Comparing the structure of an emerging market with a mature one under global perturbation

In this paper we investigate the Tehran stock exchange (TSE) and Dow Jones Industrial Average (DJIA) in terms of perturbed correlation matrices. To perturb a stock market, there are two methods, namely local and global perturbation. In the local method, we replace a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series, whereas in the global method, we reconstruct the correlation matrix after replacing the original return series with Gaussian-distributed time series. The local perturbation is just a technical study. We analyze these markets through two statistical approaches, random matrix theory (RMT) and the correlation coefficient distribution. By using RMT, we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks. We find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with Gaussian-distributed time series, the mean values of correlation coefficients, the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the RMT prediction fall sharply in both markets. By comparing these two markets, we can see that the DJIA is more sensitive to global perturbations. These findings are crucial for risk management and portfolio selection.     

Identifying the structure of group correlation in the Korean financial market

We investigate the structure of the cross-correlation in the Korean stock market. We analyze daily cross-correlations between price fluctuations of 586 different Korean stock entities for the 6-year time period from 2003 to 2008. The main purpose is to investigate the structure of group correlation and its stability by undressing the market-wide effect using the Markowitz multi-factor model and the network-based approach. We find the explicit list of significant firms in the few largest eigenvectors from the undressed correlation matrix. We also observe that each contributor is involved in the same business sectors. The structure of group correlation can not remain constant during each 1-year time period with different starting points, whereas only two largest eigenvectors are stable for 6 years 8-9 eigenvectors remain stable for half-year. The structure of group correlation in the Korean financial market is disturbed during a sufficiently short time period even though the group correlation exists as an ensemble for the 6-year time period in the evolution of the system. We verify the structure of group correlation by applying a network-based approach. In addition, we examine relations between market capitalization and businesses. The Korean stock market shows a different behavior compared to mature markets, implying that the KOSPI is a target for short-positioned investors.     

Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Mar?enko–Pastur distribution.     

Characteristics of the Korean stock market correlations

We establish in this study a network structure of the Korean stock market, one of the emerging markets, with its minimum spanning tree through the correlation matrix. Based on this analysis, it is found that the Korean stock market does not form the clusters of the business sectors or of the industry categories. When the MSCI (Morgan Stanley Capital International Inc.) index is exploited, we find that the clusters of the Korean stock market is formed. This finding implicates that the Korean market, in this context, is characteristically different from the mature markets.     

Analysis of stock prices of mining business

Stock exchanges have a diversity of so-called business groups and much evidence has been presented by covariance matrix analysis (Laloux et al. (1999) [6], Plerou et al. (2002) [7], Plerou et al. (1999) [8], Mantegna (1999) [9], Utsugi et al. (2004) [21] and Lim et al. (2009) [26]). A market-wide effect plays a crucial role in shifting the correlation structure from random to non-random. In this work, we study the structural properties of stocks related to the mining industry, especially rare earth minerals, listed on two exchanges, namely the TSX (Toronto stock exchange) and the TSX-V (Toronto stock exchange-ventures). In general, raw-material businesses are sensitively affected by the global economy while each firm has its own cycle. We prove that the global crisis during 2006–2009 affected the mineral market considerably. These two aspects compete to control price fluctuations. We show that the internal cycle overwhelms the global economic environment in terms of random matrix theory and overlapping matrices. However, during the period of 2006–2009, the effect of the global economic environment emerges. This result is well explained by the recent global financial/economic crisis. For comparison, we analyze the time stability of business clusters of the KOSPI, that is, the electric/electronic business, using an overlapping matrix. A clear difference in behavior is confirmed. Consequently, rare earth minerals in the raw-material business should be classified not by standard business classifications but by the internal cycle of business.     

One-factor model for the cross-correlation matrix in the Vietnamese stock market

Random matrix theory (RMT) has been applied to the analysis of the cross-correlation matrix of a financial time series. The most important findings of previous studies using this method are that the eigenvalue spectrum largely follows that of random matrices but the largest eigenvalue is at least one order of magnitude higher than the maximum eigenvalue predicted by RMT. In this work, we investigate the cross-correlation matrix in the Vietnamese stock market using RMT and find similar results to those of studies realized in developed markets (US, Europe, Japan) , , , , , , , ,  and  as well as in other emerging markets, ,  and . Importantly, we found that the largest eigenvalue could be approximated by the product of the average cross-correlation coefficient and the number of stocks studied. We demonstrate this dependence using a simple one-factor model. The model could be extended to describe other characteristics of the realistic data.     

Theoretical analyses of stock correlations affected by subprime crisis and total assets: Network properties and corresponding physical mechanisms

In the field of statistical mechanics and system science, it is acknowledged that the financial crisis has a profound influence on stock market. However, the influence of total asset of enterprise on stock quote was not considered in the previous studies. In this work, a modified cross-correlation matrix that focuses on the influence of total asset on stock quote is introduced into the analysis of the stocks collected from Asian and American stock markets, which is different from the previous studies. The key results are obtained as follows. Firstly, stock is more greatly correlated with big asset than with small asset. Secondly, the higher the correlation coefficient among stocks, the larger the eigenvector is. Thirdly, in different periods, like the pre-subprime crisis period and the peak of subprime crisis period, Asian stock quotes show that the component of the third eigenvector of the cross-correlation matrix decreases with the asset of the enterprise decreasing.Fourthly, by simulating the threshold network, the small network constructed by 10 stocks with large assets can show the large network state constructed by 30 stocks. In this research we intend to fully explain the physical mechanism for understanding the historical correlation between stocks and provide risk control strategies in the future.     

Associated relaxation time and intensity correlation function of a bistable system driven by cross-correlation additive and multiplicative coloured noise sources

The associated relaxation time and the intensity correlation function of a bistable system driven by an additive and a multiplicative coloured noise with coloured cross-correlation are investigated. Using the Novikov theorem and the projection operator method, the analytic expressions of the stationary probability distribution P_st(x), the relaxation time T_c, and the normalized correlation function C(s) of the system are obtained. The effects of the noise intensity, the cross-correlation strength λ and the cross-correlation time τ are discussed. By numerical computation, it is found that the cross-correlation strength |λ| and the quantum noise intensity D decrease the relaxation of the system from unstable points. The cross-correlation time τ delays relaxation of the system from unstable points. The cross-correlation strength λ and the cross-correlation time τ can alter the effects of the pump noise intensity Q. Thus, the relaxation time T_c is a stochastic resonant phenomenon, and distribution curves exhibit a single-maximum structure.     

Dynamic structure of stock communities: a comparative study between stock returns and turnover rates

The detection of community structure in stock market is of theoretical and practical significance for the study of financial dynamics and portfolio risk estimation. We here study the community structures in Chinese stock markets from the aspects of both price returns and turnover rates, by using a combination of the PMFG and infomap methods based on a distance matrix. An empirical study using the overall data set shows that for both returns and turnover rates the largest communities are composed of specific industrial or conceptional sectors and the correlation inside a sector is generally larger than the correlation between different sectors. However, the community structure for turnover rates is more complex than that for returns, which indicates that the interactions between stocks revealed by turnover rates may contain more information. This conclusion is further confirmed by the analysis of the changes in the dynamics of community structures over five sub-periods. Sectors like banks, real estate, health care and New Shanghai take turns to comprise a few of the largest communities in different sub-periods, and more interestingly several specific sectors appear in the communities with different rank orders for returns and turnover rates even in the same sub-period. To better understand their differences, a comparison between the evolution of the returns and turnover rates of the stocks from these sectors is conducted. We find that stock prices only had large changes around important events while turnover rates surged after each of these events relevant to specific sectors, which shows strong evidence that the turnover rates are more susceptible to exogenous shocks than returns and its measurement for community detection may contain more useful information about market structure.     

Hierarchical structure in financial markets

I find a hierarchical arrangement of stocks traded in a financial market by investigating the daily time series of the logarithm of stock price. The topological space is a subdominant ultrametric space associated with a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between all pairs of stocks of the portfolio by considering the synchronous time evolution of the difference of the logarithm of daily stock price. The hierarchical tree of the subdominant ultrametric space associated with the graph provides a meaningful economic taxonomy. Received 24 March 1999 and Received in final form 28 June 1999     

Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.     

Associated relaxation time and the correlation function for a tumor cell growth system subjected to color noises

The associated relaxation time Tc and the normalized correlation function C(s) for a tumor cell growth system subjected to color noises are investigated. Using the Novikov theorem and Fox approach, the steady probability distribution is obtained. Based on them, the expressions of Tc and C(s) are derived by means of projection operator method, in which the effects of the memory kernels of the correlation function are taken into account. Performing the numerical computations, it is found: (1) With the cross-correlation intensity |λ|, the additive noise intensity α and the multiplicative noise self-correlation time τ₁ increasing, the tumor cell numbers can be restrained; And the cross-correlation time τ₃, the multiplicative noise intensity D can induce the tumor cell numbers increasing; However, the additive noise self-correlation time τ₂ cannot affect the tumor cell numbers; The relaxation time Tc is a stochastic resonant phenomenon, and the distribution curves exhibit a single-maximum structure with D increasing. (2) The cross-correlation strength λ weakens the related activity between two states of the tumor cell numbers at different time, and enhances the stability of the tumor cell growth system in the steady state; On the contrast, τ₁ and τ₃ enhance the related activity between two states at different time; However, τ₂ has no effect on the related activity between two states at different time.     

Exponentially Weighted Multivariate HAR Model with Applications in the Stock Market

This paper considers a multivariate time series model for stock prices in the stock market. A multivariate heterogeneous autoregressive (HAR) model is adopted with exponentially decaying coefficients. This model is not only suitable for multivariate data with strong cross-correlation and long memory, but also represents a common structure of the joint data in terms of decay rates. Tests are proposed to identify the existence of the decay rates in the multivariate HAR model. The null limiting distributions are established as the standard Brownian bridge and are proven by means of a modified martingale central limit theorem. Simulation studies are conducted to assess the performance of tests and estimates. Empirical analysis with joint datasets of U.S. stock prices illustrates that the proposed model outperforms the conventional HAR models via OLSE and LASSO with respect to residual errors.     

Cross-correlation dynamics in financial time series

The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross-correlation matrix, over these time windows, oppose those of the largest eigenvalue. This behaviour is shown to be independent of the size of the time window and the number of stocks examined.A basic one-factor model is then proposed, which captures the main dynamical features of the eigenvalue spectrum of the empirical data. Through the addition of perturbations to the one-factor model, (leading to a ‘market plus sectors’ model), additional sectoral features are added, resulting in an Inverse Participation Ratio comparable to that found for empirical data. By partitioning the eigenvalue time series, we then show that negative index returns, (drawdowns), are associated with periods where the largest eigenvalue is greatest, while positive index returns, (drawups), are associated with periods where the largest eigenvalue is smallest. The study of correlation dynamics provides some insight on the collective behaviour of traders with varying strategies.     

Topological properties of stock market networks: The case of Brazil

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.     

Detection of Mutual Exciting Structure in Stock Price Trend Dynamics

We investigated a comprehensive analysis of the mutual exciting mechanism for the dynamic of stock price trends. A multi-dimensional Hawkes-model-based approach was proposed to capture the mutual exciting activities, which take the form of point processes induced by dual moving average crossovers. We first performed statistical measurements for the crossover event sequence, introducing the distribution of the inter-event times of dual moving average crossovers and the correlations of local variation (LV), which is often used in spike train analysis. It was demonstrated that the crossover dynamics in most stock sectors are generally more regular than a standard Poisson process, and the correlation between variations is ubiquitous. In this sense, the proposed model allowed us to identify some asymmetric cross-excitations, and a mutually exciting structure of stock sectors could be characterized by mutual excitation correlations obtained from the kernel matrix of our model. Using simulations, we were able to substantiate that a burst of the dual moving average crossovers in one sector increases the intensity of burst both in the same sector (self-excitation) as well as in other sectors (cross-excitation), generating episodes of highly clustered burst across the market. Furthermore, based on our finding, an algorithmic pair trading strategy was developed and backtesting results on real market data showed that the mutual excitation mechanism might be profitable for stock trading.     

Detecting community structure from coherent oscillation of excitable systems

Many networks are proved to have community structures. On the basis of the fact that the dynamics on networks are intensively affected by the related topology, in this paper the dynamics of excitable systems on networks and a corresponding approach for detecting communities are discussed. Dynamical networks are formed by interacting neurons; each neuron is described using the FHN model. For noisy disturbance and appropriate coupling strength, neurons may oscillate coherently and their behavior is tightly related to the community structure. Synchronization between nodes is measured in terms of a correlation coefficient based on long time series. The correlation coefficient matrix can be used to project network topology onto a vector space. Then by the K-means cluster method, the communities can be detected. Experiments demonstrate that our algorithm is effective at discovering community structure in artificial networks and real networks, especially for directed networks. The results also provide us with a deep understanding of the relationship of function and structure for dynamical networks.     

An analysis of cross-correlations in an emerging market

We apply random matrix theory to compare correlation matrix estimators C$C$ obtained from emerging market data. The correlation matrices are constructed from 10 years of daily data for stocks listed on the Johannesburg stock exchange (JSE) from January 1993 to December 2002. We test the spectral properties of C$C$ against random matrix predictions and find some agreement between the distributions of eigenvalues, nearest neighbour spacings, distributions of eigenvector components and the inverse participation ratios for eigenvectors. We show that interpolating both missing data and illiquid trading days with a zero-order hold increases agreement with RMT predictions. For the more realistic estimation of correlations in an emerging market, we suggest a pairwise measured-data correlation matrix. For the data set used, this approach suggests greater temporal stability for the leading eigenvectors. An interpretation of eigenvectors in terms of trading strategies is given, as opposed to classification by economic sectors.     

Synchronization analysis of singular hybrid coupled networks

In this Letter, singular hybrid coupled systems are introduced to describe complex networks with a special class of constraints. The synchronization problem of singular hybrid coupled systems with time-varying nonlinear perturbation is investigated. A sufficient condition for global synchronization is derived based on the Lyapunov stability theory. The singular system is regular and impulse free. Finally, a numerical example is provided to illustrate the effectiveness of the proposal conditions.