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

- 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 gamma-coefficients must match the number of alpha-coefficients.
- 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.
- 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

## 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.

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