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Hello,

I have a question in state-space modeling: I want the residuals in two signal equations to be uncorrelated.

For example, using demo.wf1,

c=1
sspace ss
ss.append @ename e1
ss.append @ename e2
ss.append @signal d(GDP)=st1*d(GDP(-1))+C(2)*d(m1(-1))+C(3) + e1
ss.append @signal d(M1)=C(4)*d(pr)+C(5)*d(GDP(-1))+C(6)*d(M1(-1))+C(7) +e2
ss.append @state st1=st1(-1)
ss.append @evar var(e1)=exp(c(8))
ss.append @evar var(e2)=exp(c(9))
ss.append @evar cov(e1,e2)=0
ss.ml(m=9999)
show ss

But if I remove the line ss.append @evar cov(e1,e2)=0, I get the same results as the above program which does not remove the line.

I am not sure if this is a bug in the state-space object.

Unless you specify otherwise, EViews' state space object assumes diagonal variance both in signal and state equations. That is to say residuals are uncorrelated by default. Therefore, the line you refer to is actually redundant.

Trubador,
Does this assume the residuals are I uncorrelated but not enforce it on the estimated residuals?

Hi Startz. That is a very good point. Yes, orthogonality of residuals is only an assumption, which may or may not be fulfilled. My personal observation in practice is that allowing correlations among residuals eases convergence problems and reduces parameter instability even if they turn out to be insignificant after the estimation. The situation is analogous to inclusion of the "constant" term in the regression equation. As you know, however, computational burden will increase for moderate or large systems and will lead to other estimation problems if we specify the full covariance matrix.

Hi Trubador,

Thanks for your replies.

If I want to enforce the correlation to be zero, is there a way to do it?

Best,
Wilshire