A review of the fractal market hypothesis for trading and market price prediction
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Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
MPDI
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.
Description
Keywords
Fractal geometry, Random walk hypothesis, Efficient market hypothesis, Future price prediction, Machine learning, Trading
Citation
Blackledge, J., & Lamphiere, M. (2022). A review of the fractal market hypothesis for trading and market price prediction. Mathematics ,10(1), 117. https://doi.org/10.3390/math10010117