One way to impose complex nonlinear constraints for the estimation of a state-space model using the Econometrics Toolbox is to exclude the bad parameter values in the domain of the mapping from the parameters to 'ssm' coefficient matrices 'A', 'B', 'C' and 'D'. Then, the numerical optimization program will search solutions within the constrained parameter space when calling the 'estimate' function using the aforementioned definition of 'ssm'.
For instance, provided that the requirement is that all eigenvalues of the state transition matrix are positive, one can define a mapping with the constrained domain in the following manner,
function [A,B,C,D] = myfun(params)
A = …; B = …; C = …; D =…;
if any(abs(eig(A))>1)
A = zeros(2);
end
end
The underlying idea is that when the parameters violate the eigenvalue constraints, the transition matrix is reduced to zero matrix, which must correspond to a small log-likelihood value. Therefore, the optimization program will stay away from these bad parameter values.
