Hi, in my model, there is no permanent technology process, so that I use HP-filtered data when estimation with prefilter=1 option.

However, I think I have not to choose this option.

This is because since all of the series of my data are deviations from its trend, demeaning themselves is somewhat strange.

Demeaning can be useful when we use a model with permanent technology using growth rate data
in that it is one way to handle steady state growth rate of the technology growth rate.

I would like to check if this is correct.

Is is ok to use prefilter=1 when my data is HP-filtered level? (There is no permanent technology in my model.)
If so, is the each mean itself interpreted as a trend growth rate?

Summary

If I use filtered level data, is it justifiable to use prefilter=1 ?

First of all (as always): do not use the two-sided HP filter for estimating DSGE models. See Pfeifer (2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models". If you must, use the one-sided HP filter
Depending on the filter you use, your data will be mean 0 (true for the one-sided and two-sided HP filter). Prefiltering in this case is not needed, because the empirical mean you subtract will be 0. Thus prefilter=1 will be harmless, but useless.

As you mentioned, I used one-sided HP-filter and was curious about whether demeaning is needed.
According to your comment, one-sided HP-filtered data is already mean 0. Then, prefilter=1 becomes useless.

Actually, it is a bit more complicated. With the one-sided HP filter, the mean will only be asymptotically 0. Thus, if your sample is short and depending on your view of the world, you still may want to demean. See also