ccgarch (version 0.2.3)

dcc.sim: Simulating an (E)DCC-GARCH(1,1) process

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

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 $(T \times N)$

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.

See Also

stcc.sim, eccc.sim

Examples

# 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)