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.

```
library("devtools")
install_github("UNSW-MATH/CTRE")
library(CTRE)
```

You can run the above Shiny app from within RStudio:

`runCTREshiny()`

You can

- Create a
`ctre`

object from a time series, a data frame, or two vectors. - Plot it with
`plot`

- Discard the data below a threshold with
`thin`

- Extract data with
`interarrival`

,`time`

and`magnitudes`

- Create stability plots with
`MLestimates`

- Look at diagnostic plots (
`mlqqplot`

,`acf`

,`empcopula`

)