Dynamic evolution of cross-correlations in the Chinese stock market

Looking into the Market Behaviors through the Lens of Correlations and Eigenvalues: An Investigation on the Chinese and US Markets Using RMT

This research systematically analyzes the behaviors of correlations among stock prices and the eigenvalues for correlation matrices by utilizing random matrix theory (RMT) for Chinese and US stock markets. Results suggest that most eigenvalues of both markets fall within the predicted distribution intervals by RMT, whereas some larger eigenvalues fall beyond the noises and carry market information. The largest eigenvalue represents the market and is a good indicator for averaged correlations. Further, the average largest eigenvalue shows similar movement with the index for both markets. The analysis demonstrates the fraction of eigenvalues falling beyond the predicted interval, pinpointing major market switching points. It has identified that the average of eigenvector components corresponds to the largest eigenvalue switch with the market itself. The investigation on the second largest eigenvalue and its eigenvector suggests that the Chinese market is dominated by four industries whereas the US market contains three leading industries. The study later investigates how it changes before and after a market crash, revealing that the two markets behave differently, and a major market structure change is observed in the Chinese market but not in the US market. The results shed new light on mining hidden information from stock market data.

Evolving Network Analysis of S&P500 Components: COVID-19 Influence of Cross-Correlation Network Structure

The economy is a system of complex interactions. The COVID-19 pandemic strongly influenced economies, particularly through introduced restrictions, which formed a completely new economic environment. The present work focuses on the changes induced by the COVID-19 epidemic on the correlation network structure. The analysis is performed on a representative set of USA companies-the S&P500 components. Four different network structures are constructed (strong, weak, typically, and significantly connected networks), and the rank entropy, cycle entropy, averaged clustering coefficient, and transitivity evolution are established and discussed. Based on the mentioned structural parameters, four different stages have been distinguished during the COVID-19-induced crisis. The proposed network properties and their applicability to a crisis-distinguishing problem are discussed. Moreover, the optimal time window problem is analysed.

Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market

Within the paper, the problem of globalisation during financial crises is analysed. The research is based on the Forex exchange rates. In the analysis, the power law classification scheme (PLCS) is used. The study shows that during crises cross-correlations increase resulting in significant growth of cliques, and also the ranks of nodes on the converging time series network are growing. This suggests that the crises expose the globalisation processes, which can be verified by the proposed analysis.

Trading Imbalance in Chinese Stock Market-A High-Frequency View

Although an imbalance of buying and selling profoundly affects the formation of market trends, a fine-granularity investigation of this perplexity of trading behavior is still missing. Instead of using existing entropy measures, this paper proposed a new indicator based on transaction dataset that enables us to inspect both the direction and the magnitude of this imbalance at high frequency, which we call “polarity”. The polarity aims to measure the unevenness of the very essence trading desire based on the most micro decision making units. We investigate the relationship between the polarity and the return at both market-level and stock-level and find that the autocorrelated polarities cause a positive relation between lagged polarities and returns, while the current polarity is the opposite. It is also revealed that these associations shift according to the market conditions. In fact, when aggregating the one-minute polarities into daily signals, we find not only significant correlations disclosed by the market polarity and market emotion, but also the reliability of these signals in terms of reflecting the transitions of market-level behavior. These results imply that our presented polarity can reflect the market sentiment and condition in real time. Indeed, the trading polarity provides a new indicator from a high-frequency perspective to understand and foresee the market’s behavior in a data-driven manner.

Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis

This paper discusses the effects of introducing nonlinear interactions and noise-filtering to the covariance matrix used in Markowitz’s portfolio allocation model, evaluating the technique’s performances for daily data from seven financial markets between January 2000 and August 2018. We estimated the covariance matrix by applying Kernel functions, and applied filtering following the theoretical distribution of the eigenvalues based on the Random Matrix Theory. The results were compared with the traditional linear Pearson estimator and robust estimation methods for covariance matrices. The results showed that noise-filtering yielded portfolios with significantly larger risk-adjusted profitability than its non-filtered counterpart for almost half of the tested cases. Moreover, we analyzed the improvements and setbacks of the nonlinear approaches over linear ones, discussing in which circumstances the additional complexity of nonlinear features seemed to predominantly add more noise or predictive performance.

Development of stock correlation networks using mutual information and financial big data

Stock correlation networks use stock price data to explore the relationship between different stocks listed in the stock market. Currently this relationship is dominantly measured by the Pearson correlation coefficient. However, financial data suggest that nonlinear relationships may exist in the stock prices of different shares. To address this issue, this work uses mutual information to characterize the nonlinear relationship between stocks. Using 280 stocks traded at the Shanghai Stocks Exchange in China during the period of 2014-2016, we first compare the effectiveness of the correlation coefficient and mutual information for measuring stock relationships. Based on these two measures, we then develop two stock networks using the Minimum Spanning Tree method and study the topological properties of these networks, including degree, path length and the power-law distribution. The relationship network based on mutual information has a better distribution of the degree and larger value of the power-law distribution than those using the correlation coefficient. Numerical results show that mutual information is a more effective approach than the correlation coefficient to measure the stock relationship in a stock market that may undergo large fluctuations of stock prices.

The role of global economic policy uncertainty in long-run volatilities and correlations of U.S. industry-level stock returns and crude oil

We investigate how Global Economic Policy Uncertainty (GEPU) drives the long-run components of volatilities and correlations in crude oil and U.S. industry-level stock markets. Using the modified generalized autoregressive conditional heteroskedasticity mixed data sampling (GARCH-MIDAS) and dynamic conditional correlation mixed data sampling (DCC-MIDAS) specifications, we find that GEPU is positively related to the long-run volatility of Financials and Consumer Discretionary industries; however, it is negatively related to Information Technology, Materials, Telecommunication Services and Energy. Unlike the mixed role of GEPU in the long-run volatilities, the long-run correlations are all positively related to GEPU across the industries. Additionally, the rankings of the correlations of Energy and Materials are time-invariant and classified as high, with the little exception of the latter. The Consumer Staples industry is time-invariant in the low-ranking group. Our results are helpful to policy makers and investors with long-term concerns.

Dynamic Portfolio Strategy Using Clustering Approach

The problem of portfolio optimization is one of the most important issues in asset management. We here propose a new dynamic portfolio strategy based on the time-varying structures of MST networks in Chinese stock markets, where the market condition is further considered when using the optimal portfolios for investment. A portfolio strategy comprises two stages: First, select the portfolios by choosing central and peripheral stocks in the selection horizon using five topological parameters, namely degree, betweenness centrality, distance on degree criterion, distance on correlation criterion and distance on distance criterion. Second, use the portfolios for investment in the investment horizon. The optimal portfolio is chosen by comparing central and peripheral portfolios under different combinations of market conditions in the selection and investment horizons. Market conditions in our paper are identified by the ratios of the number of trading days with rising index to the total number of trading days, or the sum of the amplitudes of the trading days with rising index to the sum of the amplitudes of the total trading days. We find that central portfolios outperform peripheral portfolios when the market is under a drawup condition, or when the market is stable or drawup in the selection horizon and is under a stable condition in the investment horizon. We also find that peripheral portfolios gain more than central portfolios when the market is stable in the selection horizon and is drawdown in the investment horizon. Empirical tests are carried out based on the optimal portfolio strategy. Among all possible optimal portfolio strategies based on different parameters to select portfolios and different criteria to identify market conditions, 65% of our optimal portfolio strategies outperform the random strategy for the Shanghai A-Share market while the proportion is 70% for the Shenzhen A-Share market.

Random matrix theory for analyzing the brain functional network in attention deficit hyperactivity disorder

Attention deficit hyperactivity disorder (ADHD) is the most common childhood neuropsychiatric disorder and affects approximately 6-7% of children worldwide. Here, we investigate the statistical properties of undirected and directed brain functional networks in ADHD patients based on random matrix theory (RMT), in which the undirected functional connectivity is constructed based on correlation coefficient and the directed functional connectivity is measured based on cross-correlation coefficient and mutual information. We first analyze the functional connectivity and the eigenvalues of the brain functional network. We find that ADHD patients have increased undirected functional connectivity, reflecting a higher degree of linear dependence between regions, and increased directed functional connectivity, indicating stronger causality and more transmission of information among brain regions. More importantly, we explore the randomness of the undirected and directed functional networks using RMT. We find that for ADHD patients, the undirected functional network is more orderly than that for normal subjects, which indicates an abnormal increase in undirected functional connectivity. In addition, we find that the directed functional networks are more random, which reveals greater disorder in causality and more chaotic information flow among brain regions in ADHD patients. Our results not only further confirm the efficacy of RMT in characterizing the intrinsic properties of brain functional networks but also provide insights into the possibilities RMT offers for improving clinical diagnoses and treatment evaluations for ADHD patients.