GARCHM_SIM - Simulated Values of a GARCH-M Model

Returns an array of cells for the model simulated values.

Syntax

GARCHM_SIM ([x], [σ], order, µ, λ, [α], [β], f, ν, t, seed)

[X]

Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).

[σ]

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

Order

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

Value	Order
1	Ascending (the first data point corresponds to the earliest date) (default).
0	Descending (the first data point corresponds to the latest date).

µ

Optional. Is the GARCH model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.

λ

Optional. Is the volatility coefficient for the mean. In finance, lambda is referenced as the risk premium. If missing, a default of 0 is assumed.

[α]

Required. Are the parameters of the ARCH(p) component model: [αo α1, α2 … αp] (starting with the lowest lag).

[β]

Optional. Are the parameters of the GARCH(q) component model: [β1, β2 … βq] (starting with the lowest lag).

F

Optional. Is the probability distribution function of the innovations/residuals (1 = Gaussian (default), 2 = t-Distribution, 3 = GED).

Value	Probability Distribution
1	Gaussian or Normal Distribution (default).
2	Student's t-Distribution.
3	Generalized Error Distribution (GED).

ν

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

T

Optional. Is the forecast time/horizon (expressed in terms of steps beyond the end of the time series). If missing, a default of 1 is assumed.

Seed

Required. 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 - [α_o α_1, α₂ … α_p] - determines the order of the ARCH component model.
5. The number of parameters in the input argument - [β_1, β₂ … β_q] - determines the order of the GARCH component model.
6. The function GARCHM_SIM was added in version 1.63 SHAMROCK.

Files Examples

Related Links

• Wikipedia - Autoregressive conditional heteroskedasticity.

References

• James Douglas Hamilton; Time Series Analysis, Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896.
• Tsay, Ruey S.; Analysis of Financial Time Series, John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740.