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# GARCHM_SIM

Returns an array of cells for the model simulated values.

## Syntax

**GARCHM_SIM**(

**X**,

**Sigmas**,

**Order**,

**mean**,

**lambda**,

**alphas**,

**betas**,

**innovation**,

**Nu**,

**T**,

**seed**)

**X**

is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)).

**Sigmas**

is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)) of the last q realized volatilities.

**Order**

is the time order in the data series (i.e. the first data point's corresponding date (earliest date=1 (default), latest date=0)).

Order | Description |
---|---|

1 | ascending (the first data point corresponds to the earliest date) (default) |

0 | descending (the first data point corresponds to the latest date) |

**mean**

is the GARCH-M^{i} model mean (i.e. mu).

**lambda**

is the volatility coefficient for the mean. In finance, lambda is referenced as the risk premium. If missing, lambda is assumed zero(0).

**alphas**

are the parameters of the ARCH(p) component model (starting with the lowest lag^{i}).

**betas**

are the parameters of the GARCH(q) component model (starting with the lowest lag).

**innovation**

is the probability distribution function of the innovations/residuals (1=Gaussian (default), 2=t-Distribution, 3=GED^{i}).

value | Description |
---|---|

1 | Gaussian or Normal Distribution (default) |

2 | Student's t-Distribution |

3 | Generalized Error Distribution (GED) |

**Nu**

is the shape parameter (or degrees of freedom) of the innovations/residuals probability distribution function.

**T**

is the simulatio path time/horizon (expressed in terms of steps beyond end of the time series).

**seed**

is an unsigned integer for setting up the random number generator(s)

## Remarks

- The underlying model is described here.
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. #N/A) at either end.
- The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
- The number of parameters in the input argument - beta - determines the order of the GARCH component model.
- The function GARCHM_SIM was added in version 1.63 SHAMROCK.

## References

- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740