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In this paper, we present and compare functional and spatio-temporal (Sp.T.)kriging approaches to predict spatial functional random processes (which canalso be viewed as Sp.T. random processes). Comparisons with respect tocomputational time and prediction performance via functional cross-validationis evaluated, mainly through a simulation study but also on two real data sets.We restrict comparisons to Sp.T. kriging versus ordinary kriging for functionaldata (OKFD), since the more flexible functional kriging approaches, pointwisefunctional kriging (PWFK) and functional kriging total model, coincide withOKFD in several situations. We contribute with new knowledge by proving thatOKFD and PWFK coincide under certain conditions. From the simulation study, itis concluded that the prediction performance for the two kriging approaches ingeneral is rather equal for stationary Sp.T. processes, with a tendency forfunctional kriging to work better for small sample sizes and Sp.T. kriging towork better for large sample sizes. For non-stationary Sp.T. processes, with acommon deterministic time trend and/or time varying variances and dependencestructure, OKFD performs better than Sp.T. kriging irrespective of sample size.For all simulated cases, the computational time for OKFD was considerably lowercompared to those for the Sp.T. kriging methods.

Prediction of spatial functional random processes: Comparing functional and spatio-temporal kriging approaches