Archimedean spectral densities for nonstationary space-time geostatistics

In this work we investigate methods for modelling space-time nonstationary data. We combine the approaches based on spatial adapting and spectral tempering of spectral densities with the desirable features of Archimedean functional. We propose a class of spectral densities whose elements are shown to have a natural ordering with respect to the set of functionals, and some interesting closed forms for the covariance functions obtained as Fourier transform of the elements of this new class are shown. Finally, we show a new class of nonstationary space-time covariance functions, that are additionally asymmetric in time, and related to this methodology.