This thesis presents a spatio-temporal extension of the GARCH process with a specific spatial dependence structure. Different simulation and estimation techniques are developed. Assuming a circular spatial structure at each time point, gives a closed and finite set of variables at each point in time, making the spatio-temporal process adapted in the temporal dimension. This assumption makes likelihood estimation trivial and we obtain an analytical expression for estimators -- both using maximum likelihood and least squares estimation. On non-circular data, this procedure leads to biased estimates, but we suggest doing a parametric bootstrap bias correction, which turns out to be very effective and improve estimates substantially. We also suggest another approach to apply the circular model to non-circular data, by using a Gibbs sampler and an EM-algorithm.