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.

中文翻译：

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转折点和振荡周期：概念、测量和使用

周期研究的早期历史涉及定位数据中的转折点。后来，光谱分析等方法的发展导致人们关注振荡。需要区分周期和振荡——两者都意味着转折点，但转折点可以在没有振荡的情况下发生。可以在非平稳序列中识别转折点，但由于难以在此类序列中以非参数方式定义振荡，因此倾向于使用谐波模型来捕获任何振荡现象。然后需要检查振荡不仅仅是由模型强加的。我们表明，模型所应用的序列中通常没有振荡。当它们出现时，有人认为需要关注 8-30 年的中期波动，而不是商业周期的标准 2-8 年。我们分析这个论点是否有很多优点，并得出结论没有。博德里等人。(2020,美国经济评论, 110 , 1-47) 也检验了诸如人均小时数等系列中存在 9/10 年周期的论点，我们发现几乎没有证据证明这一点。此外，如果实际上存在这样的振荡，它只占序列方差的不到 1%。还研究了基于内生与外生技术以及由于积累和互补机制导致的极限循环的模型的比较研究。