# 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.