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

## 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

 1 2  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 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

## Value

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

## 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 \mathbf{A} and \mathbf{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\"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

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 # 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) 

### Example output




ccgarch documentation built on May 29, 2017, 12:58 p.m.