In many standard models, the noise in the measurement equation will be correlated with the noise in the state equations. I have looked through the KF code, but cannot see how you handle this, and would like to be reassured that it is all done properly. Can you help?
If the system matrices are not time-dependent, and the system is stable, then the obvious starting value for the diffuse case is to have the initial covariance matrix of the states satisfying a Lyapunov equation. Does this take place automatically, and do you use a fast Lyapunov solver?
In Dynare the measurement errors are assumed UNcorrelated with the errors in the state equations (the structural shocks of the model).
If you want to have measurement errors correlated with shocks, you should introduce the measurement errors explicitely in the model (as for the structural shocks) and specify the correlation structure that you want.
Now you may want other reports than the one that we are providing to later distinguish the effects of shocks from measurement errors. Let’s talm about it.
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2. If the system matrices are not time-dependent, and the system is stable, then the obvious starting value for the diffuse case is to have the initial covariance matrix of the states satisfying a Lyapunov equation. Does this take place automatically, and do you use a fast Lyapunov solver?[/quote]
We have a reasonably fast Lyapunov using Schur decomposition. We could get a faster one if we were to make a DLL
For stationary variables, we initialize the filter with the unconditional mean and variance.
Now in the diffuse case, for unit-root variables, there are neither unconditional mean or variance. We initialize with infinite variance as in Durbin and Koopman and initial value of zero, but that doesn’t matter because the first period error of forecast is supposed infinite.