Constructing novel spatio-temporal difference-based covariance models

Data exhibiting negative correlation, particularly in temporal, spatial and spatio-temporal contexts, are frequently described by employing hole effect models or damped oscillation models. Nevertheless, these classical models suffer from severe limitations that reduce their adaptability. Specifically, models belonging to the Bessel class are criticized for consistently displaying a parabolic behaviour near the origin and an uncountable number of zeros. Furthermore, particular models within this class, such as the cosine model, suffer from additional drawbacks, including lack of admissibility in Euclidean spaces of dimension greater than one and not being strictly positive definite. Recently, wide classes of covariance functions, built through the difference of two correlation models, present distinct characteristics with respect to the traditional hole effect models and are considered to be sufficiently flexible, also in space–time. In this paper a further advance to construct correlation models, characterised by negative values, in a spatio-temporal domain is proposed as well as some examples and a case study are presented.