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 \times n) observations simulated from a specified bivariate time series model.

Author(s)

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

References

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

Anthony C. Davison, Simone A. Padoan and Gilles Stupfler (2023). Tail Risk Inference via Expectiles in Heavy-Tailed Time Series, Journal of Business & Economic Statistics, 41(3) 876-889.

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 0.0.4-1 Index]