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.
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