Markov Zincirleri ile Finansal Tahminleme: Teorik Bir Yaklaşım ve Uygulamalı Bir Çalışma

Yıl 2026, Cilt: 40 Sayı: 2 , 220 - 235 , 31.03.2026

Yasemin Yurtoğlu

https://doi.org/10.16951/trendbusecon.1760688

https://izlik.org/JA36BD99AW

Öz

Bu çalışma, finansal zaman serilerinde Markov zincirleri kullanılarak tahminleme yapılmasını amaçlamaktadır. Borsa İstanbul BIST 100 endeksi, USD/TRY döviz kuru ve Bitcoin (BTC/USD) fiyat verileri kullanılarak, farklı volatiliteye sahip piyasalarda modelin performansı değerlendirilmiştir. Modelde, kapanış fiyatlarına dayalı olarak belirlenen üç durum (pozitif, negatif ve nötr getirili günler) için geçiş olasılıkları hesaplanmıştır. Elde edilen geçiş olasılık matrisleri kullanılarak bir sonraki günün yönü tahmin edilmiştir. Model performansı MAE, RMSE, MAPE, RMSE / MAE oranı ve Theil’s U istatistikleriyle değerlendirilmiş; BIST 100 için yüksek doğruluk ve düşük hata oranları elde edilmiştir. USD / TRY’de orta düzey, BTC / USD’de ise yüksek hata oranları gözlemlenmiştir. Cross -validation ve out-of-sample testler ile modelin geçerliliği test edilmiştir. Sonuçlar, Markov zincirleri modelinin BIST 100 endeksi ve USD/TRY döviz kuru hareketlerini tahminlemede belirli bir performans sergilediğini, ancak yüksek volatiliteye sahip Bitcoin fiyat hareketlerinin öngörülmesinde hibrit modellere duyulan ihtiyacı ortaya koymaktadır.

Anahtar Kelimeler

Markov Zinciri , Finansal Tahminleme , Geçiş Olasılık Matrisi , MAE ve RMSE , Volatilite Analizi

Financial Forecasting with Markov Chains: A Theoretical Approach and an Application

https://izlik.org/JA36BD99AW

Öz

This study aims to perform forecasting using Markov chains in financial time series. The performance of the model was evaluated in markets with different volatilities using the Borsa Istanbul BIST 100 index, USD/TRY exchange rate, and Bitcoin (BTC/USD) price data. In the model, transition probabilities were calculated for three states (positive, negative, and neutral return days) determined based on closing prices. The direction of the next day was predicted using the obtained transition probability matrices. Model performance was evaluated using MAE, RMSE, MAPE, RMSE/MAE ratio, and Theil's U statistics; high accuracy and low error rates were obtained for BIST 100. Moderate error rates were observed for USD/TRY, and high error rates for BTC/USD. The validity of the model was tested using cross-validation and out-of-sample tests. The results show that the Markov chain model performs well in predicting BIST 100 index and USD/TRY exchange rate movements, but highlights the need for hybrid models in predicting Bitcoin price movements, which are characterized by high volatility.

Anahtar Kelimeler

Markov Chain , Financial Forecasting , Transition Probability Matrix , MAE and RMSE , Volatility Analysis

Kaynakça

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