rtimeseries {ExtremeRisks} | R Documentation |
Simulation of One-Dimensional Temporally Dependent Observations
Description
Simulates samples from parametric families of time series models.
Usage
rtimeseries(ndata, dist="studentT", type="AR", 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 |
type |
A string specifying the type of time series. By default |
par |
A vector of |
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).
The available categories of time series models are: Auto-Regressive (
type="AR"
), Auto-Regressive and Moving-Average (type="ARMA"
), Generalized-Autoregressive-Conditional-Heteroskedasticity (type="GARCH"
) and Auto-Regressive and Moving-Maxima (type="ARMAX"
).With AR(1) and ARMA(1,1) times series the available families of distributions for the innovations are:
Student-t (
dist="studentT"
) with parameters:\phi\in(-1,1)
(autoregressive coefficient),\nu>0
(degrees of freedom) specified bypar=c(corr, df)
;symmetric Frechet (
dist="double-Frechet"
) with parameters\phi\in(-1,1)
(autoregressive coefficient),\sigma>0
(scale),\alpha>0
(shape),\theta
(movingaverage coefficient), specified bypar=c(corr, scale, shape, smooth)
;symmetric Pareto (
dist="double-Pareto"
) with parameters\phi\in(-1,1)
(autoregressive coefficient),\sigma>0
(scale),\alpha>0
(shape),\theta
(movingaverage coefficient), specified bypar=c(corr, scale, shape, smooth)
.
With ARCH(1)/GARCH(1,1) time series the Gaussian family of distributions is available for the innovations (
dist="Gaussian"
) with parameters,\alpha_0
,\alpha_1
,\beta
specified bypar=c(alpha0, alpha1, beta)
. Finally, with ARMAX(1) times series the Frechet families of distributions is available for the innovations (dist="Frechet"
) with parameters,\phi\in(-1,1)
(autoregressive coefficient),\sigma>0
(scale),\alpha>0
(shape) specified bypar=c(corr, scale, shape)
.
Value
A vector of (1 \times n)
observations simulated from a specified 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
Examples
# Data simulation from a 1-dimensional AR(1) with univariate Student-t
# distributed innovations
tsDist <- "studentT"
tsType <- "AR"
# parameter setting
corr <- 0.8
df <- 3
par <- c(corr, df)
# sample size
ndata <- 2500
# Simulates a sample from an AR(1) model with Student-t innovations
data <- rtimeseries(ndata, tsDist, tsType, par)
# Graphic representation
plot(data, type="l")
acf(data)