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A Review of the Fractal Market Hypothesis for Trading and Market Price Prediction

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  • Jonathan Blackledge

    (Science Foundation Ireland, Three Park Place, Hatch Street Upper, D02 FX65 Dublin, Ireland
    Centre for Advanced Studies, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland
    Department of Computer Science, University of Western Cape, Robert Sobukwe Rd., Bellville, Cape Town 7535, South Africa
    Faculty of Arts, Science and Technology, Wrexham Glyndŵr University of Wales, Mold Rd., Wrexham LL11 2AW, UK)

  • Marc Lamphiere

    (School of Electrical and Electronic Engineering, Central Quad, Grangegorman Campus, Technological University Dublin, D07 EWV4 Dublin, Ireland
    Dublin Energy Laboratory, Technological University Dublin, D07 ADY7 Dublin, Ireland
    Mace Group, The Masonry, 151 Thomas Street, D08 PY5E Dublin, Ireland)

Abstract

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put the FMH into a broader perspective, the Random Walk and Efficient Market Hypotheses are considered together with the basic principles of fractal geometry. After exploring the historical developments associated with different financial hypotheses, an overview of the basic mathematical modelling is provided. The principal goal of this paper is to consider the intrinsic scaling properties that are characteristic for each hypothesis. In regard to the FMH, it is explained why a financial time series can be taken to be characterised by a 1 / t 1 − 1 / γ scaling law, where γ > 0 is the Lévy index, which is able to quantify the likelihood of extreme changes in price differences occurring (or otherwise). In this context, the paper explores how the Lévy index, coupled with other metrics, such as the Lyapunov Exponent and the Volatility, can be combined to provide long-term forecasts. Using these forecasts as a quantification for risk assessment, short-term price predictions are considered using a machine learning approach to evolve a nonlinear formula that simulates price values. A short case study is presented which reports on the use of this approach to forecast Bitcoin exchange rate values.

Suggested Citation

  • Jonathan Blackledge & Marc Lamphiere, 2021. "A Review of the Fractal Market Hypothesis for Trading and Market Price Prediction," Mathematics, MDPI, vol. 10(1), pages 1-46, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:117-:d:715791
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    References listed on IDEAS

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    1. Ray Ball, 2009. "The Global Financial Crisis and the Efficient Market Hypothesis: What Have We Learned?," Journal of Applied Corporate Finance, Morgan Stanley, vol. 21(4), pages 8-16, September.
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    1. Mehmet Ali Balcı & Larissa M. Batrancea & Ömer Akgüller & Lucian Gaban & Mircea-Iosif Rus & Horia Tulai, 2022. "Fractality of Borsa Istanbul during the COVID-19 Pandemic," Mathematics, MDPI, vol. 10(14), pages 1-33, July.

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