SMS scnews item created by John Ormerod at Fri 28 Apr 2017 1642
Type: Seminar
Distribution: World
Expiry: 5 May 2017
Calendar1: 5 May 2017 1400-1600
CalLoc1: Carslaw 173
CalTitle1: Extremes of events with heavy-tailed inter-arrival times
Auth: jormerod@pjormerod5.pc (assumed)

Statistics Seminar: Peter Straka (UNSW) -- Extremes of events with heavy-tailed inter-arrival times


Heavy-tailed inter-arrival times are a signature of ``bursty’’ dynamics, and 
have been observed in financial time series, earthquakes, solar flares and 
neuron spike trains. We propose to model extremes of such time series via a 
``Max-Renewal process’’ (aka ``Continuous Time Random Maxima process’’). Due 
to geometric sum-stability, the inter-arrival times between extremes are 
attracted to a Mittag-Leffler distribution: As the threshold height increases, 
the Mittag-Leffler shape parameter stays constant, while the scale parameter 
grows like a power-law. Although the renewal assumption is debatable, this 
theoretical result is observed for many datasets. We discuss approaches to 
fit model parameters and assess uncertainty due to threshold selection.

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