A New Implementation of Network GARCH Model for Stock Volatility and Co‐Volatility Forecasting

ABSTRACT Volatility clustering and spillovers are key features of financial time series with many cross‐sectional assets. While network analysis links similar or correlated stocks and helps trace volatility spillovers, contemporary multivariate ARCH‐GARCH formulations struggle to represent structured network dependence and remain parsimonious. We introduce the generalized network GARCH model under the DCC framework (DCC‐GNGARCH), that embeds the GARCH dynamics within the generalized network autoregressive (GNAR) framework to capture an asset's volatility driven by its own history and by neighboring assets in a constructed network. DCC‐GNGARCH also extends existing network GARCH formulations by adapting neighboring volatility persistence, dynamic conditional covariance updates, and allowing higher order neighboring effects beyond immediate neighbors. This paper provides the model derivation, vectorization and conversion, and an extension by incorporating threshold coefficients to capture leverage effects. We show that the DCC‐GNGARCH is a valid volatility model satisfying the stylized facts of financial return series through simulation. Parameter estimation is then performed by using squared returns as variance proxy and minimizing the negative log‐likelihood (NLL) loss function. We apply our model on 75 of the most active US stocks under a constructed network and highlight the model's ability in volatility estimation and forecast, whereas robustness checks under alternative network constructions, different proxy choices, error specifications, and sparsity levels confirm the stability of the main empirical findings.