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

Year 2025, Volume: 12 Issue: 3, 1130 - 1152, 30.09.2025

Ahmet Furkan Sak , Hüseyin Dalgar

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.

Keywords

PATSOS , Cryptocurrencies , Volatility Modelling , Long Memory , Market Efficiency

Ethical Statement

Ethics Committee approval was not required for this study. The authors declare that the study was conducted in accordance with research and publication ethics. The authors declare that, during the writing process of this manuscript, AI tools (such as language improvement assistants) were occasionally used to enhance the clarity and fluency of the English language. All content, analysis, and interpretations were solely developed by the authors. The authors declare that there are no financial conflicts of interest involving any institution, organization, or individual associated with this article. Additionally, there are no conflicts of interest among the authors. The authors state that the first and corresponding author conducted the entire research process, including the planning, data collection, analysis, and manuscript preparation. The second author, who supervised the doctoral dissertation from which this article is derived, provided academic guidance during the thesis stage.

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