  Heavy rainfall distributional modeling is essential in any impact studies
linked to the water cycle, e.g.\ flood risks. Still, statistical analyses that
both take into account the temporal and multivariate nature of extreme rainfall
are rare, and often, a complex de-clustering step is needed to make extreme
rainfall temporally independent. A natural question is how to bypass this
de-clustering in a multivariate context. To address this issue, we introduce
the stable sums method. Our goal is to incorporate time and space extreme
dependencies in the analysis of heavy tails. To reach our goal, we build on
large deviations of regularly varying stationary time series. Numerical
experiments demonstrate that our novel approach enhances return levels
inference in two ways. First, it is robust concerning time dependencies. We
implement it alike on independent and dependent observations. In the univariate
setting, it improves the accuracy of confidence intervals compared to the main
estimators requiring temporal de-clustering. Second, it thoughtfully integrates
the spatial dependencies. In simulation, the multivariate stable sums method
has a smaller mean squared error than its component-wise implementation. We
apply our method to infer high return levels of daily fall precipitation
amounts from a national network of weather stations in France.
