We address the problem of predicting spatially dependent functional data belonging to a Hilbert space, with a Functional Data Analysis approach. Having defined new global measures of spatial variability for functional random processes, we derive a Universal Kriging predictor for functional data. Consistently with the new established theoretical results, we develop a two-step procedure for predicting georeferenced functional data: first model selection and estimation of the spatial mean (drift), then Universal Kriging prediction on the basis of the identified model. The proposed methodology is applied to daily mean temperatures curves recorded in the Maritimes Provinces of Canada

We explore the use of principal differential analysis as a tool for performing dimensional reduction of functional data sets. In particular, we compare the results provided by principal differential analysis and by functional principal component analysis in the dimensional reduction of three synthetic data sets, and of a real data set concerning 65 three-dimensional cerebral geometries, the AneuRisk65 data set. The analyses show that principal differential analysis can provide an alternative and effective representation of functional data, easily interpretable in terms of exponential, sinusoidal, or damped-sinusoidal functions and providing a different insight to the functional data set under investigation. Moreover, in the analysis of the AneuRisk65 data set, principal differential analysis is able to detect interesting features of the data, such as the rippling effect of the vessel surface, that functional principal component analysis is not able to detect

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