A Kernel-Based Spectral Approach for Spatiotemporal Dynamic Models

Spatiotemporal processes can often be written as hierarchical state-space processes. In situations with complicated dynamics such as wave propagation, it is difficult to parameterize state transition functions for high-dimensional state processes. Although in some cases, prior understanding of the physical process can be used to formulate prior models for the state transition, this is not always possible. Alternatively, for processes where one considers discrete time and continuous space, integro-difference equations suggest that complicated dynamics can be modeled by allowing the associated redistribution kernel to vary with space and/or time. We show that this is indeed the case and that by considering a spectral implementation of such models, one can formulate a spatiotemporal model with relatively few parameters that can accommodate complicated dynamics.