Diagonal VEC-GARCH notation

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bball2526
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Joined: Thu Mar 30, 2017 2:20 am

Diagonal VEC-GARCH notation

Postby bball2526 » Thu Mar 30, 2017 11:16 am

Hi all,

I am using the diagonal VEC-GARCH(1,1) model to carry out a regression (N=3) and I am a bit confused by the notation of the A and B matrices.

These are the representations that I obtain from EViews:
Variance and Covariance Equations:
=====================
GARCH1 = M(1,1) + A1(1,1)*RESID1(-1)^2 + B1(1,1)*GARCH1(-1)

GARCH2 = M(2,2) + A1(2,2)*RESID2(-1)^2 + B1(2,2)*GARCH2(-1)

GARCH3 = M(3,3) + A1(3,3)*RESID3(-1)^2 + B1(3,3)*GARCH3(-1)

COV1_2 = M(1,2) + A1(1,2)*RESID1(-1)*RESID2(-1) + B1(1,2)*COV1_2(-1)

COV1_3 = M(1,3) + A1(1,3)*RESID1(-1)*RESID3(-1) + B1(1,3)*COV1_3(-1)

COV2_3 = M(2,3) + A1(2,3)*RESID2(-1)*RESID3(-1) + B1(2,3)*COV2_3(-1)

However, since this is a VEC-GARCH model, the A and B matrices are 6x6 diagonal matrices i.e. there are no off-diagonal elements like A(1,2) and A(2,3) etc. Hence both matrices only contain the diagonal elements i.e. A(1,1), A(2,2)..... A(6,6) etc.

Hence I don't understand where the A1(1,2), A1(1,3), A1(2,3) B1(1,2), B1(1,3) and B1(2,3)coefficients from the EViews representations come from, is this just a matter of different notation?

Thank you in advance for your help, greatly appreciate it!

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