Turning point and oscillatory cycles: Concepts, measurement, and use

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 can occur without oscillations. Turning points can be identified in nonstationary series but, as it is hard to define oscillations nonparametrically in such a series, harmonic models tend to be used to capture any oscillatory phenomena. One needs to check then that oscillations are not just being imposed by the model. We show that often there are no oscillations in the series the models are applied to. When they are present it has been argued that one needs to pay attention to medium‐term oscillations of 8–30 years rather than the standard 2–8 years of the business cycle. We analyze whether there is much merit in this argument and conclude there is not. Beaudry et al. (2020, American Economic Review, 110, 1–47) contention that there is a cycle of 9/10 years in series such as hours per capita is also examined and we find that there is little evidence for it. Moreover, if there is in fact such an oscillation it accounts for less than 1% of the variance of the series. Comparative studies of models based on endogenous versus exogenous technology as well as limit cycles due to accumulation and complementarity mechanisms are also examined.