EGARCH_VL - Long-run Volatility of the EGARCH Model

1. The underlying model is described here.
2. 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.
     
     $\eta=\frac{\sqrt{\nu-2}\times\Gamma(\frac{\nu-1}{2})}{\sqrt{\pi}\times\Gamma(\frac{\nu}{2})}$
3. The time series is homogeneous or equally spaced.
4. The number of gamma-coefficients must match the number of alpha-coefficients.
5. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
6. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
7. EGARCH_CHECK examines the model's coefficients for:
   
   • Coefficients are all positive

Example 1:

Files Examples

Related Links

• Wikipedia - Autoregressive conditional heteroskedasticity

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