Stable sums to infer high return levels of multivariate rainfall time series

摘要

Heavy rainfall distributional modeling is essential in any impact studies linkedto the water cycle, for example, flood risks. Still, statistical analyses that bothtake into account the temporal and multivariate nature of extreme rainfall arerare, and often, a complex de-clustering step is needed to make extreme rainfalltemporally independent. A natural question is how to bypass this de-clusteringin a multivariate context. To address this issue, we introduce the stable sumsmethod. Our goal is to incorporate time and space extreme dependencies in theanalysis of heavy tails. To reach our goal, we build on large deviations of regularlyvarying stationary time series. Numerical experiments demonstrate thatour novel approach enhances return levels inference in two ways. First, it isrobust concerning time dependencies. We implement it alike on independentand dependent observations. In the univariate setting, it improves the accuracyof confidence intervals compared to the main estimators requiring temporalde-clustering. Second, it thoughtfully integrates the spatial dependencies. Insimulation, the multivariate stable sums method has a smaller mean squarederror than its component-wise implementation. We apply our method to inferhigh return levels of daily fall precipitation amounts from a national network ofweather stations in France.