Document Type
Article
Rights
Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence
Disciplines
1.1 MATHEMATICS
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/t1−1/γ" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">1/t1−1/γ scaling law, where γ>0" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">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.
DOI
https://doi.org/10.3390/math10010117
Recommended Citation
Blackledge J, Lamphiere M. A Review of the Fractal Market Hypothesis for Trading and Market Price Prediction. Mathematics. 2022; 10(1):117. DOI: 10.3390/math10010117
Funder
Science Foundation Ireland
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Details
J M Blackledge and M Lamphiere, "A Review of the Fractal Market Hypothesis for Trading and Market Price Prediction", Special Issue on the Fractal Market Hypothesis, Trend Analysis and Future Price Prediction (Ed. J M Blackledge), MDPI
Mathematics 10(1), 117, 2021. [Online] Available at: https://www.mdpi.com/2227-7390/10/1/117