The paper initially considers the history of cycles. These involve looking at ups in downs in either the levels of variables or some transformation of them such as growth rates. The first analyses involved locating turning points in the data. Later the development of methods such as spectral analysis led to a focus on oscillations. A distinction between cycles and oscillations is needed – both imply turning points but turning points can occur without an oscillation. We investigate a variety of filtering methods to locate either turning points or oscillations in the series. It is shown that some of the filters being used are not appropriate for the nature of the series being analyzed, specifically whether they are I(1) or I(0). Moreover, often models which are used to locate an oscillation e.g. components models, are structured to assume there is an oscillation and not to discover whether there really is one. Finally, we ask how one might use the information assembled in earlier sections of the paper. In particular we ask whether the concept of a medium term cycle introduced in a widely cited paper by Comin and Gertler (2006) is useful, and how one might go about addressing an often quoted “fact” that financial cycles are of longer duration than real cycles. We find little evidence for the latter even when the statement relates to oscillations and not cycles.

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