eccc.sim {ccgarch}R Documentation

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 a student's $t$.

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 conditional variances (T times N)
eps a matrix of time series with (E)CCC-GARCH process (T times N)

Note

When "d.f=Inf", the innovations (the standardised residuals) follow the standard normal distribution. Otherwise, they follow a student's t-distribution with "d.f" degrees of freedom equal.

When model="diagonal", only the diagonal entries in A and B are used. If the ARCH and GARCH matrices do not satisfy the stationarity condition, the simulation is terminated.

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. er"{a}svirta (2008), “Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model”, Econometrics Journal, forthcoming.

Nakatani, T. and T. Ter"{a}svirta (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")

[Package ccgarch version 0.1.1 Index]