Structural Residuals

[rzulfadin]

Dear Tom,

Let the SVAR model:

B*y_t= A_1 y_{t-1}+ A_2 y_{t-2} +A_3 y_{t-3}+ A_4 y_{t-4} + V_t

How can I extract the A and B matrices? I want to obtain the V's using B*U = V to check the correlation matrix of V's. Is it uncorrelated by assumption of orthogonalized shocks?

Thank you.
Rahadian

[TomDoan]

Dear Tom,

Let the SVAR model:

B*y_t= A_1 y_{t-1}+ A_2 y_{t-2} +A_3 y_{t-3}+ A_4 y_{t-4} + V_t

How can I extract the A and B matrices? I want to obtain the V's using B*U = V to check the correlation matrix of V's. Is it uncorrelated by assumption of orthogonalized shocks?

Thank you.
Rahadian

In this GARCH model?

[rzulfadin]

In this GARCH model?

Actually for the original VAR model without the GARCH term. I think I've found what I am looking for. So below is how I can transform the U's to the V's in the original VAR. Is that right?

compute factor=%decomp(%sigma)
@structresids(factor=factor) u gstart gend vresids

done immediately after the original VAR is estimated. This transforms the OLS residuals (u) to the structural residuals (vresids). As written, this is specific to the Cholesky factor structural model used in the oil-GDP paper. With a different structural model, you would get a different factor matrix for the covariance matrix %SIGMA.

Can I also use %decomp and @structresids to transform the OLS/SUR residuals to the structural shocks for a non-recursive VAR or near VARs? In that, I just need to adjust the 'factor', is that right? Thanks.

[TomDoan]

There are some examples of @StructResids at http://www.estima.com/forum/viewtopic.php?f=4&t=684.

Yes. You can apply this to the residuals from any type of SVAR, as long as you have a factor for the covariance matrix. If you use CVMODEL, you need to use the FACTOR option to get that. And it can also be applied to the results from a SUR.