Fluctuation scaling and covariance matrix of constituents′ flows on a bipartite graph: Empirical analysis with high-frequency financial data based on a Poisson mixture model

We investigate an association between a power-law relationship of constituents′ flows (mean versus standard deviation) and their covariance matrix on a directed bipartite network. We propose a Poisson mixture model and a method to infer states of the constituents′ flows on such a bipartite network from empirical observation without a priori knowledge on the network structure. By using a proposed parameter estimation method with high frequency financial data we found that the scaling exponent and simultaneous cross-correlation matrix have a positive correspondence relationship. Consequently we conclude that the scaling exponent tends to be 1/2 in the case of desynchronous (specific dynamics is dominant), and to be 1 in the case of synchronous (common dynamics is dominant).