MomTailIndex: Moment based Tail Index Estimation
In ExtremeRisks: Extreme Risk Measures

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/UniEstimation.r View source: R/Estimation.r

Computes a point estimate of the tail index based on the Moment Based (MB) estimator.

1	MomTailIndex(data, k)

`data`	A vector of (1 x n) observations.
`k`	An integer specifying the value of the intermediate sequence k_n. See Details.

For a dataset data of sample size n, the tail index γ 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 or k_n is the value of the so-called intermediate sequence k_n, n=1,2,.... Its represents a sequence of positive integers such that k_n -> ∞ and k_n/n -> 0 as n -> ∞. Practically, the value k_n specifies the number of k+1 larger order statistics to be used to estimate γ.

An estimate of the tail index γ.

Simone Padoan, simone.padoan@unibocconi.it, http://mypage.unibocconi.it/simonepadoan/; Gilles Stupfler, gilles.stupfler@ensai.fr, http://ensai.fr/en/equipe/stupfler-gilles/

de Haan, L. and Ferreira, A. (2006). Extreme Value Theory: An Introduction. Springer-Verlag, New York.

HTailIndex, MLTailIndex, EBTailIndex

# 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