Random matrix theory analysis of cross correlations in financial markets

Abstract

We confirm universal behaviors such as eigenvalue distribution and spacings predicted by random matrix theory (RMT) for the cross correlation matrix of the daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been reported for New York Stock Exchange in previous studies. It is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present. Some deviations in the small eigenvalue statistics outside the bounds of the universality class of RMT are not completely explained with the deterministic correlations as proposed in previous studies. We study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues. This is interpreted as a reminiscent of "level repulsion" in RMT and explains some deviations from the previous studies observed in the market data. We also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on RMT. Some characteristic differences between properties of Tokyo Stock Exchange and New York Stock Exchange are found.

Systematic analysis of group identification in stock markets

“…We propose refined methods to find stock groups which dramatically reduce ambiguities as compared to identifying stock groups from the localization in a single eigenvector of the correlation matrix [9,10,11]. From the analysis of the characteristics of eigenvectors, we construct the group correlation matrix of the stock groups excluding the marketwide effect and random noise.…”

“…The group identification based on the eigenvector analysis of the stock price correlation matrix has been studied by several research groups [9,10,11]. In spite of their pioneering achievements to reveal the localization properties of eigenvectors, the classification of stocks into groups was not so clear, and it only covered about 10% of their stocks because they used only the few highest contributions of eigenvector components due to the ambiguity explained in Sec.…”

“…In the early years, a correlation-based taxonomy of stocks and stock market indices was studied by the method of the hierarchical tree [2,3]. Recently, the minimum spanning tree technique was introduced to study the structure and dynamics of the stock network [4,5,6], the random matrix theory was applied to find out the difference between the random and nonrandom property of the correlations [7,8,9,10,11], and the maximum likelihood clustering method was developed and applied to identify cluster structures in stock markets [12]. Also, these studies have been extended to the applications to the portfolio optimization in real market [5,9].…”

Multiscaled Cross-Correlation Dynamics on SenseCam Lifelogged Images

“…for financial series [9][10][11][12][13][14][15][16][17][18][19][20], electroencephalographic (EEG) recordings [21,22], magnetoencephalographic (MEG) recordings [23] and a variety of other multivariate data. In this paper, we investigate the same approach to analysis SenseCam lifelog data streams.…”

New approaches in agent-based modeling of complex financial systems

“…With the random matrix theory (RMT), for examples, communities can be identified, which are usually associated with business sectors in stock markets [68,69,70,71,72,15,7]. To simulate the sector structure with the agent-based model, we newly introduce the multi-level herding mechanism [24].…”