Calculates the outofsample conditional mean and volatility forecast.
Syntax
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)).
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). if missing, a default of 0 is assumed.
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).
innovation is the probability distribution function of the innovations/residuals (1=Gaussian (default), 2=tDistribution, 3=GED).
value  Description 

1  Gaussian or Normal Distribution (default) 
2  Student's tDistribution 
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 end of the time series). If missing, a default of 1 is assumed.
Type is an integer switch to select the forecast output type: (1=mean (default), 2=Std. Error, 3=Term Struct, 4=LL, 5=UL)
Order  Description 

1  Mean forecast value (default) 
2  Forecast standard error (aka local volatility) 
3  Volatility term structure 
4  Lower limit of the forecast confidence interval. 
5  Upper limit of the forecast confidence interval. 
alpha is the statistical significance level. 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 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 GARCH_FORE function returns a constant value equal to the model mean (i.e. $\mu$) for all horizons.
Examples
Example 1:


Formula  Description (Result)  

=GARCH_FORE($B$2:$B$32,1,$D$3,$D$4:$D$5,$D$6,1)  Forecasted conditional mean at T+1 (0.160)  
=GARCH_FORE($B$2:$B$32,1,$D$3,$D$4:$D$5,$D$6,2)  Forecasted conditional mean at T+2 (0.160)  
=GARCH_FORE($B$2:$B$32,1,$D$3,$D$4:$D$5,$D$6,3)  Forecasted conditional mean at T+3 (0.160) 
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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