# GARCH_SIM - Simulated values of an GARCH Model

Returns an array of cells for the model simulated values.

## Syntax

GARCH_SIM(X, Sigmas, Order, mean, 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 model mean (i.e. mu).

alphas are the parameters of the ARCH(p) component model (starting with the lowest lag).

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).

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 simulation path time/horizon (expressed in terms of steps beyond end of the time series). If missing, T is set to One(1).

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

## Remarks

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The time series may include missing values (e.g. #N/A) at either end.
4. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
5. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
6. By definition, the GARCH_FORE function returns a constant value equal to the model mean (i.e. $\mu$) for all horizons.
7. The function GARCH_SIM was added in version 1.63 SHAMROCK.