Models extremes of 'bursty' time series via
Continuous Time Random Exceedances (CTRE).
This R package provides tools to analyse extremes of ‘bursty’ time series. Burstiness is characterized by heavy-tailed inter-arrival times and scale-free event dynamics. The CTRE model captures burstiness by generalizing the Poisson process to a fractional Poisson process, with Mittag-Leffler inter-arrival times. Parameter estimates are read off from stability plots, and goodness of fit is assessed via diagnostic plots; see the Shiny app below.
“Peaks Over Threshold for Bursty Time Series”, Katharina Hees, Smarak Nayak, Peter Straka (2018). https://arxiv.org/abs/1802.05218
The package comes with two examples of bursty time series: solar flare magnitudes and bitcoin trading volumes. For parameter estimates of the Mittag-Leffler distribution, see the tab “Exceedance Times”. CTRE model assumptions are checked via a QQ plot of the Mittag-Leffler distribution; an empirical copula plot checking for dependence between inter-arrival times and magnitudes; and a plot of the autocorrelation function for the two series (interarrival times and magnitudes). For the standard POT model plots, see the “Exceedances” tab.
You can run the above Shiny app from within RStudio: