Eur. Phys. J. B 76, 529-535 (2010)
https://doi.org/10.1140/epjb/e2010-00252-9

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

¹ Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan
² Graduate School of Business Administration, Keio University, 4-1-1 Hiyoshi Kouhoku-ku, Yokohama Kanagawa, 223-8526, Japan

Corresponding author: ^a aki@i.kyoto-u.ac.jp

Received: 1 July 2009
Revised: 3 April 2010
Published online: 6 September 2010

Abstract

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).