We study whether there is an interrelationship between the lengths of economic cycles. Such an interrelationship would be helpful to signal future economic downturns, thus to alleviate economic and societal distress. To detect the lengths of economic cycles, we introduce an improved method, where Fourier analysis is coupled with GARCH regression, mixed distribution estimation, and harmonic regression. We apply our methodology to detect cycles in percentage GDP growth in 25 OECD countries, and in Europe. The results indicate that in each economy, between two and five cycles are present. Cycles with a length between 5–6 years and between 9–10 years appear most frequently. A meta-analysis on the detected cycle lengths reveals that the ratio between the lengths of consecutive cycles often closely matches the golden ratio, $\varphi$. Interestingly, this finding opposes several existing theories about multi-cycle structures, which imply that the lengths of shorter cycles should be integer fractions of the lengths of longer cycles. Our paper thus provides a new direction for theory development regarding economic cycles and dynamic stability.

我们研究了经济周期长度之间是否存在相互关系。这种相互关系将有助于预示未来的经济衰退，从而减轻经济和社会困扰。为了检测经济周期的长度，我们引入了一种改进的方法，其中傅里叶分析与GARCH回归，混合分布估计和谐波回归相结合。我们运用我们的方法来检测25个经合组织国家和欧洲的GDP增长百分比周期。结果表明，在每个经济体中，都存在两个到五个周期。周期介于5-6年和9-10年之间的周期最常出现。对检测到的周期长度进行的荟萃分析表明，连续周期的长度之间的比率通常与黄金比率非常接近，$\varphi$。有趣的是，这一发现与关于多周期结构的几种现有理论相反，这意味着较短周期的长度应该是较长周期的长度的整数分数。因此，我们的论文为有关经济周期和动态稳定性的理论发展提供了新的方向。