Intrinsically Stationary Variograms in Space and Time

This paper addresses the permissible problem of the product of two intrinsically stationary variograms and that of a power function of an intrinsically stationary variogram in space and time. It results in several new classes of space-time variograms, as well as power-law and other long-range dependent covariance models. In particular, the product of two isotropic variograms that are formulated in terms of Bernstein functions is shown to be a valid variogram, and the largest permissible power is determined for the power of an intrinsically stationary variogram that is constructed via the Bernstein function.