  A spatial curve dynamical model framework is adopted for functional
prediction of counts in a spatiotemporal log-Gaussian Cox process model. Our
spatial functional estimation approach handles both wavelet-based heterogeneity
analysis in time, and spectral analysis in space. Specifically, model fitting
is achieved by minimising the information divergence or relative entropy
between the multiscale model underlying the data and the corresponding
candidates in the spatial spectral domain. A simulation study is carried out
within the family of log-Gaussian Spatial Autoregressive l2-valued processes
(SARl2 processes) to illustrate the asymptotic properties of the proposed
spatial functional estimators. We apply our modelling strategy to
spatiotemporal prediction of respiratory disease mortality.
