variables which depend on previous past information that changes over time, not
constant, is the Dynamic condition correlation GARCH (DCC-GARCH) model. The condi-
tional correlation in the DCC-GARCH model is measured by the two parameters DDC Alpha
(γ1) and DCC Beta (γ2). Both γ1 and γ2 indicate the dynamic and time varying behavior in the
model estimated. DDC Alpha (γ1) describes the short run volatility impact from one economy
to another economy, which also indicates the persistency in the standard residual from previ-
ous period. DCC Beta (γ2) measures the lingering effect of the shock, which is persistent of
conditional correlation in the model. The sum of these two parameters should be less than one
that indicated the conditional correlation in the model are not constant over time and has
dynamic behavior.
Fig 10. Wavelet Granger causality Malaysia vs. Selected markets.
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Similarly, if DDC Alpha (γ1) value is not significant, it means that there is not short-term
persistence found between two stock market, where as the DCC Beta (γ2) shows the long-term
persistence between the two stock markets. In our results in Table 4, pair Malaysia-France DDC
Alpha (γ1) is significant, indicated the short-term spillover impact of Malaysian indices over
France index. DCC Beta (γ2) also in this pair significant that indicated the long-term spillover
impact of Malaysian index over France. From the Malaysia-France pair, we can conclude that
there is dynamic relationship existed between two stock markets. Our results also shows that
the volatility in the Malaysian stock market effect the volatility in stock market of France for
both short and long period of time. Similarly, Malaysia- Germany, Malaysia- India, Malaysia-
Japan, Malaysia- Pakistan, Malaysia-Singapore, Malaysia-UK, Malaysia-Indonesia and Malay-
sia-China pairs DDC Alpha (γ1) and DCC Beta (γ2) is significant, indicating the short- and
long-term persistence in the volatility between Malaysia and other group pairs. Malaysian stock
market indices have the short term and long-term spillover impact on all the selected countries
except USA. In case of Malaysia-USA pair, the DDC Alpha (γ1) and DCC Beta (γ2) is not signif-
icant, it means that there is not dynamic relationship existed between these two stock markets.
From our results, we can summarize that the volatility in the Malaysian market effected the
other trading partners stock market for both short and long run and hence, we can say that risk
co-movement transfer from Malaysia to its trading partners except USA.
5. Concluding remarks and policy implication
We investigate in our study the causality relationships between the Malaysian stock market
and its trading partners and the co-movement dynamic risk behavior. Using different wavelet
techniques, we demonstrate different risk co-movements in the short and long run, as well as
in both OECD and emerging markets. We conclude that the risk co-movement is sustainable
in both the short and long run and in both OECD and emerging markets over time.
In recent years, research has focused mostly on the co-movements of risk among financial
markets of the different regions, including developed, emerging, and less developed econo-
mies. The theoretical discussion can be broadly divided into two groups. The first group
includes fundamentally based authors who claim that stock market co-movement is an inevita-
ble result of trade connectivity movement. The second group of authors are non-fundamental
authors dependent on non-fundamental causes for stock market interdependence. This study
chooses Malaysia as a special case to study, referred to by the first category, to investigate the
risk co-movement with its trading partners on the basis of various time-frequency frameworks.
Our main hypothesis is that trading connectivity causes stock market integration, measured by
co-movement patterns. Particularly, we aimed to answer these objectives: 1) What is the effect
Table 4. Results DCC-GARCH model.
Pair DDC Alpha (γ1) P-value DCC Beta (γ2) P-value
Malaysia-France 0.0139*** 0.0000 0.9693*** 0.0000
Malaysia- Germany 0.0124*** 0.0004 0.9695*** 0.0000
Malaysia- India 0.0131*** 0.0000 0.9806*** 0.0000
Malaysia-Japan 0.0125*** 0.0022 0.9772*** 0.0000
Malaysia- Pakistan 0.0100** 0.0252 0.9569*** 0.0000
Malaysia-Singapore 0.0274*** 0.0000 0.9584*** 0.0000
Malaysia-UK 0.0142*** 0.0001 0.9629*** 0.0000
Malaysia- USA -0.0051 0.2684 0.4602 0.5760
Malaysia-Indonesia 0.0160*** 0.0000 0.9780*** 0.0000
Malaysia-China 0.0071*** 0.0000 1.0015*** 0.0000
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of risk and causality transmission from the Malaysian stock market to its trading partners
before and after the crisis (means different tome-frequency domain)? It means we will find the
risk co-movement and Causality between Malaysia and its trading partners from two different
regions. We applied a detailed Wavelet to answer these research questions: Cross wavelet
(XWT), wavelet Coherence (WCOH), and robustness through the wavelet Granger causality,
and DCC-GARCH. Our empirical findings reveal significant evidence of risk co-movement
between the Malaysian stock market and its trading partners during different frequency and
time domains. More interestingly, Malaysia has a positive relationship with all selected emerg-
ing as well as the OECD stock market during the period of financial crisis and COVID-19. In
addition, Malaysia is leading the stock market of India, USA, France, Germany, Japan, Paki-
stan, and the UK in the period of financial crisis 1997–98 in the low-frequency domain, which
means that for the short run. In the period of the financial crisis of 1997–98, Malaysia is lag-
ging behind China due to the larger interdependence between them. During the COVID-19
pandemic (2020–21), the Malaysian stock market was driven by two major trading partners,
including Indonesia and China.
Furthermore, the Granger causality test shows the bi-directional and unidirectional causal-
ity between Malaysia and its trading partners over the four frequency domains. This is consis-
tent with the idea that there will not be an issue of the leadership position between the
Malaysian stock market and its trading partners in the long run, except for Indonesia, Singa-
pore, and China. Our Granger causality findings imply that the temporary shocks of the devel-
oped or OECD country’s stock market directly impact the Malaysian stock market, extending
to the longer scale. At the same time, proximity does not affect stock market correlation as
Malaysia and its trading partners need longer to absorb each stock market shock and adjust
their prices accordingly. In addition, our time-frequencies domains causality analysis (D1, D2,
D3, and D4) sheds light on the time required by the Malaysian market to interact with its trad-
ing partners and the nature of the lead-lag relationship. This time-frequency is very helpful for
the investors to decide the investment in Malaysian stock market by considering the shock
effect and its captured period. Moreover, our DCC-GARCH findings shows that Malaysian
market shows both short term and long term volatility pattern with trading partners except
USA on the ground of the trade agreements and trade flow.
Overall, our study contributes to studies showing that the Malaysian stock market risk sig-
nificantly affects other stock market risks, either in the Asian emerging region or OECD
regions, emphasizing thus the substantial role Malaysia is playing in the rest of the world [69,
70]. Furthermore, our research demonstrates that interdependence between stock markets is
substantially correlated with trade, economic integration, and economic relationships. For
instance, it has been suggested by [53,71] that trade flow between the economies is likely to be
the driving force behind open regionalism in capital markets.
We also offer evidence to contradict claims made by certain researchers that stock market
segmentation can coexist with regional trading blocks and international economic links, such
as the ASEAN Free Trade Area [61] and the North American Free Trade Area (NAFTA) [72].
Additionally, we present evidence contradicting studies that claim Malaysia is cut off from
developed Asian as well as OECD markets. However, since Malaysia joined the World Trade
Organization in 1995, the relationship between the Malaysian stock market and the rest of the
world changed. More recently, the ASEAN Trade in Goods Agreement (ATIGA), the Trans-
Pacific Partnership Agreement (TPPA), the Comprehensive and Progressive Agreement for
the Trans-Pacific Partnership (CPTPP), Malaysia-European Free Trade Area Economic Part-
nership Agreement (MEEPA), Malaysia-EU Free Trade Agreement (MEUFTA) and others
trade agreements enforce its global leadership in term of trade and economic weight and also
international financial integrations.
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Given the significance of our study, we argue that our findings have some important and
useful implications. We find the weak co-movement between Malaysia and Pakistan. Hence,
these weak correlation countries are the best choice for Malaysian investors, and Pakistani
investors have the best investment choice in Malaysia. In this way, they can diversify their
portfolio. In addition, investors and fund managers are urged to modify their allocations in
light of our time-frequency findings, considering the choice of countries and the length of the
investment horizons, particularly how the stock markets in Malaysia and its trading partners
react to regional or global shocks and crises. To adjust their fiscal and monetary policies, pol-
icymakers in these countries consider local and international shocks and be aware of the type
and frequency of their stock market integration. This study contains some intriguing contribu-
tions regarding Malaysia’s stock market dependence on international stock markets. However,
we were limited to stock market co-movement analyses. We propose controlling other driving
elements in future studies. In addition, integrating additional trading partners would provide
further insight into the relationship between trade connectedness and stock market
integration.
Moreover, in line with improving the technical precision of the empirical findings, this
study can be held using other techniques such as machine learning and others. Moreover, dif-
ferent economies of different economic types can be part of future research investigating the
risk and causality transmission due to globalization. Future research should be conducted on
the role of the government in maintaining the stock market, especially during crises and
pandemics.
Supporting information
S1 Data.
(XLSX)
Author Contributions
Conceptualization: Muhammad Waris, Badariah Haji Din.
Data curation: Muhammad Waris.
Formal analysis: Xiaoyang Wang, Hui Guo, Muhammad Waris, Badariah Haji Din.
Investigation: Xiaoyang Wang, Muhammad Waris.
Methodology: Hui Guo, Muhammad Waris, Badariah Haji Din.
Project administration: Muhammad Waris.
Resources: Muhammad Waris.
Software: Xiaoyang Wang, Muhammad Waris.
Supervision: Badariah Haji Din.
Validation: Muhammad Waris.
Writing – original draft: Hui Guo, Muhammad Waris.
Writing – review & editing: Muhammad Waris, Badariah Haji Din.
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