Planar-Temporal Stationary Correlation Models That Depend on the Maximum Norm

It is useful to have various stochastic models to describe a wide range of spatial or spatio-temporal dependence and interaction. Two families of planar-temporal stationary correlation functions are proposed in this paper, whose planar margins are functions of the maximum norm on the plane. We formulate each of these two families through a simple development base that possesses a rational spectral density. The base for one family is the linear combination of two separable planar-temporal correlation models, while there seems to be no easy interpretation for the base of the other family. Each family is then generated by appropriately randomizing the planar and temporal coordinates of the base random field. One may treat each family as a semiparametric model, whose permissible parameter domains are identified. A common feature of the models developed is that they allow for describing positive and negative correlations. Other properties are also presented