Probabilistic insights into spatio-temporal garch model with location-dependent parameters

Abstract

Spatial data analysis is a burgeoning field with applications ranging across ecology, finance and environmental studies, among others. Particularly, the intersection of space and time in phenomena such as environmental dynamics, energy economics and urban development necessitates sophisticated modeling techniques. In this paper, we propose a novel spatio-temporal GARCH model, extending traditional GARCH models to incorporate spatial dependencies alongside temporal dynamics. Building upon prior research, we introduce stationarity conditions and explore the asymptotic normality of the process. We also demonstrate that the process can be effectively approximated by a stationary process at a fixed location, providing valuable insights into localized behavior.