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This study investigates the use of a novel market graph model for equity markets. Our graph model is built on distance correlation instead of the traditional Pearson correlation. We apply it to the study of S&P500 stocks from January 2015 to December 2022. We also compare our market graphs to the traditional market graphs in the literature, those built using Pearson correlation. To further the comparison, we also build graphs using Spearman rank correlation. Our comparisons reveal that non-linear relationships in stock returns are not captured by either Pearson correlation or Spearman rank correlation. We observe that distance correlation is a robust measure for detecting complex relationships in S&P500 stock returns. Networks built on distance correlation networks, are shown to be more responsive to market conditions during turbulent periods such as the COVID crash period. [ABSTRACT FROM AUTHOR]

Using networks to analyze time series has become increasingly popular in recent years. Univariate and multivariate time series can be mapped to networks in order to examine both local and global behaviors. Visibility graph-based time series analysis is proposed herein; in this approach, individual time series are mapped to visibility graphs that characterize relevant states. Companies listed on the emerging market index Borsa Istanbul 100 (BIST 100) had their market visibility graphs collected. To further account for the local extreme values of the underlying time series, we constructed a novel kernel function of the visibility graphs. Via the provided novel measure, sector-level and sector-to-sector analyses are conducted using the kernel function associated with this metric. To examine sectoral trends, the COVID-19 crisis period was included in the study's data set. The findings indicate that an effective strategy for analyzing financial time series has been devised. [ABSTRACT FROM AUTHOR]

This study investigates the use of a novel market graph model for equity markets. Our graph model is built on distance correlation instead of the traditional Pearson correlation. We apply it to the study of S&P500 stocks from January 2015 to December 2022. We also compare our market graphs to the traditional market graphs in the literature, those built using Pearson correlation. To further the comparison, we also build graphs using Spearman rank correlation. Our comparisons reveal that non-linear relationships in stock returns are not captured by either Pearson correlation or Spearman rank correlation. We observe that distance correlation is a robust measure for detecting complex relationships in S&P500 stock returns. Networks built on distance correlation networks, are shown to be more responsive to market conditions during turbulent periods such as the COVID crash period.

In this study, we present a model which represents the interaction of financial companies in their network. Since the long time series have a global memory effect, we present our model in the terms of fractional integro-differential equations. This model characterize the behavior of the complex network where vertices are the financial companies operating in XU100 and edges are formed by distance based on Pearson correlation coefficient. This behavior can be seen as the financial interactions of the agents. Hence, we first cluster the complex network in the terms of high modularity of the edges. Then, we give a system of fractional integro-differential equation model with two parameters. First parameter defines the strength of the connection of agents to their cluster. Hence, to estimate this parameter we use vibrational potential of each agent in their cluster. The second parameter in our model defines how much agents in a cluster affect each other. Therefore, we use the disparity measure of PMFGs of each cluster to estimate second parameter. To solve model numerically we use an efficient algorithmic decomposition method and concluded that those solutions are consistent with real world data. The model and the solutions we present with fractional derivative show that the real data of Borsa Istanbul Stock Exchange Market always seek for an equilibrium state.

Using networks to analyze time series has become increasingly popular in recent years. Univariate and multivariate time series can be mapped to networks in order to examine both local and global behaviors. Visibility graph-based time series analysis is proposed herein; in this approach, individual time series are mapped to visibility graphs that characterize relevant states. Companies listed on the emerging market index Borsa Istanbul 100 (BIST 100) had their market visibility graphs collected. To further account for the local extreme values of the underlying time series, we constructed a novel kernel function of the visibility graphs. Via the provided novel measure, sector-level and sector-to-sector analyses are conducted using the kernel function associated with this metric. To examine sectoral trends, the COVID-19 crisis period was included in the study’s data set. The findings indicate that an effective strategy for analyzing financial time series has been devised.

Abstract To examine the interdependency and evolution of Pakistan’s stock market, we consider the cross-correlation coefficients of daily stock returns belonging to the blue chip Karachi stock exchange (KSE-100) index. Using the minimum spanning tree network-based method, we extend the financial network literature by examining the topological properties of the network and generating six minimum spanning tree networks around three general elections in Pakistan. Our results reveal a star-like structure after the general elections of 2018 and before those in 2008, and a tree-like structure otherwise. We also highlight key nodes, the presence of different clusters, and compare the differences between the three elections. Additionally, the sectorial centrality measures reveal economic expansion in three industrial sectors—cement, oil and gas, and fertilizers. Moreover, a strong overall intermediary role of the fertilizer sector is observed. The results indicate a structural change in the stock market network due to general elections. Consequently, through this analysis, policy makers can focus on monitoring key nodes around general elections to estimate stock market stability, while local and international investors can form optimal diversification strategies.

To examine the interdependency and evolution of Pakistan's stock market, we consider the cross-correlation coefficients of daily stock returns belonging to the blue chip Karachi stock exchange (KSE-100) index. Using the minimum spanning tree network-based method, we extend the financial network literature by examining the topological properties of the network and generating six minimum spanning tree networks around three general elections in Pakistan. Our results reveal a star-like structure after the general elections of 2018 and before those in 2008, and a tree-like structure otherwise. We also highlight key nodes, the presence of different clusters, and compare the differences between the three elections. Additionally, the sectorial centrality measures reveal economic expansion in three industrial sectors—cement, oil and gas, and fertilizers. Moreover, a strong overall intermediary role of the fertilizer sector is observed. The results indicate a structural change in the stock market network due to general elections. Consequently, through this analysis, policy makers can focus on monitoring key nodes around general elections to estimate stock market stability, while local and international investors can form optimal diversification strategies. [ABSTRACT FROM AUTHOR]

Mutual information minimum spanning trees are used to explore nonlinear dependencies on Brazilian equity network by comparing the periods from June/01/2015 to January/26/2016, in which Brazil was under the government of President Dilma Rousseff, and from January/27/2016 to September/08/2016 which includes the government transition from President Dilma Rousseff to President Michel Temer. Minimum spanning trees from mutual information and linear correlation between stocks returns were obtained and compared. Mutual information minimum spanning trees present higher degree of robustness and evidence of power law tail in the weighted degree distribution, indicating more risk in terms of volatility transmission than it is expected by the analysis based on linear correlation. In particular, a remarkable increase of stock returns nonlinear dependencies indicates that the period including the government transition is more risky in terms of volatility transmission network structure. Also, we found evidence of network structure and stock performance relationship. Besides, those results emphasize the usefulness of mutual information network analysis for identification of Financial Markets features due to nonlinear dependencies. • Mutual information minimum spanning trees to explore nonlinear dependencies. • Brazilian equity market minimum spanning trees are obtained for two periods. • Mutual information and linear correlation minimum spanning trees are compared. • Increase of nonlinear dependencies in Brazilian market in the period of government transition. • Weighted degree distribution of mutual information minimum spanning trees with power law tail. [ABSTRACT FROM AUTHOR]

This study uses cross correlations in the daily closing prices of the London stock exchange FTSE 100 index companies from July 2010 to March 2018 to compute minimum spanning tree structures. A key aim of this study is to analyze the topological evolution of the market from the perspective of Brexit referendum. Therefore, the overall sample is divided into two sub-periods of equal time windows of pre-referendum, and post-referendum to obtain minimum spanning trees. The findings show formation of two major clusters belonging to financial, and consumer services sectors. Results further show surprising effect of Brexit referendum in form of expansion of tree after the event. The pre-referendum period tree demonstrates a less stable structure as compared to post-referendum period tree that shows weakening in the degree of connections per node. The sub metrics MST confirms the evidence of predominant central position by companies belonging to financials and consumer services sectors, while bridge role is being played by industrials sector afterwards referendum. In addition, the risk of affecting MST in the post-referendum period is lower in comparison with pre-referendum period suggesting a positive impact of Brexit referendum on FTSE 100 index companies. • MST-based network topology is used to analyze the impact of Brexit referendum. • Two major clusters of financials and consumer services sectors are being observed. • The risk of affecting MST in the post-referendum period is lower. • MST shrank in the pre and referendum period, and enormously expended afterwards. [ABSTRACT FROM AUTHOR]

Traditional approaches to portfolio management and optimization often rely on the certain statistical properties, such as expected return and price variance. But these properties generally represent the local behavior of the stocks and are thus not able to represent the stock characteristics in terms of the whole stock market. This paper considers the stock market as a complex system, where stocks affect one another due to unknown forces. It may not possible to measure the actual magnitudes and directions of these forces, but it is possible to observe their effects using the external observations such as the correlation between stocks. To forecast the dynamics, this paper proposes a seminal measure, the cohesion of the stock market network induced by the correlation of stocks. The important observations we obtained from the analyses of the real market (S&P500 and KOSPI200) in the past thirteen years are two folds: (1) the cohesion tends to increase more in a bear market than in a bull market, and (2) the cohesion of the stock market Granger causes the stock returns. Based on these observations, we implemented a stock portfolio recommending system, namely StoPoR. To evaluate the effectiveness of StoPoR system, we conducted the simulated investment based on the portfolio recommended by the StoPoR. The result shows that the monthly returns of StoPoR portfolio (1.44%) is bigger than that of Markowitz efficient portfolio (1.07%) and further bigger than that of the S&P500 index (0.50%). The similar result also holds for the Korean stock market; the monthly return of the StoPoR suggested portfolio (1.83%) gets far bigger than that of Markowitz efficient portfolio (1.61%) and further bigger than that of the KOSPI200 index (0.81%). This result indicates that the characteristics of the stock network are related to the stock returns and its dynamics can be used for constructing a stock portfolio and the prediction of the changes in the stock markets. [ABSTRACT FROM AUTHOR]

In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.

This paper provides new evidence for the predictability of excess market portfolio returns using a network approach. In particular, this article introduces a measure of interconnectedness to capture the interrelationship of returns of 100 largest stocks in S&P500 during 1990-2014. In the financial network literature, the interconnection of a stock network is often regarded as a channel through which an idiosyncratic shock propagates. The idiosyncratic risk propagation is crucial to the debate over the relationship between idiosyncratic risk and market returns because the idiosyncratic risk is not always diversified away. Rather, the network can sometimes amplify the effect of the idiosyncratic risk to cause aggregate fluctuation. In accordance with this theoretical argument, I empirically show that the network topology, measured by diameter, works together with the idiosyncratic risk, measured by average stock variance, to affect the market portfolio returns. This relationship persists after controlling for well-known variables known to forecast the stock market returns. [ABSTRACT FROM AUTHOR]

This study uses the cross-correlations in the daily closing prices of the South African Top 100 companies listed on the JSE All share index (ALSI) from June 2003 to June 2013 to compute minimum spanning tree maps. In addition to the full sample, the analysis also uses three sub-periods to investigate the topological evolution before, during, and after the 2008 financial crisis. The findings show that although there is substantial clustering and homogeneity on the JSE, the most connected nodes are in the financial and resources sectors. The sub-sample results further reveal that the JSE network tree shrank in the run-up to, and during the financial crisis, and slowly expanded afterwards. In addition, the different clusters in the network are connected by various nodes that are significantly affected by diversification and credit market dynamics. [ABSTRACT FROM AUTHOR]

We study the topological stability of stock market network by investigating the topological robustness, namely the ability of the network to resist structural or topological changes. The stock market network is extracted by minimal spanning tree (MST) and planar maximally filtered graph (PMFG). We find that the specific delisting thresholds of the listed companies exist in both MST and PMFG networks. In comparison with MST, PMFG provides more information and is better for the aim of exploring stock market network's robustness. The PMFG before the US sub-prime crisis (i.e., from June 2005 to May 2007) has a stronger robustness against the intentional topological damage than the other two sub-periods (i.e., from June 2007 to May 2009 and from June 2009 to May 2011). We also find that the nonfractal property exists in MSTs of S&P 500, i.e., the highly connected nodes link with each other directly, which indicates that the MSTs are vulnerable to the removal of such important nodes. Moreover, the financial institutions and high technology companies are important in maintaining the stability of S&P 500 network. [ABSTRACT FROM AUTHOR]

• The correlation between stocks increases when major events occur, and this impact will last for a period after the event. • The severe impact of the global financial crisis on China's stock market occurred after the crisis. • The network structure of the stock market has an indicator effect on the systemic risk contributions, which is consistent in different markets under sudden shocks. Studying the correlation structure of the stock market is crucial for systemic risk and portfolio optimization. We construct the price volatility network of the Shanghai and Shenzhen 300 index components in China's stock market in the period 2007–2020. We select three representative major emergencies: the global financial crisis in 2008, the stock disaster in 2015, and the COVID-19 epidemic in 2020. First, we find that when the stock market is impacted by the major events, the network shows a cluster phenomenon. The cluster effect of the financial crisis events is smallest, while that of the epidemic events occurs most rapidly. Second, the key nodes in the stock market network have greater risk transmission ability. The manufacturing plays a crucial role during the later stages of events, while the financial industry plays an important role during the epidemic's recovery period. Third, the network structure of the stock market has an indicator effect on the systemic risk contributions. Generally, the greater a stock's eigenvector centrality, the greater its systemic risk contribution, while its closeness centrality and clustering coefficient have opposite effects. The study has important enlightenment significance for market regulators to prevent risk diffusion and reduce portfolio risk for market participants. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the topological properties of the Brazilian stock market networks. We build the minimum spanning tree, which is based on the concept of ultrametricity, using the correlation matrix for a variety of stocks of different sectors. Our results suggest that stocks tend to cluster by sector. We employ a dynamic approach using complex network measures and find that the relative importance of different sectors within the network varies. The financial, energy and material sectors are the most important within the network. [Copyright &y& Elsevier]

This study investigates the topology of the South African stock market network pre, during, and post the level 5-lockdown period. We use the daily closing price of the 134 companies in the all-share index (ALSI) from 01 October 2019 to 30 October 2020. We construct the minimum spanning tree using the cross-correlation of the returns computed from the closing price data. The research findings show that the South African stock market network forms clusters and is homogeneous, and the finance industry plays a central role. Specifically, the results show an expansion of MST during the level 5 lockdown and shrinkage of the MST post level 5 lockdown. The average correlation coefficient decreases through all sub-periods; conversely, the average distance increases in all sub-periods. Post-level 5 lockdown period, stocks in the Health Care Equipment & Services sector form a small cluster that did not exist before the lockdown period. JSE node degree distribution for all sub-periods follows the power law. • The stock market network forms clusters and is homogeneous, and the finance industry plays a central role. • Expansion of MST during the level 5 lockdown and shrinkage of the MST post level 5 lockdown. • Average correlation coefficient decreases through all sub-periods, but the average distance increases in all sub-periods. • Stocks in the Health Care Equipment & Services sector form a small cluster that did not exist before the lockdown period. • JSE node degree distribution for all sub-periods follows the power law. [ABSTRACT FROM AUTHOR]

• More than one hundred directed weighted stock market networks are constructed by the methods of Engle-Granger test, Granger Causality test and moving window. • The average clustering coefficient and global efficiency are employed to characterize dynamic properties of the stock market networks. • An interesting finding is that, top 3 influential stocks are high price stocks which are so called "hundred shares" by Chinese investors. This paper aims to rank the influential nodes for Chinese A-share market by employing complex network analysis approach. More than one hundred directed weighted stock market networks are constructed by the methods of Engle-Granger test, Granger Causality test and moving window among 847 stocks for the time period from January 2006 to June 2019. Then the identification of important nodes is investigated by using weighted LeaderRank algorithm. The results show that: (i) the average clustering coefficient and global efficiency increase sharply in the run-up to, and during the financial crisis, and decline rapidly afterwards. (ii) 66.98% of stock market networks have scale-free property. (iii) the influential companies are generally large-capitalization companies. In addition, an interesting finding is that, top 3 influential stocks are high price stocks which are so called "hundred shares" by Chinese investors. [ABSTRACT FROM AUTHOR]