A question on this topic has been asked before: Combining a linear Kalman Filter with additional linear constraints.
And I checked out some of these references.
I will probably use estimate projection. However I have a couple of questions:
- For the log-likelihood calculation, (i.e. when fitting the model) should I use the original or projected estimates? I presume the former ?
- When forecasting should I use the original or projected estimates, in this case I think the latter ? Could someone please confirm which to use in each case and ideally why.
- Lastly for the prefect measurement method shown in the link above, why is the number of restrictions forced to be less than the number of variables ? I would have thought mathematically they could also be equal to the number of variables ?