# 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

1 |

### Arguments

`nobs` |
a number of observations to be simulated ( |

`a` |
a vector of constants in the vector GARCH equation |

`A` |
an ARCH parameter matrix in the vector GARCH equation |

`B` |
a GARCH parameter matrix in the vector GARCH equation |

`R` |
an unconditional correlation matrix |

`dcc.para` |
a vector of the DCC parameters |

`d.f` |
the degrees of freedom parameter for the |

`cut` |
the number of observations to be thrown away for removing initial effects of simulation |

`model` |
a character string describing the model. " |

### Value

A list with components:

`z` |
a matrix of random draws from |

`std.z` |
a matrix of the standardised residuals. |

`dcc` |
a matrix of the simulated dynamic conditional correlations |

`h` |
a matrix of the simulated conditional variances |

`eps` |
a matrix of the simulated time series with DCC-GARCH process |

### 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

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)
``` |