(deprecated) Returns the confidence interval limits of the conditional mean forecast.
Syntax
GARCHM_FORECI(X, Sigmas, Order, mean, lambda, alphas, betas, innovation, v, T, alpha-level, upper)
- 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-M model mean (i.e. mu).
- lambda
- is the volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.
- 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 model for 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) - v
- 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 X).
- alpha-level
- is the statistical significance level. If missing, a default of 5% is assumed.
- upper
- If true, returns the upper confidence interval limit. Otherwise, returns lower limit.
upper description 0 return lower limit 1 return upper limit
Warning
GARCHM_FORECI() function is deprecated as of version 1.63: use GARCHM_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 significance level (i.e. $\alpha$) must be greater than zero and less than one. Otherwise, the function returns #VALUE!
- The number of steps must be greater than zero. Otherwise, the function returns #VALUE!
- 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.
Examples
Example 1:
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| Formula | Description (Result) |
|---|---|
| =GARCHM_FORECI($B$2:$B$32,1,$D$3,$D$4,$D$5:$D$6,$D$7,1,0.05,1) | Upper confidence interval limit (2.0219) |
| =GARCHM_FORECI($B$2:$B$32,1,$D$3,$D$4,$D$5:$D$6,$D$7,1,0.05,0) | Lower confidence interval limit (-1.885) |
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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