Abstract: The multivariate GARCH (MGARCH) model is popular for analyzing financial time series data. However, statistical inferences for MGARCH models are quite challenging, owing to the high dimension issue. To overcome this difficulty, we propose a network GARCH model that uses information derived from an appropriately defined network structure. This decreases the number of unknown parameters and reduces the computational complexity substantially. We also rigorously establish the strict and weak stationarity of the network GARCH model. In order to estimate the model, a quasi-maximum likelihood estimator (QMLE) is developed, and its asymptotic properties are investigated. Simulation studies are carried out to assess the performance of the QMLE in finite samples, and empirical examples are analyzed to illustrate the usefulness of network GARCH models.

Key words and phrases: GARCH model, multivariate GARCH Model, network structure, quasi-maximum likelihood estimator.