GARCH_FORESD - Volatility Forecast of GARCH Model

(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)).
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)).
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).
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 the GARCH_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 number of parameters in the input argument - alpha - determines the order of the ARCH component model.
  5. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
  6. For GARCH(1,1), the squared of the forecast standard error (i.e., conditional variance) is expressed as follows: $$E[\sigma_{T+k}^2]=\alpha_o\times \frac{1-(\alpha_1+\beta_1)^k}{1-(\alpha_1+\beta_1)}+(\alpha_1+\beta_1)^k\sigma_T^2$$
  7. The forecast standard error (i.e., conditional volatility) converges monotonically to its long-run average. For the case of GARCH(1,1): $$E[\sigma_{T+k\rightarrow \infty}^2]=\frac{\alpha_o}{1-(\alpha_1+\beta_1)}$$

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