Calculates the long-run average volatility for a given E-GARCH model.
Syntax
EGARCH_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 EGARCH long-run average log variance is defined as:
$\ln V_L=\frac{\alpha_o+\eta \times \sum_{i=1}^p\alpha_i}{1-\sum_{j=1}^q\beta_j}$
Where:
- Gaussian distributed innovations/shocks:
$\eta=\sqrt{\frac{\pi}{2}}$ - GED distributed innovations/shocks.
$\eta=\frac{\Gamma(2/\nu )}{\sqrt{\Gamma(1/\nu)\times\Gamma(3/\nu)}} $ - Student's t-Distributed innovations/shocks.
$\eta=\frac{\sqrt{\nu-2}\times\Gamma(\frac{\nu-1}{2})}{\sqrt{\pi}\times\Gamma(\frac{\nu}{2})}$
- Gaussian distributed innovations/shocks:
- The time series is homogeneous or equally spaced.
- The number of gamma-coefficients must match the number of alpha-coefficients.
- 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.
- EGARCH_CHECK examines the model's coefficients for:
- Coefficients are all positive
Examples
Example 1:
|
|
Formula | Description (Result) |
---|---|
=EGARCH_VL($B$3:$B$4,$B$6) | The long-run average volatility (1.18) |
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.