stcc.sim {ccgarch} | R Documentation |
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.
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.
# 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")