With the network methods and random matrix theory, we investigate the interaction structure of communities in financial markets. In particular, based on the random matrix decomposition, we clarify that the local interactions between the business sectors (subsectors) are mainly contained in the sector mode. In the sector mode, the average correlation inside the sectors is positive, while that between the sectors is negative. Further, we explore the time evolution of the interaction structure of the business sectors, and observe that the local interaction structure changes dramatically during a financial bubble or crisis.

Agent-based modeling is a powerful simulation technique to understand the collective behavior and microscopic interaction in complex financial systems. Recently, the concept for determining the key parameters of agent-based models from empirical data instead of setting them artificially was suggested. We first review several agent-based models and the new approaches to determine the key model parameters from historical market data. Based on the agents’ behaviors with heterogeneous personal preferences and interactions, these models are successful in explaining the microscopic origination of the temporal and spatial correlations of financial markets. We then present a novel paradigm combining big-data analysis with agent-based modeling. Specifically, from internet query and stock market data, we extract the information driving forces and develop an agent-based model to simulate the dynamic behaviors of complex financial systems.

Besides the fluctuation-dissipation theorem around the stationary state, how the fluctuations in non-stationary states correlate with the future motion of the dynamic variables remains a challenging problem. Further, most temporal correlations of the dynamic variables are zero or very weak in a large class of dynamic systems if the dynamic effects of non-stationary states are not considered. We propose novel methods to compute the temporal correlation functions taking into account the dynamic effects of the non-stationary states. In various dynamic systems, we reveal that the past dynamic fluctuations do drive the future motion of the dynamic variables. This dynamic effect of the non-stationary states is a robust, intrinsic and important property of the complex dynamic systems.

The methods of complex networks have been extensively used to characterize information flow in complex systems, such as risk propagation in complex financial networks. However, network dynamics are ignored in most cases despite systems with similar topological structures exhibiting profoundly different dynamic behaviors. To observe the spatiotemporal patterns of risk propagation in complex financial networks, we combined a dynamic model with empirical networks. Our analysis revealed that hub nodes play a dominant role in risk propagation across the network and respond rapidly, thus exhibiting a degree-driven effect. The influence of key dynamic parameters, i.e., infection rate and recovery rate, was also investigated. Furthermore, the impacts of two typical characteristics of complex financial systems—the existence of community structures and frequent large fluctuations—on the spatiotemporal patterns of risk propagation were explored. About $30\%$ of the total risk propagation flow of each community can be explained by the top $10\%$ nodes. Thus, we can control the risk propagation flow of each community by controlling a few influential nodes in the community and, in turn, control the whole network. In extreme market states, hub nodes become more dominant, indicating better risk control.