Title: Extreme value theory for bursty time series
Authors: Katharina Hees - TU Dortmund University (Germany) [presenting]
Abstract: In many complex systems, inter-arrival times between events such as solar flares, trades, neuron voltages or earthquakes follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time windows and empty in others, a phenomenon which has been dubbed ``bursty''. The return times of the extremes, or more precisely of the exceedances above a high threshold, are then no longer exponential distributed and this results in a serial clustering of the extreme events. Such a behavior was also observed for midlatitude cyclones. The aim is to model extreme events of such a bursty time series with heavy tailed inter-arrival times. For high thresholds and infinite mean waiting times, we show that the times between threshold crossings are Mittag-Leffler distributed, and thus form a fractional Poisson-process, which generalizes the standard Poisson-process. We provide graphical means of estimating model parameters and assessing model fit. Along the way, we apply our inference method to a real-world time series, and show how the memory of the Mittag-Leffler distribution affects the predictive distribution for the time until the next extreme event.