Calculates the long-run average volatility for the given GARCH model.
Syntax
GARCH_VL(alphas, betas, innovation, v)
- 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.
Remarks
- The underlying model is described here.
- The long-run variance of a GARCH process is defined as follow:
- $$\sigma_{\infty}^2 \rightarrow V_L=\frac{\alpha_o}{1-\sum_{i=1}^{max(p,q)}\left(\alpha_i+\beta_i\right)}$$
- The long-run variance is not affected by our choice of shock/innovation distribution.
- 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:
|
|
| Formula | Description (Result) |
|---|---|
| =GARCH_VL($B$3:$B$4,$B$5) | GARCH long-run average volatility (0.999) |
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
Comments
Article is closed for comments.