Please consult Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models”
- It would be
A = y_t
is your model is linearized, i.e. if y_t measures percentage deviations from trend and you HP-filtered the log level.
2. You should never use the two-sided HP-filter for Bayesian estimation. Use the one-sided one or simply demeaned growth rates.