HI, DEAR PROFESSOR, I HAVE JUST READ A PAPER. IN THE ESTIMATION PART, THERE IS A SENTENCE:

"Since the model is expressed in log-deviations from steady state for estimation purposes, I take the log difference from the HP filtered trend (smoothing

parameter is set to 1600)."

I CAN NOT MATCH THIS SENTENCE TO ANY METHODS IN THE PAPER OF "A GUIDE TO SPECIFYING OBSERVATION EQUATION FOR THE ESTIMATION OF DSGE MODELS"

SO IS THE APPROACH IN THAT PAPER NOT SO REASONABLE, OR I JUST CANNOT GRASP ITS MEANING?

THANKS.

That approach is not reasonable as explained in my Guide to Observation Equations. You are not supposed to use a two-sided HP-filter for likelihood-based estimation, because it violates causality. You could use a one-sided HP-filter instead.