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Abstract:
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Many phenomena in nature are measured across space and through time. Investigating possible space-time interactions, in the presence of uncertainty, is key to understanding the science. In this talk we propose models that are defined as spatially dependent filterings of space-time innovation processes that are realizations of geostatistical processes. These models include the usual class of linear time series models, as well as standard geostatistical models, both Gaussian and non-Gaussian. The processes do not need to be stationary in time or in space, and build on the growing literature concerning nonstationary models. Leveraging both the innovations, as well as the filtering operations used to define these space-time processes, we use ideas from spatial statistics and time series to develop methods for inference and prediction in a space-time context.
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