How Do the Global Stock Markets Influence One
Another? Evidence from Finance Big Data and
Granger Causality Directed Network
Yong Tang, Jason Jie Xiong, Yong Luo, and Yi-Cheng Zhang
ABSTRACT: The recent financial network analysis approach reveals that the topolo-
gies of financial markets have an important influence on market dynamics. However,
the majority of existing Finance Big Data networks are built as undirected networks
without information on the influence directions among prices. Rather than understand-
ing the correlations, this research applies the Granger causality test to build the
Granger Causality Directed Network for 33 global major stock market indices. The
paper further analyzes how the markets influence one another by investigating the
directed edges in the different filtered networks. The network topology that evolves in
different market periods is analyzed via a sliding window approach and Finance Big
Data visualization. By quantifying the influences of market indices, 33 global major
stock markets from the Granger causality network are ranked in comparison with the
result based on PageRank centrality algorithm. Results reveal that the ranking lists are
similar in both approaches where t he U.S. indices dominate the top position followed
by other American, European, and Asian indices. The lead-lag analysis reveals that
there is lag effects among the global indices. The result sheds new insights on the
influences among global stock markets with implications for trading strategy design,
global portfolio management, risk management, and markets regulation.
KEY WORDS AND PHRASES: Finance Big Data, Granger causality directed network,
global stock markets, financial network analysis, data visualization, trading strategy,
market regulation, risk management.
Introduction
Financial markets, including stock markets, are extremely complicated sys-
tems in which participants are playing various roles with asymmetric access
to information at different market levels. The success and failure of financial
markets have significant influences on the economies. Recent financial
crises and market crashes urge practitioners and scholars to reevaluate the
markets and understand the fundamental dynamics that the traditional
financial theories fail to reveal. With the help of complex network theory,
it is possible to model and extract the network topological structures to
reveal hidden information and relationships among financial markets and
assets. This financial network analysis approach benefits portfolio manage-
ment, risk management, quantitative trading, and other financial practices
by providing better understandings as well as visualizations of market
dynamics.
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Published in "International Journal of Electronic Commerce 23(1): 85–109, 2019"
which should be cited to refer to this work.
Financial market is considered an extremely complex system supported
by various information technology innovations, including automated trad-
ing [26], off-exchange trading [20], and crowd-based stock selection [36].
Although the information is critical in the financial markets [16, 46], recent
years have witnessed an emerging development of network science in
various financial markets [54]. From Information Systems perspective,
financial network analysis is an emerging method to analyze financial
risks [48], financial cycle [60], stock market perspective [49], and risk spil-
lover network [74]. However, based on current research of financial net-
works topologies, the networks are usually undirected graphs constructed
from correlations among the price time series. Due to the lack of capability
in revealing the information of mutual influences among the stocks, it is
challenging to answer questions such as how one stock is causal to another
stock, or which stock leads or lags to another stock. As correlation does not
imply causation, other methods are needed to construct directed networks
to catch the embedded causal relationships among the interinfluences of
stocks. The study provides new tools to traditional finance studies, adds
new insights to the undirected financial networks analysis research, and
further provides implementations to research and practices.
The economies around the world are influencing one another due to
globalization. It is thus essential to understand the dynamics of global
markets. In this paper, we investigate the global stock markets comprising
33 market indices of major stock markets using Granger causal testing and
lead/lag correlation to build directed networks and quantify the global
markets dynamics. Overall, there are three research questions:
Research Question 1: Do Granger causality and lead/lag exist significantly
in the global stock markets?
Research Question 2: What are the properties of those directed networks via
Finance Big Data visualization?
Research Question 3: How do the major market indices influence one
another and their importance in the network?
Literature Review
Financial systems are typical complex systems with a large number of
heterogeneous participants interacting with one another in nonlinear
ways. For global stock markets, it is essential to understand the interdepen-
dent relationships among the stocks. Using the price time series of a port-
folio, the price correlation matrix, which indicates how assets are interacting
with one another, can be built to further construct the correlation-based
asset networks [62]. With these networks, the applications of the network
analysis from complex network theory and random matrix theory could
extract hidden information embedded in the behaviors of assets. Significant
advancements have been made in the past few years focusing on these
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directions with many nontrivial empirical findings and applications to
market crisis study, portfolio optimization, risk management, and trading
strategy design. These achievements, compared to traditional economics
and finance approaches, bring significant new insights into the understand-
ings of the market structures and behaviors.
Many recent financial network analysis studies have been conducted on
a variety of stock markets around the world, such as Brazil [68], China [32],
South Korea [57], New Zealand [64], United States [61], Iran [52], Turkey
[22], Russia [71], Sweden [42], Germany [11], European markets [14], and
global markets [56]. The body of literature on correlation and network
studies of financial markets are growing. This shows a great practical
usages in both empirical studies and modeling the correlations and con-
nectedness based on price information, as discussed in Billio et al. [7] and
Podobnik et al. [63]. Besides the stock market, the real estate stock market is
studied in Wang and Xie [73], and foreign exchange markets were studied
in Fenn et al. [28] and Jang, Lee, and Chang [43]. As an extension of recent
advances of social sentiment studies in finance, Zhang et al. [77] propose a
stock price prediction method using the network structure properties with
social sentiments. In Farmer et al. [27], a vision to model the financial
markets and economic systems as coupled networks of agents are proposed
to combine the powers of both complex network theory and computational
multiple agent simulations. In a recent 2016 Science paper, Battiston et al. [4]
argue that concepts from complexity theory like networks are necessary and
have significant potentials to anticipate financial crises because the econo-
mies and financial systems are becoming highly connected [4]. The studies
of network structure and the related properties and the dynamics provide
new insights for financial market regulators for better policy decision
makings [ 3, 63, 67].
In financial network analysis, there has been some work on the relation-
ships between economic entities like countries, companies, and board direc-
tors. For example, Battiston and Catanzaro [3] find that the network of
board directors of big companies shows a small-world feature. Glattfelder
[33] and Vitali, Glattfelder, and Battiston [70] investigated the corporate
control relationships from the perspective of ownership networks extracted
from the shareholder data. Several papers research the international world
trade networks in which countries are vertices and the international
import/export of goods among countries are used to build edges [5, 45].
All these works, in macro levels, depict the relationships of large economic
entities, and the results are inspirational for macro trading. Furthermore, as
a method of Financial Big Data, financial network analysis provides tools
for revealing the topological structures of financial markets. To enhance the
capability of financial network analysis, it would be interesting to apply it
with other big data approaches using multiple sources of data, including
price data, stock profiles, financial filings, and sentiments in social media [1,
66]. In the research conducted by Boginski, Butenko, and Pardalos [
8],
the
degree
distribution of the financial market is studied, and the statistical
results show that the power law model is valid in financial networks. They
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also reveal that network structures are stable over time intervals, and
parameters such as edge density increases in recent years indicate that
stocks are influencing one another in the U.S. stock market. In the research
conducted by Caldarelli et al. [13], the authors report that financial net-
works are extracted not only from stock prices but also from board director
and stock ownership. These results show scale-free properties. Chen et al.
[17] further discuss the relationship between the interindustry closeness
and returns industry in industrial level and the stock centrality and stock
returns in stock level. The global stock markets are not only important for
the individual country but also entangled with significant influences with
one another. The understanding of the dynamics of global stock markets is
essential to industrial practices as well as to the policymakers for a better
global economy [5, 25, 45]. In the traditional finance approaches, the
dynamics of global markets have been studied in various aspects, such as
effects of the herding [18, 37] driving factors, risk and predicting of market
returns [19, 29, 38], co-movement [31], interdependence, transmission
dynamics [50], correlation [35], and structure and performance of global
markets [6]. However, there is still a lack of study on the directed network
properties of global markets with focus on causality and lead/lag effects to
reflect the influencing relationships among global markets. It is interesting
to explore from new perspective and add new evidences to further verify
the effects, factors, predictions, and dynamics. Online Appendix provides a
summary of selected representative literatures in the logic of complex net-
work theory, financial network analysis, global stock market studies,
Granger and lead/lad, and applications.
In this study, we focus on the global stock market network constructed
from price information. The market indices are treated as the vertices,
whereas the relationships are translated as edges between stock markets.
The contribution of the research is in providing findings of global stock
market directed networks built from Granger causality information and
lead/lag effects. There is some relevant research that applies the Granger
causality tests in the study of network structures of financial markets. Using
the measurements of Granger causality networks based on monthly returns,
the study [7] shows that the financial institutional sectors (hedges funds,
banks, brokers, and insurance companies) interrelate, and banks represent
more important roles. The international business cycles are studied in
Caraiani [15] using Granger causality network approach. It reveals that
the United States plays important roles in subnetworks composed by G7
and Organisation for Economic Co-operation and Development countries.
Instead of using gross domestic product (GDP) data, we use all major global
stock markets indices data and focus on the dynamics of stock market
behavior. The Chinese stock market is studied using the cointegration
approach, and the structures are studied in Tu [69], where they apply the
Engle-Granger test to extract the subnetworks of Chinese stock market. The
study on the Granger causality networks of 20 developed markets is carried
out in Výrost, Lyócsa, and Baumöhl [72], and the survival ratio measure-
ment is used to study the stability. In Kenett et al. [47], a metacorrelation,
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which is the correlation of the index return and the market mean correla-
tion, is proposed to study the components of the Dow Jones Industrial
Average (DJIA). Authors apply the Granger causality test to validate the
results and find that the index returns correlate with the mean correlations.
In Zheng et al. [78], a dynamic causality index is used to measure the
market shifts for the U.S. stock market as well.
Data Analysis and Discussion
Whole Period
Using the return data over the whole period, the Granger causality test is
conducted for all index pairs. Details of the research methodology of
Granger causality, ADF and Unit Root Test, and Data Setting Introduction
are presented in the online Appendix. The F -statistic and critical values are
calculated. Granger binary network is generated where vertices are indices
and the directed edges are weighted as 1 if F -statistic is larger than critical
values, as
~
e
ij
¼
1 if F>c;
0 otherwise;
;
(1)
where F is the F -statistic and c represents the critical value. If F>c ,aswe
described earlier, I
i
→I
j
, that is, I
i
granger causes I
j
, then a directed edge
~
e
ij
is established from I
i
to I
j
. Figure 1 plots the average correlation of each
sliding windows. In Figure 2, the granger network of 33 indices calculated
from the return data of the whole period is presented. The total number of
edges satisfying F>c is 727 of 1,089 possible directed edges. In other words,
the network has an edge density of 0.6676. For index I
i
, which is connected
by directed edges to other indices, we denote the in-degree as d
in
i
, out-
degree as d
out
i
, and total-degree as d
total
i
¼ d
in
i
þ d
out
i
. For a given index, d
in
i
indicates how many other indices granger cause I
i
. d
out
i
indicates how many
other indices are granger caused by I
i
, more precisely,
d
in
i
¼
~
e
ki
jj
kÞi
and d
out
i
¼
~
e
ik
jj
kÞi
: (2)
To quantify the influence for each vertex, the influence factor introduced
in Caraiani [15] is adopted, in which a Granger causality network is con-
structed by using the GDP data. Based on the granger network, the influ-
ence of each vertex (country) is measured as the relative influence factor (IF ):
IF
i
¼
d
out
i
d
in
i
d
in
i
d
out
i
: (3)
It shows that Granger causal network better predicts the fluctuations, and
the United States has the largest influence over other countries, which
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