stcc.sim {ccgarch}R Documentation

Simulating Data from an STCC-GARCH$(1,1)$ process

Description

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.

Usage

    stcc.sim(nobs, a, A, B, R1, R2, tr.par, st.par, 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. (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

Value

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

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

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.

See Also

dcc.sim, eccc.sim

Examples

# 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")

[Package ccgarch version 0.1.1 Index]