MomTailIndex {ExtremeRisks} | R Documentation |
Moment based Tail Index Estimation
Description
Computes a point estimate of the tail index based on the Moment Based (MB) estimator.
Usage
MomTailIndex(data, k)
Arguments
data |
A vector of |
k |
An integer specifying the value of the intermediate sequence |
Details
For a dataset data
of sample size , the tail index
of its (marginal) distribution is computed by applying the MB estimator. The observations can be either independent or temporal dependent. For details see de Haan and Ferreira (2006).
-
k
oris the value of the so-called intermediate sequence
,
. Its represents a sequence of positive integers such that
and
as
. Practically, the value
specifies the number of
k
larger order statistics to be used to estimate
.
Value
An estimate of the tail index .
Author(s)
Simone Padoan, simone.padoan@unibocconi.it, http://mypage.unibocconi.it/simonepadoan/; Gilles Stupfler, gilles.stupfler@ensai.fr, http://ensai.fr/en/equipe/stupfler-gilles/
References
de Haan, L. and Ferreira, A. (2006). Extreme Value Theory: An Introduction. Springer-Verlag, New York.
See Also
HTailIndex, MLTailIndex, EBTailIndex
Examples
# Tail index estimation based on the Moment estimator obtained with
# 1-dimensional data simulated from an AR(1) with univariate Student-t
# distributed innovations
tsDist <- "studentT"
tsType <- "AR"
# parameter setting
corr <- 0.8
df <- 3
par <- c(corr, df)
# Big- small-blocks setting
bigBlock <- 65
smallblock <- 15
# Number of larger order statistics
k <- 150
# sample size
ndata <- 2500
# Simulates a sample from an AR(1) model with Student-t innovations
data <- rtimeseries(ndata, tsDist, tsType, par)
# tail index estimation
gammaHat <- MomTailIndex(data, k)
gammaHat