A new method to build spatio-temporal covariance functions: analysis of ozone data

Statistical analysis of natural phenomena with spatial and temporal correlations requires the specification of the correlation structure via a covariance function. A separable spatio-temporal covariance function is usually used for the ease of application. Nonetheless, the separability of the spatio-temporal covariance function can be unrealistic in many settings, where it is required to use a non-separable spatio-temporal covariance function. In this paper, the role of Stieltjes transformation in the construction of non-separable spatio-temporal covariance function is investigated. Then, structural copula function is applied to construct a family of non-separable spatio-temporal covariance function. Afterwards, it is proved that this family of covariance functions does not possess any dimple which exists in some Gneiting’s models. Finally, a modified genetic algorithm is applied to explore the spatio-temporal correlation structure of Ozone data in Tehran, Iran.