Finansal Zaman Serisi Öngörüsü için Resim Bulanık C-Ortalamalara dayalı Öngörü Fonksiyonları Topluluğu

Year 2026, Volume: 38 Issue: 1, 199 - 209, 20.03.2026

Sümeyye Polater , Ufuk Yolcu , Furkan Keskin , Ozge Cagcag Yolcu

https://doi.org/10.7240/jeps.1818060

https://izlik.org/JA28AZ22TR

Abstract

Bu çalışma, finansal zaman serileri için, Resim Bulanık C-Ortalamalar (PFCM) kümeleme yöntemine dayalı birden fazla öngörü fonksiyonunu birleştiren bir öngörü çerçevesi önermektedir. Gecikmeli değişken uzayında temsil edilen zaman serileri, PFCM yöntemi ile kümelenmekte ve her bir zaman noktası için pozitif (μ), nötr (η) ve negatif (ν) üyelik dereceleri elde edilmektedir. Her bir üyelik derecesi ve her bir resim bulanık küme (C) için, giriş değişkenleri olarak ilgili üyelik dereceleri, bu derecelerin seçilmiş doğrusal olmayan dönüşümleri ve gecikmeli zaman serisi değişkenlerini içeren ayrı bir çoklu doğrusal regresyon modeli kurulmaktadır; tüm modeller aynı hedef değerleri paylaşmaktadır. Bu işlem sonucunda, 3×C adet temel öngörü üretilmekte ve bu tahminler sırasıyla önce üyelik dereceleri, ardından belirsizlik (indeterminacy) değerleri kullanılarak birleştirilip iyileştirilmektedir. Böylece nihai öngörüler elde edilmektedir. Önerilen yaklaşım, üç farklı üyelik derecesi aracılığıyla belirsizliği daha derin bir şekilde ele almakta, aynı zamanda dönüştürülmüş derece özellikleriyle doğrusal olmayan ilişkileri, gecikmeli değişkenlerle de doğrusal ilişkileri yakalayabilmektedir. Sonuç olarak geliştirilen Resim Bulanık C-Ortalamalar tabanlı öngörü fonksiyonları topluluğu, çeşitli yaygın finansal zaman serisi veri kümeleri üzerinde deneysel olarak değerlendirilmiş ve rekabetçi tahmin performansı sergilemiştir.

Keywords

Finansal Zaman Serileri , Resim Bulanık C-Ortalamalar , Öngörü Fonksiyonları , Bayesci Optimizasyon , Topluluk Öğrenmesi

Supporting Institution

Marmara Üniversitesi Bilimsel Araştırma Projeleri Komisyonu (BAPKO)

Project Number

FYL-2025-11872

Thanks

Bu çalışma, Marmara Üniversitesi Bilimsel Araştırma Projeleri Komisyonu (BAPKO) tarafından Yüksek Lisans Tez Projesi kapsamında FYL-2025-11872 No'lu Proje kapsamında desteklenmiştir.

Picture Fuzzy C-Means–based Ensemble of Forecasting Functions for Financial Time Series Forecasting

https://izlik.org/JA28AZ22TR

Abstract

This study introduces a forecasting framework for financial time series that combines multiple forecaster functions built on Picture Fuzzy C-Means (PFCM) clustering. In the proposed framework, the time series is embedded into a lagged-variable space and clustered using Picture Fuzzy C-Means (PFCM), which assigns to each time point three degrees: positive (μ), neutral (η), and negative (ν). For each degree and each cluster, a separate multiple linear regression forecaster is constructed using the corresponding degree, selected nonlinear transformations of that degree, and lagged variables as inputs, while sharing the same target values. Consequently, the procedure produces 3×C base forecasts that are aggregated in two stages: base forecasts are first combined using the associated degree information and then refined through the neutral/indeterminacy structure to obtain the final forecast. By representing uncertainty through three complementary degrees and enriching the input space with degree-based nonlinear features, the framework captures both linear and nonlinear patterns in a transparent manner. The resulting Picture Fuzzy C-Means–based ensemble of forecasting functions is empirically evaluated on several widely used financial time-series benchmarks and demonstrates competitive forecasting performance.

Keywords

financial time series , picture fuzzy c-means clustering , forecasting functions , bayesian optimization , ensemble learning

Supporting Institution

Marmara University Scientific Research Projects Committee (BAPKO)

Project Number

FYL-2025-11872

Thanks

This study was supported by Marmara University Scientific Research Projects Committee (BAPKO) under the Master’s Thesis Project, Project No: FYL-2025-11872.

References

• Zadeh, L.A. (1965). Fuzzy sets. Information and control. 8(3), 338–353.
• Song, Q. and Chissom, B.S. (1993). Forecasting enrollments with fuzzy time series—Part I. Fuzzy sets and systems. 54(1), 1–9.
• Chen, S.-M. (1996). Forecasting enrollments based on fuzzy time series. Fuzzy sets and systems. 81(3), 311–319.
• Chen, S.-M. and Chang, Y.-C. (2010). Multi-variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques. Information sciences. 180(24), 4772–4783.
• Chen, S.-M. and Chen, C.-D. (2010). TAIEX forecasting based on fuzzy time series and fuzzy variation groups. IEEE Transactions on Fuzzy Systems. 19(1), 1–12.
• Chen, S.-M., Chu, H.-P., and Sheu, T.-W. (2012). TAIEX forecasting using fuzzy time series and automatically generated weights of multiple factors. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans. 42(6), 1485–1495.
• Jang, J.-S. (1993). ANFIS: adaptive-network-based fuzzy inference system. IEEE transactions on systems, man, and cybernetics. 23(3), 665–685.
• Egrioglu, E., et al. (2014). A new adaptive network based fuzzy inference system for time series forecasting. Aloy J Soft Comput Appl. 2(1), 25–32.
• Sarıca, B., Eğrioğlu, E., and Aşıkgil, B. (2018). A new hybrid method for time series forecasting: AR–ANFIS. Neural Computing and Applications. 29(3), 749–760.
• Türkşen, I.B. (2008). Fuzzy functions with LSE. Applied Soft Computing. 8(3), 1178–1188.
• Bas, E., et al. (2019). Type 1 fuzzy function approach based on ridge regression for forecasting. Granular Computing. 4(4), 629–637.
• Tak, N. (2020). Type-1 possibilistic fuzzy forecasting functions. Journal of Computational and Applied Mathematics. 370, 112653.
• Bas, E. and Egrioglu, E. (2022). A fuzzy regression functions approach based on Gustafson-Kessel clustering algorithm. Information Sciences. 592, 206–214.
• Homaida, A., Pekalp, M. H., & Ebegil, M. (2024). Bulanık Küme ve Bulanık Sayı: Uygulamalarla Aritmetik İşlemler. Dicle Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 13(2), 223-247.
• Homaida, A., Pekalp, M. H., & Ebegil, M. (2025). Efficient k Value Computation for Enhanced Fuzzy Ridge Regression. Journal of Computational and Applied Mathematics, 116813.
• Atanassov, K.T. (1999). Intuitionistic fuzzy sets, in Intuitionistic fuzzy sets: theory and applications, Springer. p. 1–137.
• Cagcag Yolcu, O., et al. (2020). A new intuitionistic fuzzy functions approach based on hesitation margin for time-series prediction. Soft Computing-A Fusion of Foundations, Methodologies & Applications. 24(11).
• Bas, E., Yolcu, U., and Egrioglu, E. (2021). Intuitionistic fuzzy time series functions approach for time series forecasting. Granular computing. 6(3), 619–629.
• Arslan, S.N. and Cagcag Yolcu, O. (2022). A hybrid sigma-pi neural network for combined intuitionistic fuzzy time series prediction model. Neural Computing and Applications. 34(15), 12895–12917.
• Cuong, B.C. and Kreinovich, V. (2013). Picture fuzzy sets-a new concept for computational intelligence problems. in 2013 third world congress on information and communication technologies (WICT 2013). IEEE.
• Egrioglu, E., et al. (2020). Picture fuzzy time series: Defining, modeling and creating a new forecasting method. Engineering Applications of Artificial Intelligence. 88, 103367.
• Bas, E., Egrioglu, E., and Tunc, T. (2023). Multivariate picture fuzzy time series: New definitions and a new forecasting method based on Pi-sigma artificial neural network. Computational Economics. 61(1), 139–164.
• Rath, S. and Dutta, D. (2024). Picture Fuzzy Time Series Forecasting with a Novel Variant of Particle Swarm Optimization. SN Computer Science. 5(1), 193.
• Thong, P.H. and Son, L.H. (2015). A new approach to multi-variable fuzzy forecasting using picture fuzzy clustering and picture fuzzy rule interpolation method. in Knowledge and Systems Engineering: Proceedings of the Sixth International Conference KSE 2014. Springer.
• Bas, E., Yolcu, U., and Egrioglu, E. (2020). Picture fuzzy regression functions approach for financial time series based on ridge regression and genetic algorithm. Journal of Computational and Applied Mathematics. 370, 112656.
• Tak, N. and İnan, D. (2022). Type-1 fuzzy forecasting functions with elastic net regularization. Expert Systems with Applications. 199, 116916.