Value for funtional form of the variance (h.equation)

[deleted_user]

Hi all,

I am trying to run a ARMA+GARCH model for modeling the wind speed
and my code is follows;

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proc model data = Erman;
parms ar1 ar2 ma1 ma2 ma3 mu arch0 arch1 garch1;
y = mu + ar1 * zlag1(y - mu) + ar2 * zlag2(y-mu)+ ma1 *
zlag1(resid.y)+ ma2 * zlag2(resid.y) + ma3 * zlag3(resid.y);
h.y = arch0 + arch1 * xlag(resid.y ** 2, mse.y) +
garch1 * xlag(h.y, mse.y);
spredict=pred.y;
vsgarch=h.y;
fit y / method = marquardt fiml out = forecast outresid;
outvars vsgarch spredict;
bounds arch0>=0;
bounds garch1>=0;
bounds arch1>=0;

run;
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I am able to output the h.y values. The question is how those values
are calculated based on the available data? As far as I understand,
the SAS runs a regression model to find the parameters for arch0,
arch1, and garch1 based on h.y values treating h.y values as dependent
variables. I am wondering how the actual h.y values are calculated for running those regression equation, if anybody can provide me an equation for calculating that value (h.y),
it would be great. Thank you very much for your interest. Have a nice
day.

Regards
Ergin