Disentangling the enigma of multi-structured economic cycles - A new appearance of the golden ratio
研究经济周期长度之间的关联，提出结合傅里叶分析、GARCH回归等方法检测25个OECD国家GDP增长中的周期，发现相邻周期长度之比常接近黄金比例，挑战了传统整数倍理论。
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, ϕ. 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.