HP filter in linear models

[jpfeifer]

You did not say “one-sided” before. Using a two-sided HP filter would clearly be problematic. The one-sided one is a more defensible choice. It has for example been used in the context of Bayesian estimation in
https://doi.org/10.3982/QE1297
See also

Detrending filters

@sadia: linear filtering typically means regressing on a constant and a trend. The constant will take out the mean. If you do not use a constant, you also need to demean. Note that the Stock-Watson argument applies to DSGE models as well. Their solution takes the form of a VARMA-process and the likelihood minimizes the forecast error. Two papers using the one-sided HP-filter in the context of DSGE model estimation are Mingming Jiang (2016): “By force of demand: Explaining cyclical fluctuatio…

That being said, pretty much any filtering device will be controversial as you need to (implicitly or explicitly) take a stand on the underlying DGP, where your prior may be different from the referee’s. See also
https://www.sciencedirect.com/science/article/abs/pii/S030439321400083X