Principle Fluctuation Modes of the Global Stock Market

The purpose of this work is to study the principle fluctuation modes of the global stock market, which is regarded as a complex system. It is proposed that the systematic risk can be reflected by the trace calculated from the cross-correlation matrix, and the integrity can be classified into clusters according to the plus-minus signs of the elements of the eigenvectors corresponding to several top largest eigenvalues whose total value accounts for more than 60 percent of the trace. The principle fluctuation modes of 30 stock markets are in the same direction in each year of 2005–2010. According to the classification criteria proposed here, the stock markets of the Americas, Europe and Asia & Oceania are automatically classified into different clusters, while Brazil, Russia and China are separated.