EGARCH_FORE - Forecasting for EGARCH Model

Calculates the out-of-sample forecast statistics: mean, volatility, and confidence interval.

Syntax

EGARCH_FORE(X, Sigmas, Order, Mean, Alphas, Gammas, Betas, Innovation, $\nu$, T, Type, $\alpha$)

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)).

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).

Mean

is the E-GARCH model mean (i.e., mu). If missing, a default of 0 is assumed.

Alphas

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

Gammas

are the leverage parameters (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	Innovation
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 forecast time/horizon (expressed in terms of steps beyond the end of the time series).

Type

is an integer switch to select the forecast output type: (1 = mean (default), 2 = Std. Error, 3 = Term Struct, 4 = LL, 5 = UL)

Value	Type
1	Mean forecast value (default).
2	Forecast standard error (aka local volatility).
3	Volatility term structure.
4	The lower limit of the forecast confidence interval.
5	The upper limit of the forecast confidence interval.

$\alpha$

is the statistical significance level (i.e., alpha). If missing, a default of 5% is assumed.

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 gamma-coefficients must match the number of alpha-coefficients.
5. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
6. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
7. By definition, the EGARCH_FORE function returns a constant value equal to the model mean (i.e., $\mu$) for all horizons.

Files Examples

Related Links

• Wikipedia - Autoregressive conditional heteroskedasticity.

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.