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SUMMARY:Rainfall\, volatility and roughness: an intriguing story across sc
 ales - Marc Hoffmann (Université Paris-Dauphine)
DTSTART:20260227T140000Z
DTEND:20260227T150000Z
UID:TALK243211@talks.cam.ac.uk
CONTACT:Po-Ling Loh
DESCRIPTION:Hydrologists have long modelled rainfall with discrete or cont
 inous time models based on point processes.  In a first part\, we show tha
 t most of the desired phenomenological properties of rainfall models are c
 aptured by critical Hawkes processes. Viewing this approach as a microscop
 ic modelling\, we zoom out in a second part our data to build a macroscopi
 c model of aggregated rainfall. On several macroscopic data sets\, we empi
 rically establish that rainfall behaves like a rough fractional process wi
 th Hurst parameter close to 0.1\; we further rigorously analyse the compat
 ibility of this our approach across time scales\, implying a heavy-tailed 
 behaviour for Hawkes rainfall models which we observe in practice. As a co
 nsequence\, an unexpected analogy with the theory of rough volatility seem
 s to emerge for rainfall modelling. We discuss the consequences of these f
 indings from a statistical point of view\, in particular how it advocates 
 for the need of better tools for analysing nonstationary or nearly station
 ary data. \n\nJoint work with Thomas Deschatre (EDF Labs) and Mathieu Rose
 nbaum (Paris Dauphine-PSL).
LOCATION:MR12\, Centre for Mathematical Sciences
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