I recently read a discussion about ARIMA models where someone said (referring to d as in ARIMA (p, d, q)):
Its true that d=1 takes out deterministic trends when they are present (they would appear only in the drift term.) But it does more than that.
I know that's not much context, but I seem to remember reading something similar in regards to detrending via differencing.
Does differencing (not just in an ARIMA context) do something more to your data than just detrend it? If so, what else does it do? (Add or remove?)
There are other detrending methods, such as fitting a curve (loess, linear regression) and using the residuals as detrended data. Would these other methods not do the "more than that" that differencing does? (Hence, might they be preferrable?)