Some peculiar families of correlation functions

In this paper a generalization of some families of correlation functions has been proposed; in particular, a generalization of the rational correlation family, as well as a generalization of a subclass of Matérn family have given, together with some relevant properties involving the two classes. Moreover, an extension of the subclass of Matérn family for the two-dimensional and three-dimensional Euclidean spaces has been provided; in addition, the importance of the proposed models for analysing temporal, spatial and, more generally, spatio-temporal data has been underlined, since the same models can be utilized to construct separable as well as non separable correlation functions. It will be shown that these new classes of models are flexible enough to describe both positive and negative correlation structures. On the other hand, with respect to the classical negative correlation models, the proposed families present some features which cannot be found in the same classical negative correlation functions: these relevant properties allow to get new flexible models, which can be helpful for practitioners to accommodate further case studies, as will be shown through some applications.