Simulating an (E)DCC-GARCH(1,1) process

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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

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    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.

See Also

stcc.sim, eccc.sim

Examples

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# 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)

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