Spatio-temporal processes for functional data with application in climate monitoring

The underlying idea of this thesis is to move from a spatio-temporal process to a functional spatio-temporal process. In order to do that it is important firstly to specify the spatio-temporal framework of our interest. For our purposes, we are interested in processes evolving in continuous space and discrete time. Formally that means the spatial processes of interest will be limited on geostatistical processes and the temporal processes of interest will be time series. Since the rise of functional data analysis as an important tool for statistical analysis of data observed as curves, many classical statistical tools have been extended to their functional versions in order to handle data observed as curves, namely functional data. The new concept here is that a record observed as a vector of finite number of points is considered as a single entity. This single entity is built as linear combination of coefficients and basis functions through a non parametric statistical methods. The main question we have to answer is: how can we put together a geostatistical spatio-temporal process and the new concept of functional data in order to build a geostatistical spatio-temporal process for functional data. In other words, the motivation of this thesis is to build a dynamical spatio-temporal model for data observed as functions or curves in order to extend an already existing tool for mapping to handle functional data.