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

TL;DR

This paper introduces a network entropy measure for bipartite graphs to analyze collective behavior in financial markets, revealing correlations between entropy and macroeconomic conditions, and models extreme events with Gumbel distributions.

Contribution

It proposes a novel entropy-based metric for bipartite networks and applies it to financial data, demonstrating its effectiveness in detecting macroeconomic states and modeling extreme events.

Findings

Network entropy per link correlates with macroeconomic conditions.

Gumbel mixture models fit the distribution of minimum entropy values.

Entropy measure can predict the likelihood of extreme market events.

Abstract

This article proposes a method to quantify the structure of a bipartite graph using a network entropy per link. The network entropy of a bipartite graph with random links is calculated both numerically and theoretically. As an application of the proposed method to analyze collective behavior, the affairs in which participants quote and trade in the foreign exchange market are quantified. The network entropy per link is found to correspond 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 is 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.