Measuring information flow among international stock markets: An approach of entropy-based networks on multi time-scales

Information flow among stock markets leads to the co-movement of stock prices and even the financial risk contagion globally. Measuring information flow on multi time-scales helps to develop optimal portfolio strategy for market participants and establish targeted financial regulation for policy makers, but is a challenge for traditional econometrics. This study aims to construct the information flow networks on multi time-scales among international stock markets. First, we use the data of 31 stock market indices during 2007 to 2018, and decompose each of stock index series into short and mid-long time-scale components by empirical mode decomposition (EMD). Then, we extend a novel concept in information science, called transfer entropy (TE), to measure information flow and characterize causality structure between two stock markets, and find that information flows inside of EU stock markets only cluster on short time-scale but not on mid-long time-scale. Moreover, both out-node and in-node centrality measurements for developed markets in the entropy-based networks are much higher on short time-scale, indicating that these markets are more dominant but more vulnerable to short-term risk contagion. Finally, based on the minimum spanning tree (MST) model, we extract the most probable risk contagion paths from entropy-based networks. The results show that outflow MSTs on short time-scale follow a star-like structure to precipitate the risk contagion in the international stock markets, especially during crisis period (2007∼2010). Overall, we emphasize the financial risk contagion on short time-scale.