Maximum Likelihood and matrices

[adfung]

Hamilton (1994) says pn page 332 that maximisation of the likelihood function (11.6.32) will produce estimates of B0 (the contemporaneous relationships between the variables) and D (the variance matrix of the structural innovations).

Given that the estimates need to satisfy

inv(B0)*D*(inv(B0))' = omega

where omega is the observed variance-covariance matrix of residuals estimated previously, my question is how would I use the above matrix equation as the basis for specifying the assignment equations? Do I need to effectively multiply out the matrices by hand and then input those as the equations?

[EViews Gareth]

Unfortunately a major weakness of the LogL object is that it cannot use matrix objects. Thus any likelihood function that cannot be expressed in terms of series objects only can not be maximised. If you are able to specify your likelihood in terms of series objects, then you should be able to maximise it.

[adfung]

Thanks Gareth.

I think I can see the series issue, which I guess stems from the fact that it log likelihood is typically used to estimate equation coefficients in conjunction with the variance.

I am thinking that one possible way around this is to essentially set up a dummy series of 1's. Proper use of this series (i.e. multiplying some element by 1) would allow me to construct a time series where effectively every observation is the same.