An empirical analysis of conjunctural fluctuations using the fibonacci golden ratio: The case of the Turkish economy

This study investigates the frequency-based structure of Turkey's business cycles using quarterly real GDP growth data from 1961 to 2024 and the Hodrick-Prescott (HP) filter. This study tested the hypothesis that successive cycle lengths converge toward the golden ratio (1.618) or its inverse (0.618). Methodologically, the series was normalized using a GARCH(1,1) model, dominant frequencies were identified via Fourier transformation, and cycle lengths were classified using a Gaussian mixture model before being projected via harmonic regression. Validation using the Harding and Pagan (2002) Concordance Index and phase synchronization analysis confirmed a high degree of alignment between the model and real growth data. The results indicate that short- and medium-term cycles cluster around the inverse of the golden ratio (0.618), suggesting that Turkish economic fluctuations are not random but are governed by regular structural rhythms that are aligned with historical turning points.