1. Modeling Volatility Dynamics
ARCH and GARCH
Modeling Volatility Dynamics

2. Modeling Unequal Variability
Equal Variability: Homoscedasticity
Unequal Variability: Heteroscedasticity
Means any variability (around the mean) that is not homoscedasticity
Models must be developed for specific cases

3. What These Acronym Mean?
ARCH
Autoregressive Conditional Heteroscedasticity
GARCH
Generalized ARCH

4. Information in e2 Let et have the mean 0 and the variance st.
Let et be the residual of a model fitted.
Then:
et estimates et
et2 estimates the variance st2.

5. ARCH Modeling of st2.
ARCH(1)
ARCH as AR(1) on

6. GARCH
GARCH(1)
GARCH (1) as ARMA(1,1) on

7. Asymmetry in GARCH - TARCH
d = 1 if et < 0, and = 0 if et > 0

8. Asymmetry in GARCH - EGARCH

9. ARCH(p, q) series_name c
Eviews Command
ARCH(p, q) series_name c