Description Usage Arguments Details Value Author(s) References See Also Examples
Simulates samples from parametric families of bivariate time series models.
1 | rbtimeseries(ndata, dist="studentT", type="AR", copula="Gumbel", par, burnin=1e+03)
|
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 |
copula |
A string specifying the type copula to be used. By default |
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. |
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 bivariate time series models are: Auto-Regressive (type="AR"
), Auto-Regressive and Moving-Average (type="ARMA"
), Generalized-Autoregressive-Conditional-Heteroskedasticity (type="GARCH"
) and Auto-Regressive.
With AR(1) times series the available families of distributions for the innovations and the dependence structure (copula) are:
Student-t (dist="studentT"
and copula="studentT"
) with marginal parameters (equal for both distributions): phi in(-1,1) (autoregressive coefficient), ν>0 (degrees of freedom) and dependence parameter dep in (-1,1). The parameters are specified as par <- list(corr, df, dep)
;
Asymmetric Student-t (dist="AStudentT"
and copula="studentT"
) with marginal parameters (equal for both distributions): phi in(-1,1) (autoregressive coefficient), ν>0 (degrees of freedom) and dependence parameter dep in (-1,1). The paraters are specified as par <- list(corr, df, dep)
. Note that in this case the tail index of the lower and upper tail of the first marginal are different, see Padoan and Stupfler (2020) for details;
With ARMA(1,1) times series the available families of distributions for the innovations and the dependence structure (copula) are:
symmetric Pareto (dist="double-Pareto"
and copula="Gumbel"
or copula="Gaussian"
) with marginal parameters (equal for both distributions): phi in(-1,1) (autoregressive coefficient), σ>0 (scale), α>0 (shape), θ (movingaverage coefficient), and dependence parameter dep (dep>0 if copula="Gumbel"
or dep in (-1,1) if copula="Gaussian"
). The parameters are specified as par <- list(corr, scale, shape, smooth, dep)
.
symmetric Pareto (dist="double-Pareto"
and copula="Gumbel"
or copula="Gaussian"
) with marginal parameters (equal for both distributions): phi in(-1,1) (autoregressive coefficient), σ>0 (scale), α>0 (shape), θ (movingaverage coefficient), and dependence parameter dep (dep>0 if copula="Gumbel"
or dep in (-1,1) if copula="Gaussian"
). The parameters are specified as par <- list(corr, scale, shape, smooth, dep)
. Note that in this case the tail index of the lower and upper tail of the first marginal are different, see Padoan and Stupfler (2020) for details;
With ARCH(1)/GARCH(1,1) time series the distribution of the innovations are symmetric Gaussian (dist="Gaussian"
) or asymmetric Gaussian dist="AGaussian"
. In both cases the marginal parameters (equal for both distributions) are: α_0, α_1, β. In the asymmetric Gaussian case the tail index of the lower and upper tail of the first marginal are different, see Padoan and Stupfler (2020) for details. The available copulas are: Gaussian (copula="Gaussian"
) with dependence parameter dep\in(-1,1), Student-t (copula="studentT"
) with dependence parameters dep in (-1,1) and ν>0 (degrees of freedom), Gumbel (copula="Gumbel"
) with dependence parameter dep>0. The parameters are specified as par <- list(alpha0, alpha1, beta, dep)
or par <- list(alpha0, alpha1, beta, dep, df)
.
A vector of (2 x n) observations simulated from a specified bivariate time series model.
Simone Padoan, simone.padoan@unibocconi.it, http://mypage.unibocconi.it/simonepadoan/; Gilles Stupfler, gilles.stupfler@ensai.fr, http://ensai.fr/en/equipe/stupfler-gilles/
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, http://arxiv.org/abs/2004.04078.
rtimeseries, expectiles
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | # 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")
|
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