MLestimates: Mittag-Leffler estimates for varying thresholds

In strakaps/CTRE: Thresholding Bursty Time Series

Description

For a range of thresholds, return the parameters of the Mittag-Leffler distribution fitted to the threshold exceedance times.

Usage

MLestimates(
  ctre,
  plot_me = TRUE,
  tail = NULL,
  scale = NULL,
  ks = 5:length(ctre)
)

Arguments

ctre	A ctre object
plot_me	Should the estimates be plotted?
tail	Tail parameter of the Mittag-Leffler distribution, if known. Appears as a dashed line in the plot of the tail parameter estimates, and transforms the scale parameter estimates. If not known, scale parameter estimates are untransformed (tail is set to 1).
scale	Scale parameter of the Mittag-Leffler distribution, if known. Appears as a dashed line in the plot of scale parameter estimates.
ks	The values of k at for which estimates are computed. If e.g. k=10, then the threshold is set at the 10th order statistic (10th largest magnitude), and Mittag-Leffler parameter estimates are coputed for the threshold exceedance times. By default, all order statistics are used except the 5 largest, and the estimates are returned in a data frame.

Details

In the resulting "stability plots", parameter estimates are read off as seemingly constant values within an interval of threshold-values delineated by too few exceedances (high variance, left) and too many exceedances (high bias, right). If β \in (0,1) is the tail parameter estimate and σ > 0 the scale parameter estimate, then the inter-arrival time T(k) for magnitudes higher than the k-th magnitude is distributed as

T(k) ~ \sim ML(β, k^{-1/β} σ).

Value

A data.frame of Mittag-Leffler parameter estimates, one row for each threshold, which is returned invisibly unless plot_me = FALSE.

Examples

  library(magrittr)
  par(mfrow = c(1,2))
  flares %>% ctre() %>% thin(k=1000) %>% MLestimates(tail = 0.9, scale = 3E7)

  bitcoin %>% ctre() %>% thin(k=500) %>% MLestimates(tail = 0.9, scale = 2.5E3)
  bitcoin %>% ctre() %>% thin(k=500) %>% MLestimates(plot_me = FALSE) %>% str()

strakaps/CTRE documentation built on Sept. 12, 2021, 6:12 p.m.