AMS2004-7: Spatio-Temporal Models Based on Discrete Convolutions

Bruno Sanso and Alexandra Schmidt
12/31/2004 09:00 AM
Applied Mathematics & Statistics
We consider a class of models for spatio-temporal processes based on convolving independent processes with a discrete kernel that is represented by a lower triangular matrix. We consider two separate families: one obtained by convolving spatial Gaussian processes with isotropic correlations where the kernel provides temporal dependencies. A second one is based on considering convolutions of AR(p) processes and using the kernel to provide spatial interactions. We find that the proposed families of models provide a rich variety of covariance structures. These include covariance functions that are stationary and separable in space and time as well as time dependent non-separable and non-isotropic ones.