GPD_shape_plot: Fitted GPD Shape as a Function of the Threshold

In qrmtools: Tools for Quantitative Risk Management

Fitted GPD Shape as a Function of the Threshold

Description

Fit GPDs to various thresholds and plot the fitted GPD shape as a function of the threshold.

Usage

GPD_shape_plot(x, thresholds = seq(quantile(x, 0.5), quantile(x, 0.99),
                                   length.out = 65),
               estimate.cov = TRUE, conf.level = 0.95,
               CI.col = adjustcolor(1, alpha.f = 0.2),
               lines.args = list(), xlim = NULL, ylim = NULL,
               xlab = "Threshold", ylab = NULL,
               xlab2 = "Excesses", plot = TRUE, ...)

Arguments

x	vector of numeric data.
thresholds	numeric vector of thresholds for which to fit a GPD to the excesses.
estimate.cov	logical indicating whether confidence intervals are to be computed.
conf.level	confidence level of the confidence intervals if estimate.cov.
CI.col	color of the pointwise asymptotic confidence intervals (CIs); if NA, no CIs are shown.
lines.args	list of arguments passed to the underlying lines() for drawing the shape parameter as a function of the threshold.
xlim, ylim, xlab, ylab	see plot().
xlab2	label of the secondary x-axis.
plot	logical indicating whether a plot is produced.
...	additional arguments passed to the underlying plot().

Details

Such plots can be used in the peaks-over-threshold method for determining the optimal threshold (as the smallest after which the plot is (roughly) stable).

Value

Invisibly returns a list containing the thresholds considered, the corresponding excesses and the fitted GPD objects as returned by the underlying fit_GPD_MLE().

Author(s)

Marius Hofert

Examples

set.seed(271)
X <- rt(1000, df = 3.5)
GPD_shape_plot(X)

qrmtools documentation built on July 24, 2025, 3:02 a.m.