# dcc_sim: Simulating an (E)DCC-GARCH(1,1) process In ccgarch: Conditional Correlation GARCH models

## Description

This function simulates data either from the original DCC-GARCH by Engle (2002) or from the Extended DCC-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 a vector.

## Usage

 1  dcc.sim(nobs, a, A, B, R, dcc.para, 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) R an unconditional correlation matrix (N \times N) dcc.para a vector of the DCC parameters (2 \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:

 z a matrix of random draws from N(\mathbf{0}, \mathbf{I}). (T \times N) std.z a matrix of the standardised residuals. \mathnormal{std.z}_{t} \sim N(0, \mathbf{R}_{t}) where \mathbf{R}_{t} is the DCC matrix at t. If d.f is set to a finite positive real number, \mathbf{z}_{t} \sim t_{d.f}(0, \mathbf{R}_{t}) (T \times N) dcc a matrix of the simulated dynamic conditional correlations (T \times N^2) h a matrix of the simulated conditional variances (T \times N) eps a matrix of the simulated time series with DCC-GARCH process (T \times N)

## 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.

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

Engle, R.F. and K. Sheppard (2001), “Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH.” Stern Finance Working Paper Series FIN-01-027 (Revised in Dec. 2001), New York University Stern School of Business.

Engle, R.F. (2002), “Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models.” Journal of Business and Economic Statistics 20, 339–350.

stcc.sim, eccc.sim
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 # Simulating data from the original DCC-GARCH(1,1) process nobs <- 1000; cut <- 1000; nu <- 8 a <- c(0.003, 0.005, 0.001) A <- diag(c(0.2,0.3,0.15)) B <- diag(c(0.75, 0.6, 0.8)) uncR <- matrix(c(1.0, 0.4, 0.3, 0.4, 1.0, 0.12, 0.3, 0.12, 1.0),3,3) dcc.para <- c(0.01,0.98) ## Not run: # for normally distributed innovations dcc.data <- dcc.sim(nobs, a, A, B, uncR, dcc.para, model="diagonal") # for t distributed innovations dcc.data.t <- dcc.sim(nobs, a, A, B, uncR, dcc.para, d.f=nu, model="diagonal") ## End(Not run)