expectiles {ExtremeRisks}R Documentation

Expectile Computation

Description

Computes the true expectile for some families of parametric models.

Usage

expectiles(par, tau, tsDist="gPareto", tsType="IID", trueMethod="true",
           estMethod="LAWS", nrep=1e+05, ndata=1e+06, burnin=1e+03)

Arguments

par

A vector of (1 x p) parameters of the time series parametric family. See Details.

tau

A real in (0,1) specifying the level τ of the expectile to be computed. See Details.

tsDist

A string specifying the parametric family of the innovations distribution. By default tsDist="gPareto" specifies a Pareto family of distributions. See Details.

tsType

A string specifying the type of time series. By default tsType="IID" specifies a sequence of independent and indentically distributed random variables. See Details.

trueMethod

A string specifying the method used to computed the expecile. By default trueMethod="true" specifies that the true analytical expression to computed the expectile is used. See Details.

estMethod

A string specifying the method used to estimate the expecile. By default est="LAWS" specifies the use of the direct LAWS estimator. See Details.

nrep

A positive interger specifying the number of simulations to use for computing an approximation of the expectile. See Details.

ndata

A positive interger specifying the number of observations to genreated for each simulation. See Details.

burnin

A positive interger specifying the number of initial observations to discard from the simulated sample.

Details

For a parametric family of time series models or a parametric family of distributions (for the case of independent observations) the τ-th expectile (or expectile of level tau) is computed.

Value

The τ-th expectile.

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

Padoan A.S. and Stupfler, G. (2020). Extreme expectile estimation for heavy-tailed time series. arXiv e-prints arXiv:2004.04078, https://arxiv.org/abs/2004.04078.

See Also

rtimeseries

Examples

# Derivation of the true tau-th expectile for the Pareto distribution
# via accurate simulation

# parameter value
par <- c(1, 0.3)

# Intermediate level (or sample tail probability 1-tau)
tau <- 0.99

trueExp <- expectiles(par, tau)
trueExp


# tau-th expectile of the AR(1) with Student-t innovations
tsDist <- "studentT"
tsType <- "AR"

# Approximation via Monte Carlo methods
trueMethod <- "approx"

# parameter setting
corr <- 0.8
df <- 3
par <- c(corr, df)

# Intermediate level (or sample tail probability 1-tau)
tau <- 0.99

trueExp <- expectiles(par, tau, tsDist, tsType, trueMethod)
trueExp


[Package ExtremeRisks version 0.0.4 Index]