Psi*e = Fu
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_y.append(svar) @VEC(F) = NA, NA, NA, 0, NA, NA, 0, 0, NA
For the following note that u and e are related by Su = e, where S = A^(-1)B. Moreover, the underlying VAR is stable. The notation in this post tries to approximate the one used in the EViews documentation.
When trying to recover the orthonormal structural shocks u I ran into trouble and have the following issues.
(1) the residuals S^(-1) e, which should give us the structural shocks, are far from orthonormal. In particular, they are highly cross-correlated.
(2) Psi S != F, although identity is clearly implied (I calculated Psi = (I_3- A1-A2)^(-1) )
(3) Although the general approach with restrictions on F should not allow to get estimates for A or B, both are in fact available when calling
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matrix bmat = _y.@svarbmat
matrix amat = _y.@svaramat
A turns out to be the identity matrix (and B=S). It seems the estimation procedure makes this assumption on A automatically whenever restrictions are placed on F. Even when trying prevent restrictions on A via
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_y.append(svar) @VEC(F) = NA, NA, NA, 0, NA, NA, 0, 0, NA
_y.append(svar) @VEC(A) =NA, NA, NA, NA, NA, NA, NA, NA, NA
A is still the identity matrix.
What am I missing here?
Any help would be much appreciated!