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

Jonathan Blackledge and Marc Lamphiere
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Jonathan Blackledge: Science Foundation Ireland, Three Park Place, Hatch Street Upper, D02 FX65 Dublin, Ireland
Marc Lamphiere: School of Electrical and Electronic Engineering, Central Quad, Grangegorman Campus, Technological University Dublin, D07 EWV4 Dublin, Ireland

Mathematics, 2021, vol. 10, issue 1, 1-46

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.

Keywords: fractal geometry; financial time series analysis; random walk hypothesis; Efficient Market Hypothesis; fractal market hypothesis; future price prediction; machine learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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