  Spatio-temporal models are widely used for inference in statistics and many
applied areas. In such contexts interests are often in the fractal nature of
the sample surfaces and in the rate of change of the spatial surface at a given
location in a given direction. In this paper we apply the theory of Yaglom
(1957) to construct a large class of space-time Gaussian models with stationary
increments, establish bounds on the prediction errors and determine the
smoothness properties and fractal properties of this class of Gaussian models.
Our results can be applied directly to analyze the stationary space-time models
introduced by Cressie and Huang (1999), Gneiting (2002) and Stein (2005),
respectively.
