stcc_sim: Simulating Data from an STCC-GARCH$(1,1)$ process
In hoanguc3m/ccgarch: Conditional Correlation GARCH models

Description Usage Arguments Value Note References See Also Examples

This function simulates data either from the original STCC-GARCH by Silvennoinen and Ter\"asvirta (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 distribution.

The dimension (N) is determined by the number of elements in the \mathbf{a} vector.

1 2	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 vector GARCH equation (N \times 1)
`A`	an ARCH parameter matrix in the vector GARCH equation. (N \times N)
`B`	a GARCH parameter matrix in the vector 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 matrix of conditional variances (T \times N)
`eps`	a matrix of time series with DCC-GARCH process (T \times N)
`tr.var`	a vector 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 \mathbf{A} and \mathbf{B} are used. If the ARCH and GARCH matrices do not satisfy the stationarity condition, the simulation is terminated.

Silvennoinen, A. and T. Ter\"asvirta (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.

dcc.sim, eccc.sim

# 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

## Not run: 
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")

## End(Not run)