Bitcoin Fiyatları İçin Naive ve SARIMA Modellerinin Örneklem Dışı Karşılaştırması

Öz

Bu çalışma, Bitcoin fiyat tahmininde mevsimsel ARIMA (SARIMA) modelinin öngörü performansını, basit bir Naive kıyas modeliyle açık biçimde karşılaştırarak yeniden değerlendirmeyi amaçlamaktadır. Analiz, 12 Mart 2021 ile 12 Mart 2026 dönemini kapsayan günlük Bitcoin kapanış fiyatlarına dayanmaktadır. Seri logaritmik forma dönüştürülmüş ve durağanlık özellikleri fark alma işlemleriyle incelenmiştir. İlk aşamada mevsimsel olmayan ARIMA modelleri tahmin edilmiş, ardından mevsimsel dinamikleri içeren alternatif SARIMA modelleri değerlendirilmiştir. Model seçiminde parametre anlamlılığı ile Ljung-Box tanı istatistikleri dikkate alınmış ve mevsimsel hareketli ortalama bileşeninin kısmen anlamlı olduğu görülmüştür. Bu çerçevede SARIMA(0,1,1)(0,1,1)[30] nihai mevsimsel aday model olarak belirlenmiştir. Tahmin performansı değerlendirmesi, yalnızca model uyumuna değil, örneklem dışı tahmin doğruluğuna odaklanmaktadır. Bu amaçla SARIMA modelinin performansı, ortalama mutlak hata (MAE) ve hata kareler ortalamasının karekökü (RMSE) ölçütleri kullanılarak Naive model ile karşılaştırılmıştır. Bulgular, örneklem dışı dönemde Naive modelin SARIMA modeline göre belirgin biçimde daha düşük tahmin hataları ürettiğini göstermektedir. Naive model için MAE 0.016011 ve RMSE 0.023173 iken, SARIMA modeli için bu değerler sırasıyla 0.23172 ve 0.28931’dir. Sonuçlar, Bitcoin gibi yüksek oynaklığa sahip finansal zaman serilerinde daha karmaşık mevsimsel yapıların her zaman daha üstün tahmin performansı sağlamadığını göstermektedir.

Anahtar Kelimeler

• Bitcoin
• tahminleme
• naive model
• SARIMA
• ARIMA
• out-of-sample performans

Out-of-Sample Comparison of Naive and SARIMA Models for Bitcoin Prices

Öz

This study reassesses the forecasting performance of the seasonal ARIMA (SARIMA) model in Bitcoin price prediction by explicitly comparing it with a simple Naive benchmark model. The analysis is based on daily Bitcoin closing prices covering the period from March 12, 2021 to March 12, 2026. The series is transformed into logarithmic form, and its stationarity properties are examined through differencing procedures. In the first stage, non-seasonal ARIMA models are estimated, followed by the evaluation of alternative SARIMA specifications that incorporate seasonal dynamics. During model selection, parameter significance and Ljung-Box diagnostic statistics are taken into account, and the seasonal moving average component is found to be partially meaningful. Accordingly, SARIMA(0,1,1)(0,1,1)[30] is selected as the final seasonal candidate model. The forecasting evaluation emphasizes out-of-sample forecast accuracy rather than relying only on model fit. For this purpose, the performance of the SARIMA model is compared with that of a Naive benchmark model using mean absolute error (MAE) and root mean square error (RMSE). The findings reveal that the Naive model produces substantially lower forecast errors than the SARIMA model over the out-of-sample period. While the Naive model yields an MAE of 0.016011 and an RMSE of 0.023173, the corresponding values for the SARIMA model are 0.23172 and 0.28931, respectively. The results suggest that more complex seasonal structures do not necessarily improve forecasting performance in highly volatile financial time series such as Bitcoin.

Anahtar Kelimeler

• Bitcoin
• forecasting
• Naive model
• SARIMA
• ARIMA
• Out-of-Sample Performance

Kaynakça

1. Agrawal, A., Mani, M. and Varshney, S. (2023). Bitcoin forecasting performance measurement: A comparative study of econometric, machine learning and artificial intelligence-based models. Journal of International Commerce, Economics and Policy, 14(02), 2350008. https://doi.org/10.1142/S1793993323500084
2. Ahmed, M., Suha, S. A., Mahi, F. H. and Ahmed, F. U. (2024). Evaluating the performance of Bitcoin price forecasting using machine learning techniques on historical data. Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska, 14(2), 101–108. https://doi.org/10.35784/iapgos.5657
3. Akba, F., Medeni, I. T., Guzel, M. S. and Askerzade, I. (2021). Manipulator detection in cryptocurrency markets based on forecasting anomalies. IEEE Access, 9, 108819–108831. https://doi.org/10.1109/ACCESS.2021.3101528
4. Adcock, R. and Gradojević, N. (2019). Non-fundamental, non-parametric Bitcoin forecasting. Physica A: Statistical Mechanics and its Applications, 531, 121727. https://doi.org/10.1016/j.physa.2019.121727
5. Baumann, S., Busch, K. A. and Gardi, H. A. (2024). Comparison of different artificial neural networks for Bitcoin price forecasting. arXiv elektronik ön baskı. Erişim adresi https://arxiv.org/abs/2407.17930
6. Ben Hamadou, F., Mezghani, T., Zouari, R. and Boujelbène-Abbes, M. (2025). Forecasting Bitcoin returns using machine learning algorithms: Impact of investor sentiment. EuroMed Journal of Business, 20(1), 179–200.
7. Cornelya, N., Cahyawati, D., Eliyati, N., Sitepu, R., Susanti, E., Dewi, N. R. and Bangun, P. B. J. (2023). Forecasting of Bitcoin cryptocurrency price using the autoregressive integrated moving average (ARIMA) method.
8. Proceedings of the Sriwijaya International Conference on Basic and Applied Sciences, 1–10. https://doi.org/10.4108/eai.3-11-2023.2347905

9. El Abaji, M. and Haraty, R. A. (2025). Enhancing Bitcoin forecast accuracy by integrating AI, sentiment analysis, and financial models. International Journal of Computing and Digital Systems, 17(1), 1–15. https://doi.org/10.12785/ijcds/1571026011
10. Gawali, N. (2022). Bitcoin price prediction using neural network (Yayımlanmamış doktora tezi). National College of Ireland.
11. Hajek, P. and Olej, V. (2023). Hierarchical intuitionistic TSK fuzzy system for Bitcoin price forecasting. IEEE International Conference on Fuzzy Systems (FUZZ) (1–6. ss.). IEEE. https://doi.org/10.1109/FUZZ52849.2023.10309793
12. Lewis, C. D. (1982). Industrial and business forecasting methods: A practical guide to exponential smoothing and curve fitting. London: Butterworth Scientific.
13. Ma, J. and Mahmoudinia, E. (2025). Comprehensive modeling approaches for forecasting Bitcoin transaction fees: A comparative study. arXiv elektronik ön baskı. Erişim adresi https://arxiv.org/abs/2502.01029
14. Modi, P. D., Arshi, K., Kunz, P. J. and Zoubir, A. M. (2023). A data-driven deep learning approach for Bitcoin price forecasting. arXiv elektronik ön baskı. Erişim adresi https://arxiv.org/abs/2311.06280
15. Mousa, R., Afrookhteh, M., Khaloo, H., Bengari, A. A. and Heidary, G. (2025). Forecasting of Bitcoin prices using hashrate features: Wavelet and deep stacking approach. arXiv elektronik ön baskı. Erişim adresi https://arxiv.org/abs/2501.13136
16. Pabuçcu, H., Ongan, S. and Ongan, A. (2020). Forecasting the movements of Bitcoin prices: An application of machine learning algorithms. arXiv elektronik ön baskı. Erişim adresi https://arxiv.org/abs/2303.04642
17. Seabe, P. L., Pindza, E., Moutsinga, C. R. B. and Aphane, M. (2024). Temporal attention-enhanced stacking networks: Revolutionizing multi-step Bitcoin forecasting. Forecasting, 7(1), 2. https://doi.org/10.3390/forecast7010002
18. Šestanović, T. (2024). A comprehensive approach to Bitcoin forecasting using neural networks. Ekonomski pregled, 75(1), 62–85.
19. Sossi-Rojas, S., Velarde, G. and Zieba, D. (2023). A machine learning approach for Bitcoin forecasting. Engineering Proceedings, 39(1), 27. https://doi.org/10.3390/engproc2023039027
20. Tripathy, N., Hota, S., Mishra, D., Satapathy, P. and Nayak, S. K. (2024). Empirical forecasting analysis of Bitcoin prices: A comparison of machine learning, deep learning, and ensemble learning models. International Journal of Electrical and Computer Engineering Systems, 15(1), 21–29. https://doi.org/10.32985/ijeces.15.1.3
21. Uras, N., Marchesi, L., Marchesi, M. and Tonelli, R. (2020). Forecasting Bitcoin closing price series using linear regression and neural networks models. PeerJ Computer Science, 6, e279.
22. Zhang, X., Kang, Y., Li, C., Wang, W. and Wang, K. (2025). LSTM-conformal forecasting-based Bitcoin forecasting method for enhancing reliability. PLoS One, 20(5), e0319008. https://doi.org/10.1371/journal.pone.0319008