Measures of globalization based on cross-correlations of world financial indices

Abstract

The cross-correlation matrix of daily returns of stock market indices in a diverse set of 37 countries worldwide was analyzed. Comparison of the spectrum of this matrix with predictions of random matrix theory provides an empirical evidence of strong interactions between individual economies, as manifested by three largest eigenvalues and the corresponding set of stable, non-random eigenvectors. The observed correlation structure is robust with respect to changes in the time horizon of returns ranging from 1 to 10 trading days, and to replacing individual returns with just their signs. This last observation confirms that it is correlations between signs and not absolute values of fluctuations, which are mostly responsible for the observed effect. Negative changes in the index are somewhat more correlated than the positive ones. Also, in our data set the reaction of Asian stock indices to changes in European and American ones persists for about 3 days.