In this paper we present a new measure to investigate the functional structure of financial markets, the Sector Dominance Ratio (SDR). We study the information embedded in raw and partial correlations using random matrix theory (RMT) and examine the evolution of economic sectoral makeup on a yearly and monthly basis for four stock markets, those of the US, UK, Germany and Japan, during the period from January 2000 to December 2010. We investigate the information contained in raw and partial correlations using the sector dominance ratio and its variation over time. The evolution of economic sectoral activities can be discerned through the largest eigenvectors of both raw correlation and partial correlation matrices. We find a characteristic change of the largest eigenvalue from raw and partial correlations and the SDR that coincides with sharp breaks in asset valuations. Finally, we propose the SDR as an indicator for changes in VIX indexes
Lisa Uechi, Tatsuya Akutsu, H Eugene Stanley, Alan J Marcus, Dror Y Kenett
Physica A: Statistical Mechanics and its Applications, (421) 488–509.
Complex issues and Complex networks