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Ironman
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Posts: 0
Joined: November 28th, 2001, 3:21 am

Garch with exogenous variables

January 28th, 2002, 1:28 pm

Garch is a useful tool and it is relatively easy to estimate an univariate standard Garch(p,q) model
with only lagged volatility estimates and innovations, as many statistics/econometric package such
as SAS, Matlab, EView already has this function.

However, it is another story for a Garch model with exogenous variables, such as the following
Garch-in-mean model,with error term in Normal distribution or t-distribution.There is a dummy
for day-of-the-week or holiday effect.

R(t)=a+b*h(t)+residualR(t)
h(t)=alpha+beta*h(t-1)+lamda*sqr(residual(t-1))+ kappa*Dummy+residualh(t)

Other exogenous variables which people may think help explain the volatility may also be
present in the Garch model. The question is:

Do you think it is worthy adding more exogenous variables?
How to estimate the Garch with exogenous variables? Any software for the function available?

Sometimes, multivariate Garch model (in some way, it like a VAR(vector autoregression model with
garch/hecteroskedastic volatility) is used to find the interaction between several markets (spot, option, futures...)
simultaneously? These Multivariate garch model with exogenous variables are even difficult to estimate.

 
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matthewcroberts
Posts: 1
Joined: October 18th, 2001, 7:52 pm

Garch with exogenous variables

January 28th, 2002, 2:43 pm

Ironman,
it is not only reasonable to use exogenous variables to estimate GARCH models, it is pretty common. I have written a number of papers doing precisely this. SAS allows you to use covariates in the first & second moments, I believe, I'm not sure, though, because 90% of my work is in Matlab.
If you are interested, I have a small Matlab toolbox that will allow you to estimate these models--at least for linear GARCH, I haven't added a GARCH in Means model. The toolbox is here (scroll down for GARCHKIT)

Also, the first paper, (Commodities, Options and Volatility) uses this technique.


Matt.
 
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AVt
Posts: 90
Joined: December 29th, 2001, 8:23 pm

Garch with exogenous variables

January 28th, 2002, 7:59 pm

Matthew,

may i ask for help (ok, it is only related to the topic)?

Having Maple (not Matlab) i can not use your code, but worked with
the Excel example on Garch(1,1), which was placed here some time ago.

Trying it for an equity index (german Dax) the results are poor
and i would like to have a look at a Tgarch estimation. Having
a look in your code gives the 'functions', but i can not find the
sum of likelihoods to be maximized. Could you please provide it? TIA.

Axel
 
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matthewcroberts
Posts: 1
Joined: October 18th, 2001, 7:52 pm

Garch with exogenous variables

January 28th, 2002, 9:31 pm

AVt,

I actually should go back and remove that tool. I found a problem with the optimization routine in it which causes some very strange behavior.

As for your question, if you go here, you will find a paper that lays out the likelihood functions for Gaussian & t-GARCH.

If you need more details, let me know.

Matt.
 
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Ironman
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Joined: November 28th, 2001, 3:21 am

Garch with exogenous variables

January 29th, 2002, 5:15 am

Thank you, Matthew.
Wish you be promoted to senior member soon.