Correlation and network analysis of global financial indices

Sunil Kumar · Nivedita Deo

156 citations0/0 files storedPhysical Review E

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Complex Systems and Time Series Analysis Complex Network Analysis Techniques Financial Risk and Volatility Modeling

Abstract

Random matrix theory (RMT) and network methods are applied to investigate the correlation and network properties of 20 financial indices. The results are compared before and during the financial crisis of 2008. In the RMT method, the components of eigenvectors corresponding to the second largest eigenvalue form two clusters of indices in the positive and negative directions. The components of these two clusters switch in opposite directions during the crisis. The network analysis uses the Fruchterman-Reingold layout to find clusters in the network of indices at different thresholds. At a threshold of 0.6, before the crisis, financial indices corresponding to the Americas, Europe, and Asia-Pacific form separate clusters. On the other hand, during the crisis at the same threshold, the American and European indices combine together to form a strongly linked cluster while the Asia-Pacific indices form a separate weakly linked cluster. If the value of the threshold is further increased to 0.9 then the European indices (France, Germany, and the United Kingdom) are found to be the most tightly linked indices. The structure of the minimum spanning tree of financial indices is more starlike before the crisis and it changes to become more chainlike during the crisis. The average linkage hierarchical clustering algorithm is used to find a clearer cluster structure in the network of financial indices. The cophenetic correlation coefficients are calculated and found to increase significantly, which indicates that the hierarchy increases during the financial crisis. These results show that there is substantial change in the structure of the organization of financial indices during a financial crisis.

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References

1999Hierarchical structure in financial markets 1999Introduction to Econophysics 1995Scaling behaviour in the dynamics of an economic index 2003A theory of power-law distributions in financial market fluctuations 1999Noise Dressing of Financial Correlation Matrices 1999Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series 2003Dynamics of market correlations: Taxonomy and portfolio analysis 1999Statistical properties of the volatility of price fluctuations

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