rbtimeseries {ExtremeRisks}R Documentation

Simulation of Two-Dimensional Temporally Dependent Observations

Description

Simulates samples from parametric families of bivariate time series models.

Usage

rbtimeseries(ndata, dist="studentT", type="AR", copula="Gumbel", par, burnin=1e+03)

Arguments

ndata

A positive interger specifying the number of observations to simulate.

dist

A string specifying the parametric family of the innovations distribution. By default dist="studentT" specifies a Student-t family of distributions. See Details.

type

A string specifying the type of time series. By default type="AR" specifies a linear Auto-Regressive time series. See Details.

copula

A string specifying the type copula to be used. By default copula="Gumbel" specifies the Gumbel copula. See Details.

par

A list of p parameters to be specified for the bivariate time series parametric family. See Details.

burnin

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

Details

For a time series class (type), with a parametric family (dist) for the innovations, a sample of size ndata is simulated. See for example Brockwell and Davis (2016).

Value

A vector of (2 x n) observations simulated from a specified bivariate time series model.

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

Brockwell, Peter J., and Richard A. Davis. (2016). Introduction to time series and forecasting. Springer.

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, expectiles

Examples

# Data simulation from a 2-dimensional AR(1) with bivariate Student-t distributed
# innovations, with one marginal distribution whose lower and upper tail indices
# that are different

tsDist <- "AStudentT"
tsType <- "AR"
tsCopula <- "studentT"

# parameter setting
corr <- 0.8
dep <- 0.8
df <- 3
par <- list(corr=corr, dep=dep, df=df)

# sample size
ndata <- 2500

# Simulates a sample from an AR(1) model with Student-t innovations
data <- rbtimeseries(ndata, tsDist, tsType, tsCopula, par)

# Extreme expectile estimation
plot(data, pch=21)
plot(data[,1], type="l")
plot(data[,2], type="l")

[Package ExtremeRisks version 0.0.4 Index]