Confusion with hp filter

Hello everyone

If I have the gdp expressed in logarithms, that is, lgdp= 100*ln(gdp), then if I apply the one side hp filter, as Professor Johannes suggests, the units that I get directly from applying the hp filter to lgdp are percentage (deviation from trend) right?

Now, if I have the annualized inflation (\Pi) and I directly apply the hp filter to \Pi, is the cyclic variable that I get also in percentage?

Thanks in advance

The logarithm will eliminate units and result in approximately percentage deviations. If you don’t apply the logarithm, your result will have the same units as the original variable. Thus, it matters if you measure inflation in percent, but typically that’s the case.