stcc.sim: Simulating Data from an STCC-GARCH$(1,1)$ process

Description

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.

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 vector of constants in the vector GARCH equation $(N \times 1)$

an ARCH parameter matrix in the vector GARCH equation. $(N \times N)$

a GARCH parameter matrix in the vector GARCH equation. $(N \times N)$

a conditional correlation matrix in regime 1 $(N \times N)$

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:
ha matrix of conditional variances $(T \times N)$
epsa matrix of time series with DCC-GARCH process $(T \times N)$
tr.vara vector of the transition variable
sta vector of time series of the transition function
vecRa $(T \times N^{2})$ matrix of Smooth Transition Conditional Correlations

References

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.

Examples

Run this code

# 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")