Exponential Spatiotemporal GARCH Model with Asymmetric Volatility Spillovers

Abstract: This paper introduces a spatiotemporal exponential generalised autoregressive conditional heteroscedasticity (spatiotemporal E-GARCH) model, extending traditional spatiotemporal GARCH models by incorporating asymmetric volatility spillovers, while also generalising the time-series E-GARCH model to a spatiotemporal setting with instantaneous, potentially asymmetric volatility spillovers across space. The model allows for both temporal and spatial dependencies in volatility dynamics, capturing how financial shocks propagate across time, space, and network structures. We establish the theoretical properties of the model, deriving stationarity conditions and moment existence results. For estimation, we propose a quasi-maximum likelihood (QML) estimator and assess its finite-sample performance through Monte Carlo simulations. Empirically, we apply the model to financial networks, specifically analysing volatility spillovers in stock markets. We compare different network structures and analyse asymmetric effects in instantaneous volatility interactions.