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Optimisation of Cryptocurrency Trading Using the Fractal Market Hypothesis with Symbolic Regression

Author

Listed:
  • Jonathan Blackledge

    (Science Foundation Ireland, Three Park Place, Hatch Street Upper, Saint Kevin’s, D02 FX65 Dublin, Ireland
    Centre for Advanced Studies, Warsaw University of Technology, PI. Politechniki 1, 00-661 Warsaw, Poland
    Department of Computer Science, University of Western Cape, Robert Sobukwe Rd, Bellville, Cape Town 7535, South Africa
    School of Electrical and Electronic Engineering, Technological University Dublin, D07 EWV4 Dublin, Ireland)

  • Anton Blackledge

    (Department of Electronic and Electrical Engineering, Faculty of Engineering and Design, University of Bath, Claverton Down, Bath BA2 7AY, UK
    Department of Computing, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, UK)

Abstract

Cryptocurrencies such as Bitcoin can be classified as commodities under the Commodity Exchange Act (CEA), giving the Commodity Futures Trading Commission (CFTC) jurisdiction over those cryptocurrencies deemed commodities, particularly in the context of futures trading. This paper presents a method for predicting both long- and short-term trends in selected cryptocurrencies based on the Fractal Market Hypothesis (FMH). The FMH applies the self-affine properties of fractal stochastic fields to model financial time series. After introducing the underlying theory and mathematical framework, a fundamental analysis of Bitcoin and Ethereum exchange rates against the U.S. dollar is conducted. The analysis focuses on changes in the polarity of the ‘Beta-to-Volatility’ and ‘Lyapunov-to-Volatility’ ratios as indicators of impending shifts in Bitcoin/Ethereum price trends. These signals are used to recommend long, short, or hold trading positions, with corresponding algorithms (implemented in Matlab R2023b) developed and back-tested. An optimisation of these algorithms identifies ideal parameter ranges that maximise both accuracy and profitability, thereby ensuring high confidence in the predictions. The resulting trading strategy provides actionable guidance for cryptocurrency investment and quantifies the likelihood of bull or bear market dominance. Under stable market conditions, machine learning (using the ‘TuringBot’ platform) is shown to produce reliable short-horizon estimates of future price movements and fluctuations. This reduces trading delays caused by data filtering and increases returns by identifying optimal positions within rapid ‘micro-trends’ that would otherwise remain undetected—yielding gains of up to approximately 10%. Empirical results confirm that Bitcoin and Ethereum exchanges behave as self-affine (fractal) stochastic fields with Lévy distributions, exhibiting a Hurst exponent of roughly 0.32, a fractal dimension of about 1.68, and a Lévy index near 1.22. These findings demonstrate that the Fractal Market Hypothesis and its associated indices provide a robust market model capable of generating investment returns that consistently outperform standard Buy-and-Hold strategies.

Suggested Citation

  • Jonathan Blackledge & Anton Blackledge, 2025. "Optimisation of Cryptocurrency Trading Using the Fractal Market Hypothesis with Symbolic Regression," Commodities, MDPI, vol. 4(4), pages 1-58, October.
    • Handle: RePEc:gam:jcommo:v:4:y:2025:i:4:p:22-:d:1764730
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    References listed on IDEAS

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    1. Al-Yahyaee, Khamis Hamed & Mensi, Walid & Ko, Hee-Un & Yoon, Seong-Min & Kang, Sang Hoon, 2020. "Why cryptocurrency markets are inefficient: The impact of liquidity and volatility," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    2. Caporale, Guglielmo Maria & Gil-Alana, Luis & Plastun, Alex, 2018. "Persistence in the cryptocurrency market," Research in International Business and Finance, Elsevier, vol. 46(C), pages 141-148.
    3. Jonathan Blackledge & Derek Kearney & Marc Lamphiere & Raja Rani & Paddy Walsh, 2019. "Econophysics and Fractional Calculus: Einstein’s Evolution Equation, the Fractal Market Hypothesis, Trend Analysis and Future Price Prediction," Mathematics, MDPI, vol. 7(11), pages 1-57, November.
    4. Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393-393.
    5. Bariviera, Aurelio F. & Basgall, María José & Hasperué, Waldo & Naiouf, Marcelo, 2017. "Some stylized facts of the Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 82-90.
    6. Alvarez-Ramirez, J. & Rodriguez, E. & Ibarra-Valdez, C., 2018. "Long-range correlations and asymmetry in the Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 948-955.
    7. Nadarajah, Saralees & Chu, Jeffrey, 2017. "On the inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 150(C), pages 6-9.
    8. Jiang, Yonghong & Nie, He & Ruan, Weihua, 2018. "Time-varying long-term memory in Bitcoin market," Finance Research Letters, Elsevier, vol. 25(C), pages 280-284.
    9. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 59-82, Winter.
    10. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    11. Mohsen Soltanifar, 2021. "A Generalization of the Hausdorff Dimension Theorem for Deterministic Fractals," Mathematics, MDPI, vol. 9(13), pages 1-9, July.
    12. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    13. Urquhart, Andrew, 2016. "The inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 148(C), pages 80-82.
    14. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    15. repec:pri:cepsud:91malkiel is not listed on IDEAS
    16. Chu, Jeffrey & Zhang, Yuanyuan & Chan, Stephen, 2019. "The adaptive market hypothesis in the high frequency cryptocurrency market," International Review of Financial Analysis, Elsevier, vol. 64(C), pages 221-231.
    17. Stanis{l}aw Dro.zd.z & Robert Gk{e}barowski & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marcin Wk{a}torek, 2018. "Bitcoin market route to maturity? Evidence from return fluctuations, temporal correlations and multiscaling effects," Papers 1804.05916, arXiv.org, revised Jul 2018.
    18. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    19. Celeste, Valerio & Corbet, Shaen & Gurdgiev, Constantin, 2020. "Fractal dynamics and wavelet analysis: Deep volatility and return properties of Bitcoin, Ethereum and Ripple," The Quarterly Review of Economics and Finance, Elsevier, vol. 76(C), pages 310-324.
    20. Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Marcin Wk{a}torek, 2023. "What is mature and what is still emerging in the cryptocurrency market?," Papers 2305.05751, arXiv.org.
    21. Hu, Yang & Valera, Harold Glenn A. & Oxley, Les, 2019. "Market efficiency of the top market-cap cryptocurrencies: Further evidence from a panel framework," Finance Research Letters, Elsevier, vol. 31(C), pages 138-145.
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