Dynamic Spatial Network Quantile Autoregression

This paper proposes a dynamic spatial autoregressive quantile model. Using predetermined network information, we study dynamic tail event driven risk using a system of conditional quantile equations. Extending Zhu, Wang, Wang and Härdle (2019), we allow the contemporaneous dependency of nodal responses by incorporating a spatial lag in our model. For example, this is to allow a firm’s tail behavior to be connected with a weighted aggregation of the simultaneous returns of the other firms. In addition, we control for the common factor effects. The instrumental variable quantile regressive method is used for our model estimation, and the associated asymptotic theory for estimation is also provided. Simulation results show that our model performs well at various quantile levels with different network structures, especially when the node size increases. Finally, we illustrate our method with an empirical study. We uncover significant network effects in the spatial lag among financial institutions.