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Abstract:
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Discrete-time spatial time series data arise routinely in meteorological and environmental studies. Inference and prediction associated with them are mostly carried out using linear state space models popularly known as linear dynamic spatio-temporal models (LDSTMs). However, real world environmental processes are highly complex and are seldom representable by models with such simple linear structure. Hence, nonlinear dynamic spatio-temporal models (NLDSTMs) based on the idea of nonlinear observational and evolutionary equations have been proposed as an alternative. However, the caveat lies in selecting the specific form of nonlinearity from a large class of potentially appropriate nonlinear functions. We address this problem by introducing the Gaussian random functional dynamic spatio-temporal model (GRFDSTM). Unlike the LDSTMs or NLDSTMs, in GRFDSTM the functions governing the observational and evolutionary equations are composed of Gaussian random functions. We study properties of GRFDSTM and demonstrate how model fitting and prediction can be carried out coherently using a Bayesian framework. Application of GRFDSTM to simulated and real datasets shows encouraging results.
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