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Re: st: A univariate GARCH model


From   Jorge Eduardo Pérez Pérez <perez.jorge@ur.edu.co>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: A univariate GARCH model
Date   Mon, 25 Jul 2011 16:00:16 -0400

To estimate GARCH models, use the -arch- command. For example, to
estimate a GARCH(1,1) model similar to what you specified (did not
test the code, not sure if it converges):

webuse wpi1
arch D.ln_wpi, arima(4,0,0) arch(1) garch(1)

and to get the standardized residuals e(star)

predict res, resid
predict h, var
gen stdres=res/h

_______________________
Jorge Eduardo Pérez Pérez



On Mon, Jul 25, 2011 at 12:45 PM, Erkal Ersoy <erkal6@gmail.com> wrote:
>
> 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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