eccc.sim {ccgarch} | R Documentation |
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.
eccc.sim(nobs, a, A, B, R, d.f=Inf, cut=1000, model)
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 |
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) |
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.
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.
# 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")