(deprecated) Calculates the estimated error/standard deviation of the conditional mean forecast.

## Syntax

**GARCH_FORESD** (**X**, **Sigmas**, Order, **Mean**, **Alphas**, **Betas**, **T**, **Local**)

**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 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).
**T**- is the forecast time/horizon (expressed in terms of steps beyond the end of the time series X). If missing, t = 1 is assumed.
**Local**- is the type of desired volatility output (Term Structure = 0, Local/Step = 1). If missing, local volatility is assumed.

* *Warning

GARCH_FORESD() function is deprecated as of version 1.63: use the GARCH_FORE function instead.

## 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 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.
- For GARCH(1,1), the squared of the forecast standard error (i.e., conditional variance) is expressed as follows: $$E[\sigma_{T+k}^2]=\alpha_o\times \frac{1-(\alpha_1+\beta_1)^k}{1-(\alpha_1+\beta_1)}+(\alpha_1+\beta_1)^k\sigma_T^2$$
- The forecast standard error (i.e., conditional volatility) converges monotonically to its long-run average. For the case of GARCH(1,1): $$E[\sigma_{T+k\rightarrow \infty}^2]=\frac{\alpha_o}{1-(\alpha_1+\beta_1)}$$

## 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.

## Comments

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