Thread Subject:

Stability of VARMAX model

Hello Everyone,

I want to make parameter estimation for vector autoregressive moving average exogenous input (VARMAX) model.

 my model;
y(k)=-A1*y(k-1)-A2*y(k-2)+B1*u(k-1)+e(k)+C1*e(k-1)

where y is nx1 vector, A and C are nxn matrices, u is singular, B is n,1 vector, e(k) is nx1 vector.

I found the link below which describe the stability condition for VARMAX model:
http://www.mathworks.com/help/toolbox/econ/bswxr7m.html

here it says if
det(I-A1*z-A2*z^2)~=0 for abs(z)<1 then the model is stable. In other words it says the roots of that polynomial matrix should lie outside the unit circle.

Since i am doing estimation, than i have to create some constraints on matrices A1 and A2 thus they satisfy the condition above.


Can anybody tell me how can i define constraints on A matrices?

Regards

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