Forecasting the cost of drought events in France by Super Learning from a short time series of many slightly dependent data

Drought events are the second most expensive type of natural disaster within the French legal framework known as the natural disasters compensation scheme. In recent years, drought events have been remarkable in their geographical location and scale and in their intensity. We develop and apply a new methodology to forecast the cost of a drought event in France. The methodology hinges on Super Learning (van der Laan et al. in Stat Appl Genet Mol Biol 6:23, 2007; Benkeser et al. Stat Med 37:249-260, 2018), a general aggregation strategy to learn a feature of the law of the data identified through an ad hoc risk function by relying on a library of algorithms. The algorithms either compete (discrete Super Learning) or collaborate (continuous Super Learning), with a cross-validation scheme determining the best performing algorithm or combination of algorithms. The theoretical analysis reveals that our Super Learner can learn from a short time series where each time-t-specific data-structure consists of many slightly dependent data indexed by a. We use a dependency graph to model the amount of conditional independence within each t-specific data-structure and a concentration inequality by Janson (Random Struct Algorithms 24:234-248, 2004) and leverage a large ratio of the number of distinct a-s to the degree of the dependency graph in the face of a small number of t-specific data-structures.