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 function of the innovations/residuals (1 = Gaussian (default), 2 = t-Distribution, 3 = GED).
Value Innovation 1 Gaussian or Normal Distribution (default). 2 Student's t-Distribution. 3 Generalized Error Distribution (GED). - v
- is the shape factor (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 follows: $$\sigma_{\infty}^2 \rightarrow V_L=\frac{\alpha_o}{1-\sum_{i=1}^{max(p,q)}\left(\alpha_i+\beta_i\right)}$$
- 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.
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.
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