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