Title: A spatio-temporal GARCH model
Authors: Hans Arnfinn Karlsen - University of Bergen (Norway) [presenting]
Sondre Holleland - University of Bergen (Norway)
Abstract: A spatio-temporal GARCH model is considered on an infinite spatial temporal grid. Due to the time dimension of the model it possible to extend the time series GARCH model to a spatial setting. By using this approach we obtain conditions for the existence of a stationary ergodic solution of the spatio-temporal GARCH model. We also see that the squared variables of the solution satisfy a spatial temporal ARMA model. For estimation of the unknown parameter vector a conditional likelihood method, as used in the time series case, suffers from a boundary that increases with sample size. However, the problem is solved by maximizing a modified likelihood function. This gives both consistent estimates and asymptotic normality. Extension to a spatial temporal ARMA model with GARCH residuals is also discussed.