(Séminaire commun proba) - Rainfall, volatility and roughness: an intriguing story across scales

par Marc Hoffmann (Université Paris-Dauphine et INRIA)

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

Amphi Schwartz (1R3)

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. 

 joint work with Thomas Deschatre and Mathieu Rosenbaum