In this paper the filter of Hodrick and Prescott, the band-pass filter of Baxter
and King, "the ideal filter" and the first-differencing are analyzed. It is shown
that ideal filters are able to produce spurious cycles not only when a unit root
is present in the data but also when the root is less than unity. The main
critiques of first-differencing are outlined and further analyzed. The conclusion
is that differencing and more generally methods in conformity with the
underlying properties of non-stationary series are the preferable choice. At
the same time the application of ideal filters and their approximations (including
HP and BP) is very dangerous and their usage is to be avoided.
