Thresholding Bursty Time Series • CTRE

The CTRE package fits a CTRE model (“Continuous Time Random Exceedances”) to extremes of ‘bursty’ time series.

A bursty time series typically has heavy-tailed inter-arrival times.
Given a high threshold, the times between threshold crossings follow a Mittag-Leffler distribution, whose scale parameter increases with the threshold.

The magnitudes of the extremes is modelled via the POT (“Peaks-Over-Threshold”) method, which is standard in Extreme Value Theory. It is the time between threshold crossings that is the focus of the CTRE model.

Installation

Stable release on CRAN

You can install CTRE from CRAN via

install.packages("CTRE")
library(CTRE)

Development version on Github

Install the devtools package first, then

# install.packages("devtools")
devtools::install_github("strakaps/CTRE")
library("CTRE")

Usage

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)

Shiny App

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”.
For the POT model fit, see the tab “Exceedances”
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
a plot of the autocorrelation function for the two series (interarrival times and magnitudes).

To run the Shiny app from within RStudio: