ARCH and GARCH. Modeling Volatility Dynamics

Сентябрь 14, 2022

Главная
Математика
ARCH and GARCH. Modeling Volatility Dynamics

Содержание

2. Modeling Unequal Variability Equal Variability: Homoscedasticity Unequal Variability: Heteroscedasticity Means any variability (around the mean) that
3. What These Acronym Mean? ARCH Autoregressive Conditional Heteroscedasticity GARCH Generalized ARCH
4. Information in e2 Let εt have the mean 0 and the variance σt. Let et be
5. ARCH Modeling of σt2. ARCH(1) ARCH as AR(1) on
6. GARCH GARCH(1) GARCH (1) as ARMA(1,1) on
7. Asymmetry in GARCH - TARCH TARCH(1,1) d = 1 if εt 0
8. Asymmetry in GARCH - EGARCH EGARCH(1,1)
10. Скачать презентацию

Слайд 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

Слайд 3

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

Слайд 4

Information in e2
Let εt have the mean 0 and the variance

σt.
Let et be the residual of a model fitted.
Then:
et estimates εt
et2 estimates the variance σt2.

Слайд 5

ARCH Modeling of σt2.
ARCH(1)
ARCH as AR(1) on

Слайд 6

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

Слайд 7

Asymmetry in GARCH - TARCH
TARCH(1,1)
d = 1 if εt < 0,

and = 0 if εt > 0

Слайд 8

Asymmetry in GARCH - EGARCH
EGARCH(1,1)