> I'm interested in methods that don't "subtract" simple "trends" and "seasonality"
a 2nd order difference equation can model a single harmonic frequency - that is, if your data is a pure sine and sampled at regular intervals, then
x_n =~ a x_n-1 + b x_n-2
can model any frequency with the proper a and b values (machine precision limits apply in real world scenarios, of course); That is, if your data looks like a sine wave with a yearly period, you still need no more than one sample per minute and 2nd order model to filter it out.
It's likely not a perfect sinewave, so you'd need a lot more - but if you are incredibly lucky and your periodic underlying admits a (relatively) sparse harmonic decomposition, and the signal riding on it has (very) low amplitude compared to the periodic signal, you can model very long periods implicitly by just having enough recent samples.
a 2nd order difference equation can model a single harmonic frequency - that is, if your data is a pure sine and sampled at regular intervals, then
can model any frequency with the proper a and b values (machine precision limits apply in real world scenarios, of course); That is, if your data looks like a sine wave with a yearly period, you still need no more than one sample per minute and 2nd order model to filter it out.It's likely not a perfect sinewave, so you'd need a lot more - but if you are incredibly lucky and your periodic underlying admits a (relatively) sparse harmonic decomposition, and the signal riding on it has (very) low amplitude compared to the periodic signal, you can model very long periods implicitly by just having enough recent samples.