Impulse Response Functions: Magnitude of Shocks

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alex_hk90
Posts: 19
Joined: Tue Feb 22, 2011 1:48 pm

Impulse Response Functions: Magnitude of Shocks

Postby alex_hk90 » Mon Apr 04, 2011 2:45 am

When running the Impulse Response procedure in EViews for the Structural Factorisation, it gives "Structural One S.D. Innovations" - how exactly are these calculated? In other words, what is it "One S.D." of and how could I calculate it manually?

I tried to check by replicating the Cholesky decomposition for the SVAR:
@e1 = C(1)*@u1
@e2 = C(2)*@e1 + C(3)*@u2
@e3 = C(4)*@e1 + C(5)*@e2 + C(6)*@u3

And it seems that the shocks that EViews uses are just the rows of the inverse of the A0 matrix (A0)^(-1), where:
A*e_t = B*u_t
A0*e_t = u_t
e_t = (A0)^(-1)*u_t

How does this relate to "One S.D.", and is it always the case regardless of the Structural Factorisation?

Looking at the SVAR section of the manual, I'm guessing that this follows from the assumption that the covariance matrix of the structural innovations is an identity matrix (orthonormal structural innovations), and applies for Structural Factorisation done using the VAR object in EViews, but not necessarily a manually derived system that may not make this assumption.

Thanks in advance for any help. :)

alex_hk90
Posts: 19
Joined: Tue Feb 22, 2011 1:48 pm

Re: Impulse Response Functions: Magnitude of Shocks

Postby alex_hk90 » Tue Apr 05, 2011 8:01 am

On the same topic, how are the standard errors computed (for the +/- 2.S.E. error bands that EViews displays on the graph, and shows on the table)?


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