Correlation and network analysis of global financial indices

Change in hierarchy of the financial networks: A study on firms of an emerging market in Bangladesh

We investigate the hierarchical structure of Dhaka stocks' financial networks, known as an emerging market, from 2008 to 2020. To do so, we determine correlations from the returns of the firms over a one-year time window. Then, we construct a minimum spanning tree (MST) from correlations and calculate the hierarchy of the tree using the hierarchical path. We find that during the unprecedented crisis in 2010-11, the hierarchy of this emerging market did not sharply increase like in developed markets, implying the absence of a compact cluster in the center of the tree. Noticeably, the hierarchy fell before the big crashes in the Bangladeshi local market, and the lowest value was found in 2010, just before the 2011 Bangladesh market scam. We also observe a lower hierarchical MST during COVID-19, which implies that the network is fragile and vulnerable to financial crises not seen in developed markets. Moreover, the volatility in the topological indicators of the MST indicates that the network is adequately responding to crises and that the firms that play an important role in the market during our analysis periods are financial, particularly the insurance companies. We notice that the largest degrees are minimal compared to the total number of nodes in the tree, implying that the network nodes are somewhat locally compact rather than globally centrally coupled. For this random structure of the emerging market, the network properties do not properly reflect the hierarchy, especially during crises. Identifying hierarchies, topological indicators, and significant firms will be useful for understanding the movement of an emerging market like Dhaka Stock exchange (DSE), which will be useful for policymakers to develop the market.

Simplicial Persistence of Financial Markets: Filtering, Generative Processes and Structural Risk

We introduce simplicial persistence, a measure of time evolution of motifs in networks obtained from correlation filtering. We observe long memory in the evolution of structures, with a two power law decay regimes in the number of persistent simplicial complexes. Null models of the underlying time series are tested to investigate properties of the generative process and its evolutional constraints. Networks are generated with both a topological embedding network filtering technique called TMFG and by thresholding, showing that the TMFG method identifies high order structures throughout the market sample, where thresholding methods fail. The decay exponents of these long memory processes are used to characterise financial markets based on their efficiency and liquidity. We find that more liquid markets tend to have a slower persistence decay. This appears to be in contrast with the common understanding that efficient markets are more random. We argue that they are indeed less predictable for what concerns the dynamics of each single variable but they are more predictable for what concerns the collective evolution of the variables. This could imply higher fragility to systemic shocks.

Evolution of Cohesion between USA Financial Sector Companies before, during, and Post-Economic Crisis: Complex Networks Approach

Various mathematical frameworks play an essential role in understanding the economic systems and the emergence of crises in them. Understanding the relation between the structure of connections between the system’s constituents and the emergence of a crisis is of great importance. In this paper, we propose a novel method for the inference of economic systems’ structures based on complex networks theory utilizing the time series of prices. Our network is obtained from the correlation matrix between the time series of companies’ prices by imposing a threshold on the values of the correlation coefficients. The optimal value of the threshold is determined by comparing the spectral properties of the threshold network and the correlation matrix. We analyze the community structure of the obtained networks and the relation between communities’ inter and intra-connectivity as indicators of systemic risk. Our results show how an economic system’s behavior is related to its structure and how the crisis is reflected in changes in the structure. We show how regulation and deregulation affect the structure of the system. We demonstrate that our method can identify high systemic risks and measure the impact of the actions taken to increase the system’s stability.

Supervision of Banking Networks Using the Multivariate Threshold-Minimum Dominating Set (mT-MDS)

The global financial crisis of 2008, triggered by the collapse of Lehman Brothers, highlighted a banking system that was widely exposed to systemic risk. The minimization of the systemic risk via a close and detailed monitoring of the entire banking network became a priority. This is a complex and demanding task considering the size of the banking systems; in the US and the EU they include more than 10,000 institutions. In this paper, we introduce a methodology which identifies a subset of banks that can: (a) efficiently represent the behavior of the whole banking system, and (b), provide, in the case of a failure, a plausible range of the crisis dispersion. The proposed methodology can be used by the regulators as an auxiliary monitoring tool to identify groups of banks that are potentially in distress and try to swiftly remedy their problems and minimize the propagation of the crisis by restricting contagion. This methodology is based on graph theory, and more specifically, complex networks. We termed this setting a “multivariate Threshold–Minimum Dominating Set” (mT-MDS), and it is an extension of the Threshold–Minimum Dominating Set methodology. The method was tested on a dataset of 570 U.S. banks, including 429 solvent ones and 141 failed ones. The variables used to create the networks were as follows: the total interest expense; the total interest income; the tier 1 (core) risk-based capital; and the total assets. The empirical results reveal that the proposed methodology can be successfully employed as an auxiliary tool for the efficient supervision of a large banking network.

Parallel Machine Learning for Forecasting the Dynamics of Complex Networks

Forecasting the dynamics of large, complex, sparse networks from previous time series data is important in a wide range of contexts. Here we present a machine learning scheme for this task using a parallel architecture that mimics the topology of the network of interest. We demonstrate the utility and scalability of our method implemented using reservoir computing on a chaotic network of oscillators. Two levels of prior knowledge are considered: (i) the network links are known, and (ii) the network links are unknown and inferred via a data-driven approach to approximately optimize prediction.

A 2D Lévy-flight model for the complex dynamics of real-life financial markets

We report on the emergence of scaling laws in the temporal evolution of the daily closing values of the S&P 500 index prices and its modeling based on the Lévy flights in two dimensions (2D). The efficacy of our proposed model is verified and validated by using the extreme value statistics in the random matrix theory. We find that the random evolution of each pair of stocks in a 2D price space is a scale-invariant complex trajectory whose tortuosity is governed by a 2/3 geometric law between the gyration radius R_g(t) and the total length ℓ(t) of the path, i.e., R_g(t)∼ℓ(t)^2/3. We construct a Wishart matrix containing all stocks up to a specific variable period and look at its spectral properties for over 30 years. In contrast to the standard random matrix theory, we find that the distribution of eigenvalues has a power-law tail with a decreasing exponent over time-a quantitative indicator of the temporal correlations. We find that the time evolution of the distance of 2D Lévy flights with index α=3/2 from origin generates the same empirical spectral properties. The statistics of the largest eigenvalues of the model and the observations are in perfect agreement.

Cocoa bean fingerprinting via correlation networks

Cocoa products have a remarkable chemical and sensory complexity. However, in contrast to other fermentation processes in the food industry, cocoa bean fermentation is left essentially uncontrolled and is devoid of standardization. Questions of food authenticity and food quality are hence particularly challenging for cocoa. Here we provide an illustration how network science can support food fingerprinting and food authenticity research. Using a large dataset of 140 cocoa samples comprising three cocoa fermentation/processing stages and eight countries, we obtain correlation networks between the cocoa samples by computing measures of pairwise correlation from their liquid chromatography-mass spectrometry (LC-MS) profiles. We find that the topology of correlation networks derived from untargeted LC-MS profiles is indicative of the fermentation and processing stage as well as the origin country of cocoa samples. Progressively increasing the correlation threshold firstly reveals network clusters based on processing stage and later country-based clusters. We present both, qualitative and quantitative evidence through network visualization, network statistics and concepts from machine learning. In our view, this network-based approach for classifying mass spectrometry data has broad applicability beyond cocoa.

A Pattern New in Every Moment: The Temporal Clustering of Markets for Crude Oil, Refined Fuels, and Other Commodities

The identification of critical periods and business cycles contributes significantly to the analysis of financial markets and the macroeconomy. Financialization and cointegration place a premium on the accurate recognition of time-varying volatility in commodity markets, especially those for crude oil and refined fuels. This article seeks to identify critical periods in the trading of energy-related commodities as a step toward understanding the temporal dynamics of those markets. This article proposes a novel application of unsupervised machine learning. A suite of clustering methods, applied to conditional volatility forecasts by trading days and individual assets or asset classes, can identify critical periods in energy-related commodity markets. Unsupervised machine learning achieves this task without rules-based or subjective definitions of crises. Five clustering methods—affinity propagation, mean-shift, spectral, k-means, and hierarchical agglomerative clustering—can identify anomalous periods in commodities trading. These methods identified the financial crisis of 2008–2009 and the initial stages of the COVID-19 pandemic. Applied to four energy-related markets—Brent, West Texas intermediate, gasoil, and gasoline—the same methods identified additional periods connected to events such as the September 11 terrorist attacks and the 2003 Persian Gulf war. t-distributed stochastic neighbor embedding facilitates the visualization of trading regimes. Temporal clustering of conditional volatility forecasts reveals unusual financial properties that distinguish the trading of energy-related commodities during critical periods from trading during normal periods and from trade in other commodities in all periods. Whereas critical periods for all commodities appear to coincide with broader disruptions in demand for energy, critical periods unique to crude oil and refined fuels appear to arise from acute disruptions in supply. Extensions of these methods include the definition of bull and bear markets and the identification of recessions and recoveries in the real economy.

Dynamic Analyses of Contagion Risk and Module Evolution on the SSE A-Shares Market Based on Minimum Information Entropy

The interactive effect is significant in the Chinese stock market, exacerbating the abnormal market volatilities and risk contagion. Based on daily stock returns in the Shanghai Stock Exchange (SSE) A-shares, this paper divides the period between 2005 and 2018 into eight bull and bear market stages to investigate interactive patterns in the Chinese financial market. We employ the Least Absolute Shrinkage and Selection Operator (LASSO) method to construct the stock network, compare the heterogeneity of bull and bear markets, and further use the Map Equation method to analyse the evolution of modules in the SSE A-shares market. Empirical results show that (1) the connected effect is more significant in bear markets than bull markets and gives rise to abnormal volatilities in the stock market; (2) a system module can be found in the network during the first four stages, and the industry aggregation effect leads to module differentiation in the last four stages; (3) some stocks have leading effects on others throughout eight periods, and medium- and small-cap stocks with poor financial conditions are more likely to become risk sources, especially in bear markets. Our conclusions are beneficial to improving investment strategies and making regulatory policies.

Network geometry and market instability

The complexity of financial markets arise from the strategic interactions among agents trading stocks, which manifest in the form of vibrant correlation patterns among stock prices. Over the past few decades, complex financial markets have often been represented as networks whose interacting pairs of nodes are stocks, connected by edges that signify the correlation strengths. However, we often have interactions that occur in groups of three or more nodes, and these cannot be described simply by pairwise interactions but we also need to take the relations between these interactions into account. Only recently, researchers have started devoting attention to the higher-order architecture of complex financial systems, that can significantly enhance our ability to estimate systemic risk as well as measure the robustness of financial systems in terms of market efficiency. Geometry-inspired network measures, such as the Ollivier-Ricci curvature and Forman-Ricci curvature, can be used to capture the network fragility and continuously monitor financial dynamics. Here, we explore the utility of such discrete Ricci curvatures in characterizing the structure of financial systems, and further, evaluate them as generic indicators of the market instability. For this purpose, we examine the daily returns from a set of stocks comprising the USA S&P-500 and the Japanese Nikkei-225 over a 32-year period, and monitor the changes in the edge-centric network curvatures. We find that the different geometric measures capture well the system-level features of the market and hence we can distinguish between the normal or 'business-as-usual' periods and all the major market crashes. This can be very useful in strategic designing of financial systems and regulating the markets in order to tackle financial instabilities.

Measuring topological descriptors of complex networks under uncertainty

Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. To compute the various topological descriptors commonly used to characterize the structure of a complex system (e.g., the degree, the clustering coefficient, etc.), it is usually necessary to completely reconstruct the network of relations between the subsystems. Several methods are available to detect the existence of interactions between the nodes of a network. By observing some physical quantities through time, the structural relationships are inferred using various discriminating statistics (e.g., correlations, mutual information, etc.). In this setting, the uncertainty about the existence of the edges is reflected in the uncertainty about the topological descriptors. In this study, we propose a methodological framework to evaluate this uncertainty, replacing the topological descriptors, even at the level of a single node, with appropriate probability distributions, eluding the reconstruction phase. Our theoretical framework agrees with the numerical experiments performed on a large set of synthetic and real-world networks. Our results provide a grounded framework for the analysis and the interpretation of widely used topological descriptors, such as degree centrality, clustering, and clusters, in scenarios in which the existence of network connectivity is statistically inferred or when the probabilities of existence π_{ij} of the edges are known. To this purpose, we also provide a simple and mathematically grounded process to transform the discriminating statistics into the probabilities π_{ij}.

The dynamic evolution of the characteristics of exchange rate risks in countries along "The Belt and Road" based on network analysis

As of November 1, 2018, China's "One Belt and One Road" Initiative has involved 123 countries and promoted worldwide communication, cooperation and trade exchange. This paper constructs correlation networks of exchange rates among the countries along "The Belt and Road" and analyzes the risk contagion structure. It is found that when "The Belt and Road" initiative is initialized, countries in Eastern Europe occupy important positions in the network and play a vital role in the spreading of exchange rate risks; however, during the process of "The Belt and Road" initiative, the exchange rate risks are decentralized geographically, whereas they are centralized in countries that have in-depth communication and cooperation. The minimum Spanning Tree method is also proposed to investigate the structure of complex networks. It is found that the geographical link between exchange rate fluctuations and correlations among the countries has been strengthened while China has become an important node in the exchange rate network after the launch of "The Belt and Road" initiative. In addition, the influence and promotion of RMB has rapidly benefited from the initiative.

Analysis of global stock index data during crisis period via complex network approach

Considerable research has been done on the complex stock market, however, there is very little systematic work on the impact of crisis on global stock markets. For filling in these gaps, we propose a complex network method, which analyzes the effects of the 2008 global financial crisis on global main stock index from 2005 to 2010. Firstly, we construct three weighted networks. The physics-derived technique of minimum spanning tree is utilized to investigate the networks of three stages. Regional clustering is found in each network. Secondly, we construct three average threshold networks and find the small-world property in the network before and during the crisis. Finally, the dynamical change of the network community structure is deeply analyzed with different threshold. The result indicates that for large thresholds, the network before and after the crisis has a significant community structure. Though this analysis, it would be helpful to investors for making decisions regarding their portfolios or to regulators for monitoring the key nodes to ensure the overall stability of the global stock market.

Systemic risk and hierarchical transitions of financial networks

In this paper, the change in topological hierarchy, which is measured by the minimum spanning tree constructed from the cross-correlations between the stock indices from the S & P 500 for 1998-2012 in a one year moving time window, was used to analyze a financial crisis. The hierarchy increased in all minor crises in the observation time window except for the sharp crisis of 2007-2008 when the global financial crisis occurred. The sudden increase in hierarchy just before the global financial crisis can be used for the early detection of an upcoming crisis. Clearly, the higher the hierarchy, the higher the threats to financial stability. The scaling relations were developed to observe the changes in hierarchy with the network topology. These scaling relations can also identify and quantify the financial crisis periods, and appear to contain the predictive power of an upcoming crisis.

Topological Characteristics of the Hong Kong Stock Market: A Test-based P-threshold Approach to Understanding Network Complexity

In this paper, we analyze the relationship among stock networks by focusing on the statistically reliable connectivity between financial time series, which accurately reflects the underlying pure stock structure. To do so, we firstly filter out the effect of market index on the correlations between paired stocks, and then take a t-test based P-threshold approach to lessening the complexity of the stock network based on the P values. We demonstrate the superiority of its performance in understanding network complexity by examining the Hong Kong stock market. By comparing with other filtering methods, we find that the P-threshold approach extracts purely and significantly correlated stock pairs, which reflect the well-defined hierarchical structure of the market. In analyzing the dynamic stock networks with fixed-size moving windows, our results show that three global financial crises, covered by the long-range time series, can be distinguishingly indicated from the network topological and evolutionary perspectives. In addition, we find that the assortativity coefficient can manifest the financial crises and therefore can serve as a good indicator of the financial market development.

Spatiotemporal Dynamics and Fitness Analysis of Global Oil Market: Based on Complex Network

We study the overall topological structure properties of global oil trade network, such as degree, strength, cumulative distribution, information entropy and weight clustering. The structural evolution of the network is investigated as well. We find the global oil import and export networks do not show typical scale-free distribution, but display disassortative property. Furthermore, based on the monthly data of oil import values during 2005.01-2014.12, by applying random matrix theory, we investigate the complex spatiotemporal dynamic from the country level and fitness evolution of the global oil market from a demand-side analysis. Abundant information about global oil market can be obtained from deviating eigenvalues. The result shows that the oil market has experienced five different periods, which is consistent with the evolution of country clusters. Moreover, we find the changing trend of fitness function agrees with that of gross domestic product (GDP), and suggest that the fitness evolution of oil market can be predicted by forecasting GDP values. To conclude, some suggestions are provided according to the results.

Exploring Market State and Stock Interactions on the Minute Timescale

A stock market is a non-stationary complex system. The stock interactions are important for understanding the state of the market. However, our knowledge on the stock interactions on the minute timescale is limited. Here we apply the random matrix theory and methods in complex networks to study the stock interactions and sector interactions. Further, we construct a new kind of cross-correlation matrix to investigate the correlation between the stock interactions at different minutes within one trading day. Based on 50 million minute-to-minute price data in the Shanghai stock market, we discover that the market states in the morning and afternoon are significantly different. The differences mainly exist in three aspects, i.e. the co-movement of stock prices, interactions of sectors and correlation between the stock interactions at different minutes. In the afternoon, the component stocks of sectors are more robust and the structure of sectors is firmer. Therefore, the market state in the afternoon is more stable. Furthermore, we reveal that the information of the sector interactions can indicate the financial crisis in the market, and the indicator based on the empirical data in the afternoon is more effective.

Structure of local interactions in complex financial dynamics

With the network methods and random matrix theory, we investigate the interaction structure of communities in financial markets. In particular, based on the random matrix decomposition, we clarify that the local interactions between the business sectors (subsectors) are mainly contained in the sector mode. In the sector mode, the average correlation inside the sectors is positive, while that between the sectors is negative. Further, we explore the time evolution of the interaction structure of the business sectors, and observe that the local interaction structure changes dramatically during a financial bubble or crisis.

Dynamic evolution of cross-correlations in the Chinese stock market

The analysis of cross-correlations is extensively applied for the understanding of interconnections in stock markets and the portfolio risk estimation. Current studies of correlations in Chinese market mainly focus on the static correlations between return series, and this calls for an urgent need to investigate their dynamic correlations. Our study aims to reveal the dynamic evolution of cross-correlations in the Chinese stock market, and offer an exact interpretation for the evolution behavior. The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving window with a size of 400 days. The evolutions of the statistical properties of the correlation coefficients, eigenvalues, and eigenvectors of the correlation matrices are carefully analyzed. We find that the stock correlations are significantly increased in the periods of two market crashes in 2001 and 2008, during which only five eigenvalues significantly deviate from the random correlation matrix, and the systemic risk is higher in these volatile periods than calm periods. By investigating the significant contributors of the deviating eigenvectors in different time periods, we observe a dynamic evolution behavior in business sectors such as IT, electronics, and real estate, which lead the rise (drop) before (after) the crashes. Our results provide new perspectives for the understanding of the dynamic evolution of cross-correlations in the Chines stock markets, and the result of risk estimation is valuable for the application of risk management.