(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)) 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.
Warning
GARCH_FORESD() function is deprecated as of version 1.63: use 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 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 long-run average. For the case of GARCH(1,1): $$E[\sigma_{T+k\rightarrow \infty}^2]=\frac{\alpha_o}{1-(\alpha_1+\beta_1)}$$
Examples
Example 1:
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| 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 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
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