Statistical inference for inter-arrival times of extreme events in bursty time series

Katharina Hees, Smarak Nayak and Peter Straka

Computational Statistics & Data Analysis, 2021, vol. 155, issue C

Abstract: In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages 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”. A new model for the inter-exceedance times of such events above high thresholds is proposed. For high thresholds and infinite-mean waiting times, it is shown that the times between threshold crossings are Mittag-Leffler distributed, and thus form a “fractional Poisson Process” which generalizes the standard Poisson Process of threshold exceedances. Graphical means of estimating model parameters and assessing model fit are provided. The inference method is applied to an empirical bursty time series, and it is shown how the memory of the Mittag-Leffler distribution affects prediction of the time until the next extreme event.

Keywords: Heavy tails; Renewal process; Extreme value theory; Peaks over threshold; Clustering (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:155:y:2021:i:c:s0167947320301870

DOI: 10.1016/j.csda.2020.107096

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