A Functional-Coefficient VAR Model for Dynamic Quantiles and Its Application to Constructing Nonparametric Financial Network

In this article, we investigate a functional coefficient vector autoregressive model for conditional quantiles, in which the interdependences among tail risks such as Value-at-Risk are allowed to vary smoothly with a variable of general economy. Methodologically, we develop an easy-to-implement two-stage procedure to estimate functionals in the dynamic network system based on the deep learning method of neural networks and the local linear smoothing technique. We establish the consistency and the asymptotic normality of the proposed estimator under geometrically β-mixing time series settings. The simulation studies are conducted to show that our new methods work fairly well. The potential of the proposed estimation procedures is demonstrated by an empirical study of constructing and estimating a new type of nonparametric dynamic financial network.