Random matrix theory and cross-correlations in global financial indices and local stock market indices

Abstract

We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compared eigenvalues and components of the largest and the second largest eigenvectors of the cross-correlation matrix before, during, and after the global financial the crisis in the year 2008. We find that the majority of its eigenvalues fall within the RMT bounds [λ_, λ + ], where λ and λ are the lower and the upper bounds of the eigenvalues of random correlation matrices. The components of the eigenvectors for the largest positive eigenvalues indicate the identical financial market mode dominating the global and local indices. On the other hand, the components of the eigenvector corresponding to the second largest eigenvalue are positive and negative values alternatively. The components before the crisis change sign during the crisis, and those during the crisis change sign after the crisis. The largest inverse participation ratio (IPR) corresponding to the smallest eigenvector is higher after the crisis than during any other periods in the global and local indices. During the global financial the crisis, the correlations among the global indices and among the local stock indices are perturbed significantly. However, the correlations between indices quickly recover the trends before the crisis.

Market Correlation Structure Changes Around the Great Crash: A Random Matrix Theory Analysis of the Chinese Stock Market

“…The market correlation structure changes around financial crashes. The average correlation after the critical point of crash is higher than that before the crash [3,17,24]. Also, the correlation network becomes more connected after the crash [25].…”

“…-Financial markets evolve in a selforganized manner with the interacting elements forming complex networks at different levels, including international markets [1][2][3][4], individual markets [5][6][7][8], and security trading networks [9][10][11][12][13][14][15][16]. There are well-documented stylized facts of stock return time series within individual markets unveiled by the random matrix theory (RMT) analysis [6,17]: (1) The largest eigenvalue reflects the market effect such that its eigenportfolio returns are strongly correlated with the market returns; (2) Other largest eigenvalues contain information of industrial sectors; and (3) The smallest eigenvalues embed stock pairs with large correlations.…”

To lag or not to lag? How to compare indices of stock markets that operate on different times

“…In 2012, Livan and Rebecchi [13] used daily prices of stocks belonging to the stock exchanges of the USA and of the UK, and looked for the emergence of correlations between the two markets in the eigenvalue spectrum of their non symmetric correlation matrix, also considering time-lagged correlations over short lags. In 2013, Nobi, Maeng, Ha, and Lee [14] used same-day cross-correlations in order to study some global and local financial market indices; Li [15] found that asymmetric comovements between upturns and downturns of stock markets exist between the USA stock market and the stock markets of Canada, France, Germany, and the United Kingdom, but not necessarily between the USA stock market and the Japanese stock market.…”

Topological properties of networks in structural classification of proteins

“…The network has emerged as a crucial framework in biological networks when researchers study and analyze an open and novel problem in complex systems [1][2][3][4]. The most important properties of biological networks are the structural and the topological ones involving interacting amino acids.…”