tsdep.plot: Diagnostic for Dependence within Time Series Extremes

In POT: Generalized Pareto Distribution and Peaks Over Threshold

Diagnostic for Dependence within Time Series Extremes

Description

A diagnostic tool to assess for short range asymptotic dependence within a stationary time series.

Usage

tsdep.plot(data, u, ..., xlab, ylab, n.boot = 100, show.lines = TRUE,
lag.max, ci = 0.95, block.size = 5 * lag.max, angle = 90, arrow.length =
0.1)

Arguments

data	The time series observations.
u	The threshold.
...	Optional arguments to be passed to the plot function.
xlab, ylab	The x and y-axis labels.
n.boot	Numeric. The number of replicates to compute the bootstrap confidence interval.
show.lines	Logical. If TRUE (the default), the theoretical lines for the asymptotic dependence and “near” independence are drawn.
lag.max	The maximum lag to be explored - may be missing.
ci	The level for the bootstrap confidence interval. The default is the 95% confidence interval.
block.size	The size for the contiguous bootstrap approach.
angle	The angle at the end of the error bar. If 0, error bars are only segments.
arrow.length	The length to be passed in the function arrows.

Details

Let X_t be a stationary sequence of unit Frechet random variables. By stationarity, the joint survivor function \overline{F}_\tau(\cdot, \cdot) of (X_t, X_{t+\tau}) does not depend on t.

One parametric representation for \overline{F}_\tau(\cdot, \cdot) is given by

\overline{F}_\tau(s,s)=L_\tau(s) s^{-1/\eta_\tau}

for some parameter \eta_\tau \in (0,1] and a slowly varying function L_\tau.

The \Lambda_\tau statistic is defined by

\Lambda_\tau = 2 \eta_\tau - 1

This statistic belongs to (-1,1] and is a measure of extremal dependence. \Lambda_\tau = 1 corresponds to asymptotic dependence, 0 < \Lambda_\tau < 1 to positive extremal association, \Lambda_\tau = 0 to “near” independence and \Lambda_\tau < 0 to negative extremal association.

Value

This function plot the \Lambda_\tau statictics against the lag. Bootstrap confidence intervals are also drawn. The function returns invisibly this statistic and the confidence bounds.

Author(s)

Mathieu Ribatet

References

Ledford, A. and Tawn, J. (2003) Diagnostics for dependence within time series extremes. L. R. Statist. Soc. B. 65, Part 2, 521–543.

Ledford, A. and Tawn, J (1996) Statistics for near independence in multivariate extreme values. Biometrika 83 169–187.

See Also

chimeas, tailind.test

Examples

##An independent case
tsdep.plot(runif(5000), u = 0.95, lag.max = 5)

##Asymptotic dependence
mc <- simmc(5000, alpha = 0.2)
tsdep.plot(mc, u = 0.95, lag.max = 5)

POT documentation built on Oct. 17, 2024, 5:06 p.m.