GARCHM_FORECI - Forecasting Confidence Interval of GARCH-M Model

(Deprecated) Returns the confidence interval limits of the conditional mean forecast.

Syntax

GARCHM_FORECI ([x], [σ], order, µ, λ, [α], [β], f, ν, t, α, upper)

[X]
Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).
[σ]
Optional. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)) of the last q realized volatilities.
Order
Optional. Is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).
Value Order
1 Ascending (the first data point corresponds to the earliest date) (default).
0 Descending (the first data point corresponds to the latest date).
µ
Optional. Is the GARCH model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.
λ
Optional. Is the volatility coefficient for the mean. In finance, lambda is referenced as the risk premium. If missing, a default of 0 is assumed.
[α]
Required. Are the parameters of the ARCH(p) component model: [αo α1, α2 … αp] (starting with the lowest lag).
[β]
Optional. Are the parameters of the GARCH(q) component model: [β1, β2 … βq] (starting with the lowest lag).
F
Optional. Is the probability distribution function of the innovations/residuals (1 = Gaussian (default), 2 = t-Distribution, 3 = GED).
Value Probability Distribution
1 Gaussian or Normal Distribution (default).
2 Student's t-Distribution.
3 Generalized Error Distribution (GED).
ν
Optional. Is the shape parameter (or degrees of freedom) of the innovations/residuals’ probability distribution function.
T
Optional. Is the forecast time/horizon (expressed in terms of steps beyond the end of the time series). If missing, a default of 1 is assumed.
α
Optional. Is the statistical significance level (i.e., alpha). If missing or omitted, an alpha value of 5% is assumed.
Upper
Required. If true, returns the upper confidence interval limit. Otherwise, returns lower limit.
Value Upper
0 Returns the lower limit.
1 Returns the upper limit.

 Warning

GARCHM_FORECI(.) function is deprecated as of version 1.63: use GARCHM_FORE(.) function instead.

Remarks

  1. The underlying model is described here.
  2. The time series is homogeneous or equally spaced.
  3. The time series may include missing values (e.g., #N/A) at either end.
  4. The significance level (α) must be greater than zero and less than one. Otherwise, the function returns #VALUE!
  5. The number of steps must be greater than zero. Otherwise, the function returns #VALUE!
  6. The number of parameters in the input argument - [αo α1, α2 … αp] - determines the order of the ARCH component model.
  7. The number of parameters in the input argument - [β1, β2 … βq] - determines the order of the GARCH component model.

Files Examples

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