Volatility Modelling of Cryptocurrencies According to Different Investment Horizons: The Case of Bitcoin

Year 2025, Volume: 12 Issue: 2, 724 - 749, 30.06.2025

Aslan Aydoğdu , Hafize Meder Çakır

https://doi.org/10.30798/makuiibf.1609311

Abstract

In this study, the fractal structure, efficiency, and long memory features of Bitcoin are investigated according to different investment horizons. The study utilized daily returns from 01.01.2017 to 22.11.2023, applying the maximum overlap discrete wavelet transform, Rescaled Range (R/S) analysis, and volatility models. The analysis results revealed a deviation of Bitcoin returns from the average and a negative correlation, indicating a lack of permanent behaviour in the series. The analysis demonstrates the rejection of the efficient market hypothesis and reveals a chaotic structure in the Bitcoin market. Furthermore, we observed a hyperbolic rate of decrease in returns at long-term investment horizons due to information shocks. This indicates that past returns can predict future returns. This suggests that instead of the efficient market hypothesis, the fractal market hypothesis is valid due to the existence of recurring trends. Finally, we determined the most appropriate volatility models for Bitcoin. The analysis shows that information shocks in Bitcoin returns at medium- and long-term investment horizons decrease over time, and past returns can predict future returns. However, volatility and information shocks are transitory at short- and medium-term investment horizons but can vary. All analysis methods yield consistent and compatible results, suggesting their potential extension to other cryptocurrency markets beyond the Bitcoin market.

Keywords

Cryptocurrency , Investment Horizon , Wavelet Analysis , Efficient Market Hypothesis , Fractal Market Hypothesis , Volatility , Bitcoin

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 confirm that Artificial Intelligence tools were employed solely to enhance the clarity and fluency of the language. Following the use of these tools, the authors thoroughly reviewed and edited the content as needed and assume full responsibility for the final version of the published article. 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 affirm that they contributed equally to all processes of the research.

Volatility Modelling of Cryptocurrencies According to Different Investment Horizons: The Case of Bitcoin

Abstract

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