ccgarch (version 0.2.2)

eccc.sim: Simulating an (E)CCC-GARCH(1,1) process

Description

This function simulates data either from the original CCC-GARCH by Bollerslev (1990) or from the Extended CCC-GARCH that has non-zero off-diagonal entries in the parameter matrices in the GARCH equation. The innovations (the standardised residuals) can be either a normal or student's $t$ distribution. The dimension $(N)$ is determined by the number of elements in the $\mathbf{a}$ vector.

Usage

eccc.sim(nobs, a, A, B, R, d.f=Inf, cut=1000, model)

Arguments

nobs

a number of observations to be simulated $(T)$

a

a vector of constants in the GARCH equation $(N \times 1)$

A

an ARCH parameter matrix in the GARCH equation. $\mathbf{A}$ can be a diagonal matrix for the original CCC-GARCH model or a full matrix for the extended model $(N \times N)$

B

a GARCH parameter matrix in the GARCH equation. $\mathbf{B}$ can be a diagonal matrix for the original CCC-GARCH model or a full matrix for the extended model $(N \times N)$

R

a constant conditional correlation matrix $(N \times N)$

d.f

the degrees of freedom parameter for the $t$-distribution

cut

the number of observations to be thrown away for removing initial effects of simulation

model

a character string describing the model. "diagonal" for the diagonal model and "extended" for the extended (full ARCH and GARCH parameter matrices) model

Value

• A list with components:
• h
  a matrix of the simulated conditional variances $(T \times N)$
• eps
  a matrix of the simulated time series with (E)CCC-GARCH process $(T \times N)$

References

Bollerslev, T. (1990), Modeling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized ARCH Approach, Review of Economics and Statistics, 72, 498--505. Nakatani, T. and T. Ter"asvirta (2009), Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model, Econometrics Journal, 12, 147--163. Nakatani, T. and T. Ter"asvirta (2008), Appendix to Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model Department of Economic Statistics, Stockholm School of Economics, available at http://swopec.hhs.se/hastef/abs/hastef0649.htm.

See Also

dcc.sim, stcc.sim

Examples

# Simulating data from the original CCC-GARCH(1,1) process
nobs <- 1000; cut <- 1000; nu <- 10
a <- c(0.003, 0.005, 0.001)
A <- diag(c(0.2,0.3,0.15))
B <- diag(c(0.79, 0.6, 0.8))
R <- matrix(c(1.0, 0.4, 0.3, 0.4, 1.0, 0.12, 0.3, 0.12, 1.0),3,3) 

ccc.data   <- eccc.sim(nobs,a, A, B, R, model="diagonal")
ccc.data.t <- eccc.sim(nobs,a, A, B, R, d.f=nu, model="diagonal")