Evolution of worldwide stock markets, correlation structure, and correlation-based graphs

We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period January 1996 to July 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globalization. The fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system. We provide evidence that the short term time scale of correlation among market indices is less than 3 trading months (about 60 trading days). The average values of the nondiagonal elements of the correlation matrix, correlation-based graphs, and the spectral properties of the largest eigenvalues and eigenvectors of the correlation matrix are carrying information about the fast and slow dynamics of the correlation of market indices. We introduce a measure of mutual information based on link co-occurrence in networks in order to detect the fast dynamics of successive changes of correlation-based graphs in a quantitative way.