(deprecated) Calculates the estimated error/standard deviation of the conditional mean forecast.
Syntax
X is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)) of the last p observations.
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)).
Order  Description 

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.
Remarks
 The underlying model is described here.
 Warning: GARCH_FORESD() function is deprecated as of version 1.63: use GARCH_FORE function instead.
 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 follow: $$E[\sigma_{T+k}^2]=\alpha_o\times \frac{1(\alpha_1+\beta_1)^k}{1(\alpha_1+\beta_1)}+(\alpha_1+\beta_1)^k\sigma_T^2$$
 The forecast standard error (i.e. conditional volatility) converges monotonically to its longrun average. For the case of GARCH(1,1): $$E[\sigma_{T+k\rightarrow \infty}^2]=\frac{\alpha_o}{1(\alpha_1+\beta_1)}$$
Examples
Example 1:


Formula  Description (Result)  

=GARCH_FORESD($B$2:$B$32,1,$D$3,$D$4:$D$5,$D$6,1)  Forecasted conditional mean at T+1 (0.9992)  
=GARCH_FORESD($B$2:$B$32,1,$D$3,$D$4:$D$5,$D$6,2)  Forecasted conditional mean at T+2 (0.9992)  
=GARCH_FORESD($B$2:$B$32,1,$D$3,$D$4:$D$5,$D$6,3)  Forecasted conditional mean at T+3 (0.9992) 
Files Examples
References
 Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0691042896
 Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0471690740
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