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

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

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

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

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