  This work is motivated by the analysis of the extremal behavior of buoy and
satellite data describing wave conditions in the North Atlantic Ocean. The
available data sets consist of time series of significant wave height (Hs) with
irregular time sampling. In such a situation, the usual statistical methods for
analyzing extreme values cannot be used directly. The method proposed in this
paper is an extension of the peaks over threshold (POT) method, where the
distribution of a process above a high threshold is approximated by a
max-stable process whose parameters are estimated by maximizing a composite
likelihood function. The efficiency of the proposed method is assessed on an
extensive set of simulated data. It is shown, in particular, that the method is
able to describe the extremal behavior of several common time series models
with regular or irregular time sampling. The method is then used to analyze Hs
data in the North Atlantic Ocean. The results indicate that it is possible to
derive realistic estimates of the extremal properties of Hs from satellite
data, despite its complex space--time sampling.
