Calculates the out-of-sample conditional mean and volatility forecast.
Syntax
GARCH_FORE(X, Sigmas, Order, mean, alphas, 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)).
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=t-Distribution, 3=GED).
value Description 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 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:
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| 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 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
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