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 Innovation 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. $$\eta=\frac{\sqrt{\nu-2}\times\Gamma(\frac{\nu-1}{2})}{\sqrt{\pi}\times\Gamma(\frac{\nu}{2})}$$
- 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.
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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