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Max-stable processes have proved to be useful for the statistical modellingof spatial extremes. Several representations of max-stable random fields havebeen proposed in the literature. One such representation is based on a limit ofnormalized and scaled pointwise maxima of stationary Gaussian processes thatwas first introduced by Kabluchko, Schlather and de Haan (2009).  This paper deals with statistical inference for max-stable space-timeprocesses that are defined in an analogous fashion. We describe pairwiselikelihood estimation, where the pairwise density of the process is used toestimate the model parameters and prove strong consistency and asymptoticnormality of the parameter estimates for an increasing space-time dimension,i.e., as the joint number of spatial locations and time points tends toinfinity. A simulation study shows that the proposed method works well forthese models.

Statistical inference for max-stable processes in space and time