Title: Spatio-temporal ARMA-GARCH models
Authors: Sondre Holleland - University of Bergen (Norway) [presenting]
Hans Arnfinn Karlsen - University of Bergen (Norway)
Abstract: The ARMA-GARCH time series model is expanded to a gridded spatio-temporal situation, with both spatial and temporal dependence. The spatial dependence is limited due to a user-specified translation invariant neighbourhood structure, for instance having only the closest neighbours influence a given point. This makes the model (potentially) stationary and sparse. The GARCH process contributes with conditionally heteroskedastic, uncorrelated innovations in the MA part of the ARMA model. Wrapping the neighbourhood system onto a torus is done to avoid a boundary problem in the conditional likelihood estimation. This finite, stationary model is called a circular one and is motivated from a projection of the unlimited version. We will introduce the models, dwell on some issues, discuss estimation and show some examples of when one should include a GARCH term in the spatio-temporal ARMA and when not to. A real data example of processed cell imagery data will be presented.