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SUMMARY:(Commun SO - 9h15) - Rainfall\, volatility and roughness: an intri
 guing story across scales
DTSTART:20260113T081500Z
DTEND:20260113T094500Z
DTSTAMP:20260504T170900Z
UID:indico-event-15238@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marc Hoffmann (Paris Dauphine)\n\nJoint work with Th
 omas Deschatre and Mathieu Rosenbaum. Hydrologists have long modelled rain
 fall with discrete or continous time models based on point processes.  In
  a first part\, we show that most of the desired phenomenological properti
 es of rainfall models are captured by critical Hawkes processes. Viewing t
 his approach as a microscopic modelling\, we zoom out in a second part our
  data to build a macroscopic model of aggregated rainfall. On several macr
 oscopic data sets\, we empirically establish that rainfall behaves like a 
 rough fractional process with Hurst parameter close to 0.1\; we further ri
 gorously analyse the compatibility of this our approach across time scales
 \, implying a heavy-tailed behaviour for Hawkes rainfall models which we o
 bserve in practice. As a consequence\, an unexpected analogy with the theo
 ry of rough volatility of Gatheral and Rosenbaum seems to emerge for rainf
 all modelling. We discuss the consequences of these findings from a statis
 tical point of view\, in particular how it advocates for the need of bette
 r tools for analysing nonstationary data.\n\nhttps://indico.math.cnrs.fr/e
 vent/15238/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/15238/
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