Determinant residual covariance

[lsavaraj]

I run SURE and I got determinant residual covariance 33.87938. what does it maen for determinant residual covariance? How can I interpret such informaiton?

[EViews Gareth]

It is the determinant of the residual covariance matrix. It is fairly meaningless.

[cel]

I thought that the determinant of the residual covariance was -- up to a scale -- the same as the likelihood.

So if you estimate a system of eqns which gives a DRC of 10e-05 and another system that gives a value of 0.1, you can be certain that the first system is a relatively better fit to the data.

Or am i wrong?

[EViews Gareth]

You are right that it is a component of the likelihood.

[cel]

Thanks for that. Is it therefore ok to compare across systems as i wrote. with the implication that the system with the lowest DRC is the best fitting. Is this also the case if the systems have different paramter numbers?
thanks.

[EViews Gareth]

This is off the top of my head, so I might be wrong, but isn't the likelihood for SUR something like:

Code: Select all

T/2 det(Sigma) - (1/2)*sum(e'inv(sigma)e) + constant

[EViews Glenn]

You're both (sort of) right.

Gareth is correct about the general form of the likelihood (with the exception of the sign on the first term).

cel is correct in cases where we iterate the weights and the coefficients to convergence (or more specifically, if we solve the ML first order conditions for the conditional mean and the covariance matrix parameters). In this case, the residuals and estimated covariance are such that the term involving (e and inv(Sigma)) is a constant function of the number of equations.

The problem with using likelihoods in the one-iteration SUR case is that you haven't solved these first order conditions so you haven't really maximized the likelihood. This makes interpretation of likelihoods a bit problematic.