Spectral and network methods in the analysis of correlation matrices of stock returns

Details Spectral and network methods in the analysis of correlation matrices of stock returns Spectral and network methods in the analysis of correlation matrices of stock returns

2007-03-06

arxiv.org/abs/physics/0703061v1

Physica A 383, 147-151 (2007)

Physics

Physics and Society

6 pages, 2 figures

Scientific paper

10.1016/j.physa.2007.04.124

Correlation matrices inferred from stock return time series contain information on the behaviour of the market, especially on clusters of highly correlating stocks. Here we study a subset of New York Stock Exchange (NYSE) traded stocks and compare three different methods of analysis: i) spectral analysis, i.e. investigation of the eigenvalue-eigenvector pairs of the correlation matrix, ii) asset trees, obtained by constructing the maximal spanning tree of the correlation matrix, and iii) asset graphs, which are networks in which the strongest correlations are depicted as edges. We illustrate and discuss the localisation of the most significant modes of fluctuation, i.e. eigenvectors corresponding to the largest eigenvalues, on the asset trees and graphs.

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