The focus of this paper is on the higher order statistics of spatial simulation models for shadowing processes. Such processes are generally assumed to follow the lognormal distribution. The proposed spatial simulation model is derived from a non-realizable lognormal reference model with given correlation properties by using Rice's sum-of-sinusoids. Both exact and approximate expressions are presented for the level-crossing rate (LCR) and the average duration of fades (ADF) of the simulation model. It is pointed out that Gudmundson's correlation model results in an infinite LCR. To avoid this problem, two alternative spatial correlation models are proposed. Illustrative examples of the dynamic behavior of shadow fading processes are presented for all three types of correlation models. Emphasis will be placed on two realistic propagation scenarios capturing the shadowing effects in suburban and urban areas.