Hi,

I have a question with regard to different GARCH notations I found in the
literature, and I am wondering if anyone knows how to reconcile these
differences. Below are three different notations that supposedly all define
the GARCH(1,1) process:

In Zivot's book, MFTSWS, the GARCH(1,1) process is defined as:
[1]: Y(t) = c + e(t), and
[2]: sigma^2(t) = a0 + a1*e^2(t-1) + b1*sigma^2(t-1)

In Engle's paper, the GARCH(1,1) process is defined (in financial notation),
like this:
 [3]: r(t) = m(t) + sqrt(h(t))*e(t), and
[4]: h(t+1) = a0 + a1*h(t)*e^2(t) + b1*h(t)

In Stoffer's book, the GARCH(1,1) is define as:
[5]: Y(t) = sigma(t)*e(t), and
[6]: sigma^2(t) = a0 + a1*Y^2(t-1) + b1*sigma^2(t-1)

Does anyone know if all three above are just different ways of saying the
same thing, or are they drastically different with respect to the
specification of the GARCH model to be fitted?

Thanks!

-- 
Tom

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