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st: A univariate GARCH model


From   Erkal Ersoy <erkal6@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: A univariate GARCH model
Date   Mon, 25 Jul 2011 17:45:54 +0100

Hello Statalisters,

I am having trouble estimating a model in which I am using a
GARCH(1,1) process to compute the conditional variance of the error
term. The model can be summarized as follows (I use underscore "_" to
denote a subscript):

z_t = a + b1*z_1 + b2*z_2 + b3*z_3 + b4*z_4 + e_t.... (1)

where e_t | I_t ~ N(0, h_t) and I_t is the information set available at time t.

Also, e(hat) = z_t - z_t(hat) ..........................................(2)
and lastly,

h_t = c0 + c1*e^2_(t-1) + c2*h_(t-1) ............................(3)

What I would like to do now is construct a normalized variable,
e(star), as follows:

e(star)= e(hat) / sqrt(h_t) .............................................(4)

In order to get here, I need to estimate the coefficients c0, c1 and
c2. Obtaining the residuals in equation (1) is no problem of course.
Once I have done that, however, I am having a difficult time isolating
the variance, h_t, so that I can regress it on e(hat)-squared and the
first lag of h_t. Is there a way to do something like this?

I also took a look at Stata's dvech command, but I'm not entirely sure
that's useful here. I would appreciate any help very much. Thank you
all in advance for your time and help.

Best,
Erkal
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