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Journals / Journal of Mehmet Akif Ersoy University Economics and Administrative Sciences Faculty / 2026 / Volume: 12 Issue: 3

Long Memory Analysis and Directional Return Forecasting in Cryptocurrency Markets: An Application of the PATSOS Method

Ahmet Furkan Sak(MEHMET AKİF ERSOY ÜNİVERSİTESİ)0000-0002-6713-5773
Hüseyin Dalgar(MEHMET AKİF ERSOY ÜNİVERSİTESİ)0000-0001-9743-3766
Pages
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Publication Date
2025-09-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These findings highlight the effectiveness of hybrid models in capturing the non-linear structure of cryptocurrency returns.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This study aims to investigate the volatility dynamics of five major cryptocurrencies (Bitcoin, Ethereum, Binance Coin, Solana, and Ripple) to determine whether they exhibit long memory properties, reveal their market efficiency, and perform directional return forecasts using PATSOS, a hybrid machine learning method.
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Key Findings & Data:This study uses daily data on cryptocurrencies from 2014 to 2022.
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Conclusion & Impact:These findings highlight the effectiveness of hybrid models in capturing the non-linear structure of cryptocurrency returns.
🔬Design:Modeling & Simulation
📍Scope:2014 Verileri
⚙️Variables:PATSOS · Cryptocurrencies · Volatility Modelling

Abstract

This study aims to investigate the volatility dynamics of five major cryptocurrencies (Bitcoin, Ethereum, Binance Coin, Solana, and Ripple) to determine whether they exhibit long memory properties, reveal their market efficiency, and perform directional return forecasts using PATSOS, a hybrid machine learning method. This study uses daily data on cryptocurrencies from 2014 to 2022. According to the study results, long memory in volatility is found in the return series of Bitcoin, Binance Coin, Solana, and Ripple. Therefore, this finding reveals that the Efficient Markets Hypothesis does not hold for these cryptocurrencies’ return series, except Ethereum. Based on the tests, the most appropriate models for predicting volatility are HYGARCH(1, d, 1) for Bitcoin, IGARCH(1, 1) for Ethereum, FIGARCH(1, d, 0) for Binance Coin, FIGARCH(1, d, 1) and FIAPARCH(1, d, 1) for Solana and Ripple. Predicting future prices using past price movements is possible in these inefficient cryptocurrencies. In this context, we conduct return forecasts using the PATSOS method, which yields successful results in non-linear data. As a result, the PATSOS method produces lower RMSE, MSE, and MAE values and higher accuracy rates than the ANFIS method for all cryptocurrencies in the analysis. These findings highlight the effectiveness of hybrid models in capturing the non-linear structure of cryptocurrency returns.

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Cite This Article

Sak, A. F., Dalgar, H. (2025). Long Memory Analysis and Directional Return Forecasting in Cryptocurrency Markets: An Application of the PATSOS Method. Journal of Mehmet Akif Ersoy University Economics and Administrative Sciences Faculty, Volume: 12 Issue: 3. https://doi.org/10.30798/makuiibf.1678534

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References (72)

  1. Addai, S. (2016). Financial forecasting using machine learning [Doctoral dissertation, University of Cape Town]. ResearchGate. https://doi.org/10.13140/RG.2.1.1186.0083
  2. Aharon, D. Y., Butt, H. A., Jaffri, A., & Nichols, B. (2023). Asymmetric volatility in the cryptocurrency market: New evidence from models with structural breaks. International Review of Financial Analysis, 87, 102651. https://doi.org/10.1016/j.irfa.2023.102651
  3. Al‐Yahyaee, K. H., Mensi, W., & Yoon, S. M. (2018). Efficiency, multifractality, and the long‐memory property of the Bitcoin market: A comparative analysis with stock, currency, and gold markets. Finance Research Letters, 27, 228–234. https://doi.org/10.1016/j.frl.2018.03.017
  4. Aslam, F., Aziz, S., Nguyen, D. K., Mughal, K. S., & Khan, M. (2020). On the efficiency of foreign exchange markets in times of the COVID‐19 pandemic. Technological Forecasting and Social Change, 161, 120261. https://doi.org/10.1016/j.techfore.2020.120261
  5. Assaf, A., Bhandari, A., Charif, H., & Demir, E. (2022). Multivariate long memory structure in the cryptocurrency market: The impact of COVID‐19. International Review of Financial Analysis, 82, 102132. https://doi.org/10.1016/j.irfa.2022.102132
  6. Atsalakis, G., & Valavanis, K. (2009). Forecasting stock market short‐term trends using a neuro‐fuzzy based methodology. Expert Systems with Applications, 36, 10696–10707. https://doi.org/10.1016/j.eswa.2009.02.043
  7. Atsalakis, G. S., Atsalaki, I. G., Pasiouras, F., & Zopounidis, C. (2019). Bitcoin price forecasting with neuro‐fuzzy techniques. European Journal of Operational Research, 276(2), 770–780. https://doi.org/10.1016/j.ejor.2019.01.040
  8. Awoke, T., Minakhi, R., Mohanty, L., & Satapathy, S. C. (2020). Bitcoin price prediction and analysis using deep learning models. In Advances in intelligent systems and computing (Vol. 134, pp. 630–640). Springer. https://doi.org/10.1007/978-981-15-5397-4_63
  9. Baillie, R. T., Bollerslev, T., & Mikkelsen, H. O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74(1), 3–30. https://doi.org/10.1016/S0304-4076(95)01749-6
  10. Bariviera, A. F. (2017). The inefficiency of Bitcoin revisited: A dynamic approach. Economics Letters, 161, 1–4. https://doi.org/10.1016/j.econlet.2017.09.013
  11. Böhme, R., Christin, N., Edelman, B., & Moore, T. (2015). Bitcoin: Economics, technology, and governance. Journal of Economic Perspectives, 29(2), 213–238. https://doi.org/10.1257/jep.29.2.213
  12. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307–327. https://doi.org/10.1016/0304-4076(86)90063-1
  13. Bollerslev, T., & Mikkelsen, H. O. (1996). Modeling and pricing long-memory in stock market volatility. Journal of Econometrics, 73(1), 151–184. https://doi.org/10.1016/0304-4076(95)01736-4
  14. Bouri, E., Gil‐Alana, L. A., Gupta, R., & Roubaud, D. (2019). Modelling long memory volatility in the Bitcoin market: Evidence of persistence and structural breaks. International Journal of Finance & Economics, 24(1), 412–426. https://doi.org/10.1002/ijfe.1670
  15. Bouri, E., Molnar, P., Azzi, G., Roubaud, D., & Hagfors, L. I. (2017). On the hedge and safe haven properties of Bitcoin: Is it really more than a diversifier? Finance Research Letters, 20, 192–198. https://doi.org/10.1016/j.frl.2016.09.025
  16. Budree, A., & Nyathi, T. N. (2023). Can cryptocurrency be a payment method in a developing economy? Journal of Electronic Commerce in Organizations, 21(1), 1–21. https://doi.org/10.4018/jeco.320223
  17. Caporale, G. M., Rubio-Bezares, A., & Gil-Alana, L. A. (2024). Persistence in European stock market returns and volatility. International Journal of Business and Economics, 9(1), 56–66. https://doi.org/10.58885/ijbe.v09i1.56.gc
  18. Cavalcante, J., & Assaf, A. (2004). Long range dependence in the returns and volatility of the Brazilian stock market. European Review of Economics and Finance, 3, 5-22.
  19. Cavalli, S., & Amoretti, M. (2021). CNN‐based multivariate data analysis for Bitcoin trend prediction. Applied Soft Computing Journal, 101, 107065. https://doi.org/10.1016/j.asoc.2020.107065
  20. Charfeddine, L., & Maouchi, Y. (2019). Are shocks on the returns and volatility of cryptocurrencies really persistent? Finance Research Letters, 28, 423–430. https://doi.org/10.1016/j.frl.2018.06.017
  21. Chen, H., Wei, N., Wang, L., Mobarak, W., Albahar, M. A., & Shaikh, Z. A. (2024). The role of blockchain in finance beyond cryptocurrency: Trust, data management, and automation. IEEE Access, 12, 64861–64885. https://doi.org/10.1109/access.2024.3395918
  22. Chen, W., Xu, H., Jia, L., & Gao, Y. (2021). Machine learning model for Bitcoin exchange rate prediction using economic and technology determinants. International Journal of Forecasting, 37(1), 28–43. https://doi.org/10.1016/j.ijforecast.2020.02.008, Z., Li, C., & Sun, W. (2020). Bitcoin price prediction using machine learning: An approach to sample dimension engineering. Journal of Computational and Applied Mathematics, 365, 112395. https://doi.org/10.1016/j.cam.2019.112395
  23. CoinMarketCap. (2022). Cryptocurrency prices by market cap. CoinMarketCap. Retrieved March 2, 2022, from https://coinmarketcap.com/
  24. Çevik, E. İ., & Topaloğlu, G. (2014). Volatilitede uzun hafıza ve yapısal kırılma: Borsa İstanbul örneği. Balkan Sosyal Bilimler Dergisi, 3(6), 40–55.
  25. Davidson, J. (2004). Moment and memory properties of linear conditional heteroscedasticity models, and a new model. Journal of Business & Economic Statistics, 22, 16–29. https://doi.org/10.1198/073500103288619359
  26. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008. https://doi.org/10.2307/1912773
  27. Fakhfekh, M., & Jeribi, A. (2020). Volatility dynamics of cryptocurrencies’ returns: Evidence from asymmetric and long memory GARCH models. Research in International Business and Finance, 51, 101075. https://doi.org/10.1016/j.ribaf.2019.101075
  28. Fama, E. (1965). The behavior of stock market prices. Journal of Business, 38, 34–105. https://doi.org/10.1086/294743
  29. Festic, M., Kavkler, A., & Dajčman, S. (2012). Long memory in the Croatian and Hungarian stock market returns. Journal of Economics and Business, 30(1), 115–139.
  30. Greaves, A., & Au, B. (2015). Using the Bitcoin transaction graph to predict the price of Bitcoin [Unpublished class project]. Stanford University, CS224W: Analysis of Networks. Retrieved from https://snap.stanford.edu/class/cs224w-2015/projects_2015/Using_the_Bitcoin_Transaction_Graph_to_Predict_the_Price_of_Bitcoin.pdf
  31. Guiu, J. G., i Ribé, E. G., i Mansilla, E. B., & i Fàbrega, X. L. (1999). Automatic diagnosis with genetic algorithms and case-based reasoning. Artificial Intelligence in Engineering, 13(4), 367–372. https://doi.org/10.1016/S0954-1810(99)00009-6
  32. Guo, T., Bifet, A., & Antulov-Fantulin, N. (2018). Bitcoin volatility forecasting with a glimpse into buy and sell orders. In 2018 IEEE International Conference on Data Mining (ICDM) (pp. 989–994). IEEE. https://doi.org/10.1109/ICDM.2018.00123
  33. Gülcü, A., & Çalişkan, S. (2020). Clustering electricity market participants via FRM models. Intelligent Decision Technologies, 14(4), 481–492. https://doi.org/10.3233/IDT-200092
  34. Hagenau, M., Liebmann, M., & Neumann, D. (2013). Automated news reading: Stock price prediction based on financial news using context‐capturing features. Decision Support Systems, 55(3), 685–697. https://doi.org/10.1016/j.dss.2013.02.006
  35. Hegazy, O., Soliman, O. S., & Salam, M. A. (2013). A machine learning model for stock market prediction. arXiv preprint, 4(12), 17–23. https://doi.org/10.48550/arXiv.1402.7351
  36. Horobet, A., Belascu, L., & Barsan, A.-M. (2016). Exchange rate volatility in the Balkans and Eastern Europe: Implications for international investments. In A. Karasavvoglou, Z. Aranđelović, S. Marinković, & P. Polychronidou (Eds.), The first decade of living with the global crisis (pp. 137–164). Springer. https://doi.org/10.1007/978-3-319-24267-5_11
  37. Ibrahim, A., Hussin, S. A. S., Zahid, Z., & Khairi, S. (2018). Evaluation of long memory on the Malaysia exchange rate market. The Journal of Social Sciences Research, Special Issue 6, 653–656. https://doi.org/10.32861/jssr.spi6.653.656
  38. Jang, J. S. (1993). ANFIS: Adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man, and Cybernetics, 23(3), 665–685. https://doi.org/10.1109/21.256541
  39. Jiang, X. (2020). Bitcoin price prediction based on deep learning methods. Journal of Mathematical Finance, 10(1), 132–139. http://doi.org/10.4236/jmf.2020.101009
  40. Kapur, G., Manohar, S., Mittal, A., Jain, V., & Trivedi, S. (2024). Cryptocurrency price fluctuation and time series analysis through candlestick pattern of Bitcoin and Ethereum using machine learning. International Journal of Quality & Reliability Management, 41(8), 2055–2074. https://doi.org/10.1108/ijqrm-12-2022-0363
  41. Karaatlı, M., Güngör, İ., Demir, Y., & Kalaycı, Ş. (2005). Hisse senedi fiyat hareketlerinin yapay sinir ağları yöntemi ile tahmin edilmesi. Yönetim ve Ekonomi Araştırmaları Dergisi, 3(3), 38–48.
  42. Katsiampa, P. (2017). Volatility estimation for Bitcoin: A comparison of GARCH models. Economics Letters, 158, 3–6. https://doi.org/10.1016/j.econlet.2017.06.023
  43. Khan, Z. H., Alin, T. S., & Hussain, M. A. (2011). Price prediction of share market using artificial neural network (ANN). International Journal of Computer Applications, 22(2), 42–47. http://doi.org/10.5120/2552-3497
  44. Khuntia, S., & Pattanayak, J. K. (2020). Adaptive long memory in volatility of intra-day Bitcoin returns and the impact of trading volume. Finance Research Letters, 32, 101077. https://doi.org/10.1016/j.frl.2018.12.025
  45. Kılıç, R. (2004). On the long memory properties of emerging capital markets: Evidence from Istanbul Stock Exchange. Applied Financial Economics, 14(13), 915–922. http://doi.org/10.1080/0960310042000233638
  46. Lahmiri, S., & Bekiros, S. (2020). Intelligent forecasting with machine learning trading systems in chaotic intraday Bitcoin market. Chaos, Solitons & Fractals, 133, 109641. https://doi.org/10.1016/j.chaos.2020.109641
  47. Liu, M., Li, G., Li, J., Zhu, X., & Yao, Y. (2021). Forecasting the price of Bitcoin using deep learning. Finance Research Letters, 40, 101755. https://doi.org/10.1016/j.frl.2020.101755
  48. Liu, Y., & Tsyvinski, A. (2018). Risks and returns of cryptocurrency. National Bureau of Economic Research. https://doi.org/10.2139/ssrn.3226952
  49. Malkiel, B. G. (2003). The efficient market hypothesis and its critics. Journal of Economic Perspectives, 17(1), 59–82. https://doi.org/10.1257/089533003321164958
  50. McNally, S., Roche, J., & Caton, S. (2018). Predicting the price of bitcoin using machine learning. In 2018 26th Euromicro International Conference on Parallel, Distributed and Network-based Processing (PDP) (pp. 339–343). IEEE. https://doi.org/10.1109/PDP2018.2018.00060
  51. Mensi, W., Al-Yahyaee, K. H., & Kang, S. H. (2019). Structural breaks and double long memory of cryptocurrency prices: A comparative analysis from Bitcoin and Ethereum. Finance Research Letters, 29, 222–230. https://doi.org/10.1016/j.frl.2018.07.011
  52. Münyas, T., & Kadooğlu-Aydın, G. (2023). Etkin piyasa hipotezi ve kripto para piyasaları üzerine bir uygulama. Alanya Akademik Bakış Dergisi, 7(3), 1203–1216. https://doi.org/10.29023/alanyaakademik.1240173
  53. Nadarajah, S., Mba, J. C., Rakotomarolahy, P., & Ratolojanahary, H. T. J. E. (2025). Ensemble learning and an adaptive neuro-fuzzy inference system for cryptocurrency volatility forecasting. Journal of Risk and Financial Management, 18(2), 52. https://doi.org/10.3390/jrfm18020052
  54. Nakamoto, S. (2008). Bitcoin: A peer-to-peer electronic cash system. Bitcoin.org, https://bitcoin.org/bitcoin.pdf
  55. Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347–370. https://doi.org/10.2307/2938260
  56. Oppenheim, D., & Shani, G. (2017). Potato disease classification using convolution neural networks. Advances in Animal Biosciences, 8(2), 244–249. http://doi.org/10.1017/S2040470017001376
  57. Özçalıcı, M. (2016). Yapay sinir ağları ile çok aşamalı fiyat tahmini: BIST 30 senetleri üzerine bir araştırma. Dokuz Eylül Üniversitesi İktisadi İdari Bilimler Fakültesi Dergisi, 31(2), 209–227. https://doi.org/10.24988/deuiibf.2016312517
  58. Özdemir, A., & Çelik, İ. (2020). Pay piyasalarında etkin piyasalar hipotezinin farklı dağılım varsayımları bağlamında uzun hafıza modelleri ile tespiti: ABD ve Türkiye karşılaştırması. Dokuz Eylül Üniversitesi İşletme Fakültesi Dergisi, 21(1), 125–160. https://doi.org/10.24889/ifede.481059
  59. Phillip, A., Chan, J. S., & Peiris, S. (2018). A new look at cryptocurrencies. Economics Letters, 163, 6–9. https://doi.org/10.1016/j.econlet.2017.11.020
  60. Rabemananjara, R., & Zakoian, J. M. (1993). Threshold ARCH models and asymmetries in volatility. Journal of Applied Econometrics, 8(1), 31–49. https://doi.org/10.1002/jae.3950080104
  61. Sadique, S., & Silvapulle, P. (2001). Long‐term memory in stock market returns: International evidence. International Journal of Finance & Economics, 6(1), 59–67. https://doi.org/10.1002/ijfe.143
  62. Saleem, K. (2014). Modeling long memory in the Russian stock market: Evidence from major sectoral indices. Journal of Applied Business Research, 30(2), 567–574. https://doi.org/10.19030/jabr.v30i2.8426
  63. Seabe, P. L., Moutsinga, C. R. B., & Pindza, E. (2023). Forecasting cryptocurrency prices using LSTM, GRU, and bi-directional LSTM: A deep learning approach. Fractal and Fractional, 7(2), 203. https://doi.org/10.3390/fractalfract7020203
  64. Shah, D., & Zhang, K. (2014). Bayesian regression and Bitcoin. In 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton) (pp. 409–414). IEEE. https://doi.org/10.1109/ALLERTON.2014.7028484
  65. Soylu, P., Okur, M., Çatıkkaş, Ö., & Altintig, A. (2020). Long memory in the volatility of selected cryptocurrencies: Bitcoin, Ethereum and Ripple. Journal of Risk and Financial Management, 13(6), 107. https://doi.org/10.3390/jrfm13060107
  66. Tektaş, A., & Karataş, A. (2004). Yapay sinir ağları ve finans alanına uygulanması: Hisse senedi fiyat tahminlemesi. Atatürk Üniversitesi İktisadi ve İdari Bilimler Dergisi, 18, 3–4.
  67. Tse, Y. (1998). The conditional heteroskedasticity of the Yen-dollar exchange rate, Journal of Applied Econometrics. 13(1), 49-55. https://doi.org/10.1002/(SICI)1099-1255(199801/02)13:1%3C49::AID-JAE459%3E3.0.CO;2-O
  68. Türkyılmaz, S., & Balıbey, M. (2014). Türkiye hisse senedi piyasası oynaklığındaki asimetrik uzun hafıza özelliği. Journal of Banking and Financial Research, 1(1), 1–10.
  69. Umoru, D., Ekeoba, A. A., & Igbinovia, B. (2024). Volatility behaviour of currency exchange rates in selected countries: Long memory effect. Asian Journal of Economics, Business and Accounting, 24(8), 168–189. https://doi.org/10.9734/ajeba/2024/v24i81449
  70. Wang, Y., Andreeva, G., & Martin-Barragan, B. (2023). Machine learning approaches to forecasting cryptocurrency volatility: Considering internal and external determinants. International Review of Financial Analysis, 90, 102914. https://doi.org/10.1016/j.irfa.2023.102914
  71. Yüksel, R., & Akkoç, S. (2016). Altın fiyatlarının yapay sinir ağları ile tahmini ve bir uygulama. Doğuş Üniversitesi Dergisi, 17(1), 39–50.
  72. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353. http://doi.org/10.1016/S0019-9958(65)90241-X