Turning point and oscillatory cycles

The early history of cycles research 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 do not necessarily imply oscillations. Comin and Gertler (2006) argue that attention should be paid to medium term oscillations of 8-30 years rather than the standard 2-8 years of the business cycle, while Beaudry et al. (2019) suggest that there is a cycle of 9/10 years in series such as hours per capita. We investigate what the evidence is for the latter and find that it explains little of the variance of the data. We then show that some of the fillters being used to locate either turning points or oscillations in the series are not appropriate for the nature of the series being analyzed, specifically whether they are I(1) or I(0). Finally, we assess if the concepts of medium term and 9/10 year cycles are useful for comparing models and data. This is done by examining models of endogenous versus exogenous technology as well as limit cycles due to accumulation and complementarity mechanisms.