{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:40:05Z","timestamp":1759639205358,"version":"build-2065373602"},"reference-count":74,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,10,3]],"date-time":"2025-10-03T00:00:00Z","timestamp":1759449600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001602","name":"Science Foundation Ireland","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100001602","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Commodities"],"abstract":"<jats:p>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 \u2018Beta-to-Volatility\u2019 and \u2018Lyapunov-to-Volatility\u2019 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 \u2018TuringBot\u2019 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 \u2018micro-trends\u2019 that would otherwise remain undetected\u2014yielding gains of up to approximately 10%. Empirical results confirm that Bitcoin and Ethereum exchanges behave as self-affine (fractal) stochastic fields with L\u00e9vy distributions, exhibiting a Hurst exponent of roughly 0.32, a fractal dimension of about 1.68, and a L\u00e9vy 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.<\/jats:p>","DOI":"10.3390\/commodities4040022","type":"journal-article","created":{"date-parts":[[2025,10,3]],"date-time":"2025-10-03T16:44:50Z","timestamp":1759509890000},"page":"22","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimisation of Cryptocurrency Trading Using the Fractal Market Hypothesis with Symbolic Regression"],"prefix":"10.3390","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2986-2339","authenticated-orcid":false,"given":"Jonathan","family":"Blackledge","sequence":"first","affiliation":[{"name":"Science Foundation Ireland, Three Park Place, Hatch Street Upper, Saint Kevin\u2019s, D02 FX65 Dublin, Ireland"},{"name":"Centre for Advanced Studies, Warsaw University of Technology, PI. Politechniki 1, 00-661 Warsaw, Poland"},{"name":"Department of Computer Science, University of Western Cape, Robert Sobukwe Rd, Bellville, Cape Town 7535, South Africa"},{"name":"School of Electrical and Electronic Engineering, Technological University Dublin, D07 EWV4 Dublin, Ireland"},{"name":"School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, University Rd, Westville, Durban 3629, South Africa"},{"name":"Chandigarh Engineering College, Chandigarh Group of Colleges, Kharar Banur Hwy, Sector 112, Sahibzada Ajit Singh Nagar 140307, India"},{"name":"Office of the Vice Chancellor for Research & Innovation, INTI International University, Persiaran Perdana BBN Putra Nilai, Nilai 71800, Malaysia"},{"name":"Barnsley College University Centre, Church Street, Barnsley, South Yorkshire S70 2YW, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anton","family":"Blackledge","sequence":"additional","affiliation":[{"name":"Department of Electronic and Electrical Engineering, Faculty of Engineering and Design, University of Bath, Claverton Down, Bath BA2 7AY, UK"},{"name":"Department of Computing, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,3]]},"reference":[{"key":"ref_1","unstructured":"(2022, April 25). 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