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

## Syntax

**GARCH_FORESD** (**[x]**, [σ], order, µ, **[α]**, [β], t, return)

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

* *Warning

GARCH_FORECI(.) 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.
- For the input argument - ([α]) (parameters of the ARCH component):
- The input argument is not optional.
- The value in the first element must be positive.
- The order of the parameters starts with the lowest lag.
- One or more parameters may have missing values or error codes (i.e., #NUM!, #VALUE!, etc.).
- In the case where alpha has one non-missing entry/element (first), no ARCH component is included.
- The order of the ARCH component model is solely determined by the order (minus one) of the last value in the array with a numeric value (vs. missing or error).

- For the input argument - ([β]) (parameters of the GARCH component):
- The input argument is optional and can be omitted, in which case no GARCH component is included.
- The order of the parameters starts with the lowest lag.
- One or more parameters may have missing values or error codes (i.e., #NUM!, #VALUE!, etc.).
- The order of the GARCH component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).

- 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

- 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.

## Comments

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