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SUMMARY:(Séminaire commun proba) - Rainfall\, volatility and roughness: a
 n intriguing story across scales
DTSTART:20260113T081500Z
DTEND:20260113T094500Z
DTSTAMP:20260504T090100Z
UID:indico-event-14464@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marc Hoffmann (Université Paris-Dauphine et INRIA)\
 n\nHydrologists have long modelled rainfall with discrete orcontinous time
  models based on point processes.  In a first part\, weshow that most of 
 the desired phenomenological properties of rainfallmodels are captured by 
 critical Hawkes processes. Viewing thisapproach as a microscopic modelling
 \, we zoom out in a second part ourdata to build a macroscopic model of ag
 gregated rainfall. On severalmacroscopic data sets\, we empirically establ
 ish that rainfall behaveslike a rough fractional process with Hurst parame
 ter close to 0.1\; wefurther rigorously analyse the compatibility of this 
 our approachacross time scales\, implying a heavy-tailed behaviour for Haw
 kesrainfall models which we observe in practice. As a consequence\, anunex
 pected analogy with the theory of rough volatility of Gatheral andRosenbau
 m seems to emerge for rainfall modelling. We discuss theconsequences of th
 ese findings from a statistical point of view\, inparticular how it advoca
 tes for the need of better tools for analysingnonstationary data. \n joi
 nt work with Thomas Deschatre and Mathieu Rosenbaum \n \n\nhttps://indic
 o.math.cnrs.fr/event/14464/
LOCATION:Amphi Schwartz (1R3)
URL:https://indico.math.cnrs.fr/event/14464/
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