Inference of Extreme Synchrony with an Entropy Measure on a Bipartite Network

This article proposes a method to quantify the structure of a bipartite graph using a network entropy per link. Collective behavior of participants' quotes and trades in the foreign exchange market is quantified by applying the proposed method to high frequency data. The network entropy per link corresponded to the macroeconomic situation. A finite mixture of Gumbel distributions is used to fit the empirical distribution for the minimum values of network entropy per link in each week. The mixture of Gumbel distributions with parameter estimates by segmentation procedure was verified by the Kolmogorov-Smirnov test. The finite mixture of Gumbel distributions that extrapolate the empirical probability of extreme events has explanatory power at a statistically significant level. These findings provide insight into how to manage collective behavior in the foreign exchange market.