A diagnostic tool to assess for short range asymptotic dependence within a stationary time series.
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)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.
The time series observations.
The threshold.
Optional arguments to be passed to the plot
function.
The x and y-axis labels.
Numeric. The number of replicates to compute the bootstrap confidence interval.
Logical. If TRUE (the default), the
theoretical lines for the asymptotic dependence and ``near''
independence are drawn.
The maximum lag to be explored - may be missing.
The level for the bootstrap confidence interval. The default is the 95% confidence interval.
The size for the contiguous bootstrap approach.
The angle at the end of the error bar. If 0, error
bars are only segments.
The length to be passed in the function
arrows.
Mathieu Ribatet
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.
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.
chimeas, tailind.test
##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)
Run the code above in your browser using DataLab