Immediate causality network of stock markets

Extensive works show that a network of stocks within a single stock market stores rich information on evolutionary behaviors of the system, such as collapses and/or crises. But a financial event covers usually several markets or even the global financial system. This mismatch of scale leads to lack of concise information to coordinate the event. In this work by using the transfer entropy we reconstruct the influential network between ten typical stock markets distributed in the world. Interesting findings include, before a financial crisis the connection strength reaches a maximum, which can act as an early warning signal of financial crises. The markets in America are monodirectionally and strongly influenced by that in Europe and act as the center. Some strongly linked pairs have also close correlations. The findings are helpful in understanding the evolution and modelling the dynamical process of the global financial system. This method can be extended straightly to find early warning signals for physiological and ecological systems, etc