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.