stcc.sim {ccgarch} | R Documentation |
This function simulates data either from the original STCC-GARCH by Silvennoinen and Ter"{a}svirta (2005) or from the Extended STCC-GARCH that has non-zero off-diagonal entries in the parameter matrices in the GARCH equation, with multivariate normal or student's t distributions.
The dimension (N) is determined by the number of elements in the mathbf{a} vector.
stcc.sim(nobs, a, A, B, R1, R2, tr.par, st.par, 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. (N times N) |
B |
a GARCH parameter matrix in the GARCH equation. (N times N) |
R1 |
a conditional correlation matrix in regime 1 (N times N) |
R2 |
a conditional correlation matrix in regime 2 (N times N) |
tr.par |
a vector of Scale and location parameters in the transition function (2 times 1) |
st.par |
a vector of parameters for the GARCH(1,1) transition variable (3 times 1) |
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 (T times N) matrix of conditional variances |
eps |
a (T times N) matrix of time series with DCC-GARCH process |
tr.var |
a vector of length T of the transition variable |
st |
a vector of time series of the transition function |
vecR |
a (T times N^{2}) matrix of Smooth Transition Conditional Correlations |
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.
Silvennoinen, A. and T. Ter"{a}svirta (2005), “Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations.” SSE/EFI Working Paper Series in Economics and Finance No. 577, Stockholm School of Economics, available at http://swopec.hhs.se/hastef/abs/hastef0577.htm.
# Simulating data from the original STCC-GARCH(1,1) process nobs <- 1000; cut <- 1000 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)) # Conditional Correlation Matrix for regime 1 R1 <- matrix(c(1.0, 0.4, 0.3, 0.4, 1.0, 0.12, 0.3, 0.12, 1.0),3,3) # Conditional Correlation Matrix for regime 2 R2 <- matrix(c(1.0, 0.01, -0.3, 0.01, 1.0, 0.8, -0.3, 0.8, 1.0),3,3) # a parameter vector for the scale and location parameters # in the logistic function tr.para <- c(5,0) # a parameter vector for a GARCH(1,1) transition variable st.para <- c(0.02,0.04, 0.95) nu <- 15 stcc.data <- stcc.sim(nobs, a, A, B, R1, R2, tr.par=tr.para, st.par=st.para, model="diagonal") stcc.data.t. <- stcc.sim(nobs, a, A, B, R1, R2, tr.par=tr.para, st.par=st.para, d.f=nu, model="diagonal")