residuals dependent on regression coefficients

[mariaki]

Dear all,

I am a relatively new EViews user (have used it 10 years ago, and have forgotten the most).
Could you help me with the advice?

I need to estimate the following model:

Yt = a + b*x1(t) + c*x2(t)+d*x3(t)*x4(t)+error(t), where
Var(error(t)) =u+ (b^2)*z+ ((c+d*x3(t))^2)*w

So, variance of error term must have a structure, where u>0, z>0, w>0 and b,c,d come from the first equstion.

I was thinking in GARCH direction, but I do not have lag dependance here.
I can estimate the following:

Yt = a + b*x1(t) + c*x2(t)+d*x3(t)*x4(t)+error(t), where
Var(error(t)) =v+ ((c+d*x3(t))^2)*w+(error(t-1))^2

And this I can do without programming (as I do not know programming, I do not see, how to skip error(t-1))^2 ).


Could you advice me a direction, where to look for idea at least? Or how to convert what I have into program code, which I (hopefully) would be able to change.
Thank you very much in advance!

[EViews Glenn]

You'll have to do this in steps.

1. estimate the model without weights and obtain residuals.

2. fit the variance specification by hand--generally people just regress the squared residuals on their variance regressors.

3. create a series of weights and do weighted least squares.

[mariaki]

Thank you very much, Glenn!

From the suggested path I can do first and second step. Could you, please, comment a bit more on how to do 3? how to obtain weights series from the regression 2?

[EViews Glenn]

Create a series that has either the estimated variances, standard deviations, inverse variances, or inverse standard deviations for each observation, and then do weighted least squares as described in the manual. You'll have to choose the weighting specification that matches the series you created. I would recommend that unless you have a specific reason to do otherwise, you use Inverse standard deviations as your weighting type and then EViews scaling. This will offer the maximal backward compatibility with earlier versions of EViews. But it that's not a concern just pick the weight type with which you feel most comfortable.

[mariaki]

In order to avoid creating another topic, I will ask here.

I need to go GARCH in the model above, so my question is, how can I estimate GARCH(0,0) with particular structure of residuals. The problem is that I can not choose GARCH(0,0); it seems that I have to program it (the meaning of using GARCH is just because it lets to put a structure for residuals). Does anybody know, how can I do it?

Thank you very much in advance!