(Commun SO - 9h15) - Rainfall, volatility and roughness: an intriguing story across scales

par Marc Hoffmann (Paris Dauphine)

mardi 13 janv. 2026, 09:15 → 10:45 Europe/Paris

Amphi Schwartz

Joint work with Thomas Deschatre and Mathieu Rosenbaum. Hydrologists have long modelled rainfall with discrete or continous time models based on point processes.  In a first part, we show that most of the desired phenomenological properties of rainfall models are captured by critical Hawkes processes. Viewing this approach as a microscopic modelling, we zoom out in a second part our data to build a macroscopic model of aggregated rainfall. On several macroscopic data sets, we empirically establish that rainfall behaves like a rough fractional process with Hurst parameter close to 0.1; we further rigorously analyse the compatibility of this our approach across time scales, implying a heavy-tailed behaviour for Hawkes rainfall models which we observe in practice. As a consequence, an unexpected analogy with the theory of rough volatility of Gatheral and Rosenbaum seems to emerge for rainfall modelling. We discuss the consequences of these findings from a statistical point of view, in particular how it advocates for the need of better tools for analysing nonstationary data.