D.S.G. Pollock 305The equivalent filter in the time domain is a wrapped or circular filter. Whereas
such filters avoid the leakage that besets approximate bandpass filters, they deliver
inappropriate estimates of the business cycle when they adhere strictly to the
Baxter–King bandpass definition. Moreover, it seems that any success that the
approximate bandpass filter may have in representing the business cycle must be
due, in some measure, to the leakage.
The conclusion that we have reached ultimately is that, whereas it is some-
times possible to identify a trend-cycle complex within the data, there can be no
definitive definition of what constitutes the trend and what, in consequence, must
constitute the cyclical component. Therefore, it seems that one must be liberal in
allowing any definitions that seem to fulfil their intended purposes. Even when the
purpose is mistaken or unfulfilled, we should not automatically reject the resulting
definition or the estimates to which it gives rise.
A Computer Program
The computer program that has been used in connection with this chapter is
available at the following web address: http://www.le.ac.uk/users/dsgp1/.
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