Disentangling the enigma of multi-structured economic cycles - A new appearance of the golden ratio

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.