ARCH AND GARCH MODEL

1. ARCH and GARCH Model
Professor Abdullah Sonnet talks about it as such >> Regarding stationarity... It's important
because you need to have a well behaved variance... So the sum of ARCH and GARCH
coefficients should be less than unity....it seems you are satisfying it apparently...could
perform a WALD test to check the restriction. Regarding the diagnostic test results: ARCH LM
tests check the existence of variance clustering which is expected to become insignificant if
the variance had been modeled properly. The Jarque Bera tests the normality of the error
term(it is the most violated assumption and thus disregarded). Finally Ljung Q tests the
existence of autocorrelation in the model, this is also expected to turn out to be insignificant if
your mean equation happens to be proper. The selection of lag for Ljung Q is kind of ad hoc
and depend on prior information. Hope that helps.

2. How to handle GARCH and EGARCH model?
Professsor Muzammil Bhatti commented as such>> Lag selection can be made by AIC or
SBC while you can also chose the model with maximum significant lags of both MEAN and
Variance equations. Degree of freedom usually used is 5 PERCENT as it is standard
criterion. chose EGARCH model if you are willing to capture as well as there exist any
threshold in your series other wise simple GARCH is suitable.


3. Is there any leverage effect in this EGARCH model?
Sayed Hossain posted the figure below.



























Monis Syed commented about the following EGARCH model > C(4) depicts the leverage
effect. Basically, C(4) is a coefficient of asymmetry, its positive value means positive shocks
are more responsible for conditional variance as compare to negative developments, whereas
negative sign manifests that adverse shocks/developments are responsible more for the
generation of risk in a particular time series. Here as we can see that C(4) has a negative
value; this implies negative news/shocks/developments are more relevant for risk generation
and this might be referred as a leverage effect.


4. I have run a mean equation. Then I have taken the residual from this mean eqution
and plotted it as below. Now is there any clustering volatility in this residual (one of
the conditions) so that I can employ ARCH-GARCH model?
Sayed Hossain posted the following figure below.




















Muhammad Anees commented> I think Yes

Dhivya Keerthiga commented> I hope yes there is clustering volatility....

Sayed Hossain commented> This plotted residual derived from the mean equation. When
small level of fluctuation follows another small level fluctuation for prolonged period or when
high level of fluctuation follows another high level of fluctuation for prolonged period, then we
call it clustering volatility. We can see this type of clustering volatility in the above figure so we
can run ARCH-GARCH model. It is a graphical representation. Now we need run ARCH test
for matematical conformation. If there is ARCH effect it means we have fulfilled the conditions
to run ARCH and GARCH model.
POPOLAR BLOGS
Dave
Meo School of Research
Shishir Shakya
Noman Arshed
ARCH and GARCH Model
Hossain Academy Note