Threshold network GARCH model

Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its variations have been widely adopted in the study of financial volatilities, while the extension of GARCH‐type models to high‐dimensional data is always difficult because of over‐parameterization and computational complexity. In this article, we propose a multi‐variate GARCH‐type model that can simplify the parameterization by utilizing the network structure that can be appropriately specified for certain types of high‐dimensional data. The asymmetry in the dynamics of volatilities is also considered as our model adopts a threshold structure. To enable our model to handle data with extremely high dimension, we investigate the near‐epoch dependence (NED) of our model, and the asymptotic properties of our quasi‐maximum‐likelihood‐estimator (QMLE) are derived from the limit theorems for NED random fields. Simulations are conducted to test our theoretical results. At last we fit our model to log‐returns of four groups of stocks and the results indicate that bad news is not necessarily more influential on volatility if the network effects are considered.