Compatibility of space-time kernels with full, dynamical, or compact support

This paper deals with compatibility of space-time kernels with (either) full, spatially dynamical, or space-time compact support. We deal with the dilemma of statistical accuracy versus computational scalability, which are in a notorious trade-off. Apparently, models with full support ensure maximal information but are computationally expensive, while compactly supported models achieve computational scalability at the expense of loss of information. Hence, an inspection of whether these models might be compatible is necessary. The criterion we use for such an inspection is based on equivalence of Gaussian measures. We provide sufficient conditions for space-time compatibility. As a corollary, we deduce implications in terms of maximum likelihood estimation and misspecified kriging prediction under fixed domain asymptotics. Some results of independent interest relate about the space-time spectrum associated with the classes of kernels proposed in the paper.