ExtremeRisks (version 0.0.4-1)

MomTailIndex: 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)

Value

An estimate of the tail index \(\gamma\).

Arguments

data

A vector of \((1 \times n)\) observations.

k

An integer specifying the value of the intermediate sequence \(k_n\). See Details.

Author

Simone Padoan, , https://faculty.unibocconi.it/simonepadoan/; Gilles Stupfler, , https://math.univ-angers.fr/~stupfler/

Details

For a dataset data of sample size \(n\), the tail index \(\gamma\) 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 \(k_n\), \(n=1,2,\ldots\). Its represents a sequence of positive integers such that \(k_n \to \infty\) and \(k_n/n \to 0\) as \(n \to \infty\). Practically, the value \(k_n\) specifies the number of k\(+1\) larger order statistics to be used to estimate \(\gamma\).

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