| MomTailIndex {ExtremeRisks} | R Documentation |
Computes a point estimate of the tail index based on the Moment Based (MB) estimator.
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