  Max-stable processes are the natural analogues of the generalized
extreme-value distribution for the modelling of extreme events in space and
time. Under suitable conditions, these processes are asymptotically justified
models for maxima of independent replications of random fields, and they are
also suitable for the modelling of joint individual extreme measurements over
high thresholds. This paper extends a model of Schlather (2001) to the
space-time framework, and shows how a pairwise censored likelihood can be used
for consistent estimation under mild mixing conditions. Estimator efficiency is
also assessed and the choice of pairs to be included in the pairwise likelihood
is discussed based on computations for simple time series models. The ideas are
illustrated by an application to hourly precipitation data over Switzerland.
