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

Abstract: 

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.