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

Pelin Volkan Kocakaya; Hakan Eryüzlü

doi:10.26466/opusjsr.1855303

EN TR

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

Öz

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.

Anahtar Kelimeler

Conjunctural Fluctuations, Golden Ratio, Fibonacci Sequence, Fractal Structures, Turkish Economy

Konjonktürel dalgalanmaların fibonacci altın oran yaklaşımıyla ampirik analizi: Türkiye örneği

Öz

Bu çalışma, Türkiye ekonomisine ait 1961–2024 dönemindeki çeyreklik reel GSYH büyüme verilerini kullanarak konjonktürel dalgalanmaların frekans-temelli yapısını incelemektedir. Araştırmanın temel amacı, ardışık döngü uzunluklarının Fibonacci dizisine dayanan altın oran (φ ≈ 1.618) veya tersine (1/φ ≈ 0.618) yakınsayıp yakınsamadığını test etmektir. Bu kapsamda, serinin değişken varyans yapısı GARCH(1,1) modeliyle normalize edilmiş; Fourier dönüşümüyle baskın frekanslar belirlenmiş; elde edilen döngü uzunlukları Gaussian karışım modeli altında Expectation-Maximization algoritmasıyla sınıflandırılmış ve harmonik regresyon yöntemiyle seriye yansıtılmıştır. Analiz sonuçları, kısa ve orta vadeli döngülerin altın oranın tersi etrafında kümelendiğini göstermektedir. Ampirik güvenilirliğin sınanması amacıyla Harding ve Pagan (2002) tarafından geliştirilen Concordance indeksi uygulanmış ve model döngülerinin reel büyüme serisiyle yüksek düzeyde evre uyumu gösterdiği saptanmıştır. Faz senkronizasyonu analizi ise görece düşük katsayılara rağmen istatistiksel olarak anlamlı sonuçlar üretmiş ve döngülerin belirli ölçüde ortak bir ritim sergilediğini ortaya koymuştur. Son olarak, modelden türetilen döngülerin Türkiye’nin tarihsel dönüm noktalarıyla örtüştüğü belirlenmiştir. Bulgular, Türkiye’de konjonktürel dalgalanmaların rastlantısal değil, yapısal ritimlere dayalı düzenli örüntüler içerdiğini göstermektedir.

Anahtar Kelimeler

Konjonktürel Dalgalanmalar, Altın Oran, Fibonacci Dizisi, Fraktal Yapılar, Türkiye Ekonomisi

Kaynakça

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Ayrıntılar

Birincil Dil

İngilizce

Konular

Finansal Ekonometri

Bölüm

Araştırma Makalesi

Yazarlar

Pelin Volkan Kocakaya ^*
0000-0001-8203-5001
Türkiye

Hakan Eryüzlü
0000-0003-3715-0021
Türkiye

Yayımlanma Tarihi

15 Şubat 2026

Gönderilme Tarihi

3 Ocak 2026

Kabul Tarihi

14 Şubat 2026

Yayımlandığı Sayı

Yıl 2026 Cilt: 23 Sayı: 2026

DOI

https://doi.org/10.26466/opusjsr.1855303

IZ

https://izlik.org/JA29FY28UM

APA

Volkan Kocakaya, P., & Eryüzlü, H. (2026). An empirical analysis of conjunctural fluctuations using the fibonacci golden ratio: The case of the Turkish economy. OPUS Journal of Society Research, 23(2026), 1-15. https://doi.org/10.26466/opusjsr.1855303

AMA

1.Volkan Kocakaya P, Eryüzlü H. An empirical analysis of conjunctural fluctuations using the fibonacci golden ratio: The case of the Turkish economy. OPUS TAD. 2026;23(2026):1-15. doi:10.26466/opusjsr.1855303

Chicago

Volkan Kocakaya, Pelin, ve Hakan Eryüzlü. 2026. “An empirical analysis of conjunctural fluctuations using the fibonacci golden ratio: The case of the Turkish economy”. OPUS Journal of Society Research 23 (2026): 1-15. https://doi.org/10.26466/opusjsr.1855303.

EndNote

Volkan Kocakaya P, Eryüzlü H (01 Şubat 2026) An empirical analysis of conjunctural fluctuations using the fibonacci golden ratio: The case of the Turkish economy. OPUS Journal of Society Research 23 2026 1–15.

IEEE

[1]P. Volkan Kocakaya ve H. Eryüzlü, “An empirical analysis of conjunctural fluctuations using the fibonacci golden ratio: The case of the Turkish economy”, OPUS TAD, c. 23, sy 2026, ss. 1–15, Şub. 2026, doi: 10.26466/opusjsr.1855303.

ISNAD

Volkan Kocakaya, Pelin - Eryüzlü, Hakan. “An empirical analysis of conjunctural fluctuations using the fibonacci golden ratio: The case of the Turkish economy”. OPUS Journal of Society Research 23/2026 (01 Şubat 2026): 1-15. https://doi.org/10.26466/opusjsr.1855303.

JAMA

1.Volkan Kocakaya P, Eryüzlü H. An empirical analysis of conjunctural fluctuations using the fibonacci golden ratio: The case of the Turkish economy. OPUS TAD. 2026;23:1–15.

MLA

Volkan Kocakaya, Pelin, ve Hakan Eryüzlü. “An empirical analysis of conjunctural fluctuations using the fibonacci golden ratio: The case of the Turkish economy”. OPUS Journal of Society Research, c. 23, sy 2026, Şubat 2026, ss. 1-15, doi:10.26466/opusjsr.1855303.

Vancouver

1.Pelin Volkan Kocakaya, Hakan Eryüzlü. An empirical analysis of conjunctural fluctuations using the fibonacci golden ratio: The case of the Turkish economy. OPUS TAD. 01 Şubat 2026;23(2026):1-15. doi:10.26466/opusjsr.1855303

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

Öz

Anahtar Kelimeler

Konjonktürel dalgalanmaların fibonacci altın oran yaklaşımıyla ampirik analizi: Türkiye örneği

Öz

Anahtar Kelimeler

Kaynakça

Ayrıntılar

Birincil Dil

Konular

Bölüm

Yazarlar

Yayımlanma Tarihi

Gönderilme Tarihi

Kabul Tarihi

Yayımlandığı Sayı

DOI

IZ

Kaynak Göster