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Презентация на тему ARCH and GARCH. Modeling Volatility Dynamics

Modeling Unequal VariabilityEqual Variability: Homoscedasticity Unequal Variability: HeteroscedasticityMeans any variability (around the mean) that is not homoscedasticityModels must be developed for specific cases
ARCH and GARCHModeling Volatility Dynamics Modeling Unequal VariabilityEqual Variability: Homoscedasticity Unequal Variability: HeteroscedasticityMeans any variability (around the What These Acronym Mean?ARCHAutoregressive Conditional HeteroscedasticityGARCHGeneralized ARCH Information in e2Let εt have the mean 0 and the variance σt.Let ARCH Modeling of σt2. ARCH(1)   ARCH as AR(1) on GARCHGARCH(1)   GARCH (1) as ARMA(1,1) on Asymmetry in GARCH - TARCHTARCH(1,1)d = 1 if εt < 0, Asymmetry in GARCH - EGARCHEGARCH(1,1) Eviews CommandARCH(p, q) series_name c
Слайды презентации

Слайд 2 Modeling Unequal Variability
Equal Variability: Homoscedasticity
Unequal Variability: Heteroscedasticity
Means any

Modeling Unequal VariabilityEqual Variability: Homoscedasticity Unequal Variability: HeteroscedasticityMeans any variability (around

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

What These Acronym Mean?ARCHAutoregressive Conditional HeteroscedasticityGARCHGeneralized ARCH

Слайд 4 Information in e2
Let εt have the mean 0

Information in e2Let εt have the mean 0 and the variance

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

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

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

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

Слайд 7 Asymmetry in GARCH - TARCH
TARCH(1,1)

d = 1 if

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

εt < 0, and = 0 if εt

> 0

Слайд 8 Asymmetry in GARCH - EGARCH
EGARCH(1,1)

Asymmetry in GARCH - EGARCHEGARCH(1,1)

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