(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
- 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 follows: $$E[\sigma_{T+k}^2]=\alpha_o\times \frac{1-(\alpha_1+\beta_1)^k}{1-(\alpha_1+\beta_1)}+(\alpha_1+\beta_1)^k\sigma_T^2$$
- The forecast standard error (i.e., conditional volatility) converges monotonically to its long-run average. For the case of GARCH(1,1): $$E[\sigma_{T+k\rightarrow \infty}^2]=\frac{\alpha_o}{1-(\alpha_1+\beta_1)}$$
Files Examples
Related Links
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.
Comments
Article is closed for comments.