  A new approach for evaluating time-trends in extreme values accounting also
for spatial dependence is proposed. Based on exceedances over a space-time
threshold, estimators for a trend function and for extreme value parameters are
given, leading to a homogenization procedure for then applying stationary
extreme value processes. Extremal dependence over space is further evaluated
through variogram analysis including anisotropy. We detect significant
inhomogeneities and trends in the extremal behaviour of daily precipitation
data over a time period of 84 years and from 68 observational weather stations
in North-West Germany. We observe that the trend is not monotonous over time in
general.
  Asymptotic normality of the estimators under maximum domain of attraction
conditions are proven.
