Abstract: It is a challenging task to understand the complex dependency structures in an ultra-high dimensional network, especially when one concentrates on the tail dependency. To tackle this problem, we consider a network quantile autoregres- sion model (NQAR) to characterize the dynamic quantile behavior in a complex system. In particular, we relate responses to its connected nodes and node spe- ci c characteristics in a quantile autoregression process. A minimum contrast estimation approach for the NQAR model is introduced, and the asymptotic properties are studied. Finally, we demonstrate the usage of our model by in- vestigating the nancial contagions in the Chinese stock market accounting for shared ownership of companies.

Key Words: Social Network; Quantile Regression; Autoregression; Sys- temic Risk; Financial Contagion; Shared Ownership.