Statistical estimation of time-varying complexity in financial networks

In this paper, we propose a method to characterize the relation between financial market instability and the underlying complexity by identifying structural relationships in dynamics of stock returns. The proposed framework is amenable to statistical and econometric estimation techniques, and at the same time, provides a theoretical link between stability of a financial system and the embedded heterogeneity, in line of the May-Wigner result. We estimate the interaction matrix of stock returns through a vector autoregressive structure and compute heterogeneity in the strength of connections for time periods covering periods before the 2007-08 crisis, during the crisis and post-crisis recovery. We show that the empirically estimated heterogeneity increased substantially during time of financial crisis and subsequently tapered off, demonstrating concurrent rise and fall in the degree of instability.