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Fractal Fract
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Fractal Approaches and Machine Learning in Financial Markets
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Fractal Approaches and Machine Learning in Financial Markets

A special issue of Fractal and Fractional (ISSN 2504-3110).

Deadline for manuscript submissions: 30 September 2026 | Viewed by 1331

Special Issue Editor

Prof. Dr. Sun-Yong Choi

E-Mail Website
Guest Editor
Department of Finance and Big Data, Gachon University, Seongnam 13120, Republic of Korea
Interests: multifractal analysis; economic finance; financial mathematics; machine learning; stochastic volatility; data science
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The increasing complexity and interconnectedness of modern financial markets call for innovative analytical tools that can capture nonlinear dynamics, long-range dependence, and emergent patterns. Fractal approaches provide a powerful framework to study scaling laws, multifractality, and self-similarity in financial time series, offering deeper insights into volatility clustering, market efficiency, and systemic risk.

At the same time, machine learning techniques have advanced rapidly, enabling researchers to uncover hidden structures, forecast market movements, and design adaptive trading and risk management strategies.

This Special Issue invites contributions that combine fractal methodologies and machine learning models to address fundamental and applied questions in finance. Potential topics include, but are not limited to, fractal and multifractal analysis of asset prices, machine learning-based volatility and risk prediction, hybrid models integrating fractal features with deep learning, applications to portfolio optimization and asset pricing, and the use of fractal-inspired learning algorithms in financial decision-making. By bridging theory and practice, this issue aims to highlight the synergies between fractal approaches and machine learning, offering novel perspectives on the behavior and dynamics of global financial markets.

Prof. Dr. Sun-Yong Choi
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractal and multifractal analysis
  • machine learning
  • deep learning
  • financial market
  • volatility
  • risk management
  • portfolio optimization
  • asset pricing
  • financial decision-making

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

53 pages, 56035 KB  
Article
Comparative Analysis of Cryptocurrency Market Efficiency and Local Features Using MF-DFA and DCC-GARCH
by Do-Hyeon Kim, Jun-Hyeok Lee and Sun-Yong Choi
Fractal Fract. 2026, 10(6), 353; https://doi.org/10.3390/fractalfract10060353 (registering DOI) - 23 May 2026
Abstract
This study investigates time-varying market efficiency and cross-market correlations in cryptocurrency markets across South Korea, the United States, and Japan. Using rolling-window multifractal detrended fluctuation analysis (MF-DFA) and dynamic conditional correlation–generalized autoregressive conditional heteroskedasticity (DCC-GARCH), we analyze 11 cryptocurrency–fiat pairs—Bitcoin (BTC), Ethereum (ETH), [...] Read more.
This study investigates time-varying market efficiency and cross-market correlations in cryptocurrency markets across South Korea, the United States, and Japan. Using rolling-window multifractal detrended fluctuation analysis (MF-DFA) and dynamic conditional correlation–generalized autoregressive conditional heteroskedasticity (DCC-GARCH), we analyze 11 cryptocurrency–fiat pairs—Bitcoin (BTC), Ethereum (ETH), Ripple (XRP), and Bitcoin Cash (BCH) denominated in Korean Won (KRW), US Dollar (USD), and Japanese Yen (JPY)—from January 2018 to September 2025. MF-DFA results confirm persistent multifractality and significant time-variation in market efficiency across all markets, consistent with the Adaptive Market Hypothesis (AMH). DCC-GARCH estimates reveal a structural divergence between return integration and efficiency correlations: return-based correlations for same-asset cross-fiat pairs are exceptionally high (mean dynamic conditional correlation of approximately 0.96–0.98), whereas efficiency-based correlations are far more heterogeneous, with cross-asset pairs approaching near-zero synchronization. We interpret the Kimchi Premium as a product of institutional frictions that impede price-level arbitrage while leaving volatility transmission largely unaffected. These findings suggest that cryptocurrency market integration is multidimensional—globally synchronized in risk dynamics, yet locally segmented in the structural quality of information processing. Full article
(This article belongs to the Special Issue Fractal Approaches and Machine Learning in Financial Markets)
35 pages, 11568 KB  
Article
Unveiling Long-Memory Dynamics in Turbulent Markets: A Novel Fractional-Order Attention-Based GRU-LSTM Framework with Multifractal Analysis
by Yangxin Wang and Yuxuan Zhang
Fractal Fract. 2026, 10(5), 293; https://doi.org/10.3390/fractalfract10050293 - 26 Apr 2026
Viewed by 315
Abstract
Financial time series in turbulent markets exhibit complex long-memory dynamics and multifractal features that traditional deep learning models fail to capture due to inherent exponential forgetting mechanisms. To address this, we propose Frac-Attn-GL, a novel Fractional-order Spatiotemporal Attention-based GRU-LSTM framework. Grounded in the [...] Read more.
Financial time series in turbulent markets exhibit complex long-memory dynamics and multifractal features that traditional deep learning models fail to capture due to inherent exponential forgetting mechanisms. To address this, we propose Frac-Attn-GL, a novel Fractional-order Spatiotemporal Attention-based GRU-LSTM framework. Grounded in the Fractal Market Hypothesis, the model embeds Grünwald–Letnikov fractional-order operators into a dual-channel architecture (FracLSTM and FracGRU) to characterize long-range memory with rigorous power-law decay priors. Furthermore, an extreme-aware asymmetric loss function is designed to drive a dynamic spatiotemporal routing mechanism, enabling adaptive shifts between long-term macro trends and short-term micro shocks. Empirical tests on major U.S. stock indices reveal three significant findings. First, the Frac-Attn-GL framework substantially reduces prediction errors, achieving up to a 93.1% RMSE reduction on the highly volatile NASDAQ index compared to standard baselines. Second, the adaptively learned fractional-order parameters exhibit a consistent quantitative alignment with the market’s empirical multifractal singularity spectrum, supporting the physical interpretability of the model’s endogenous memory mechanism. Finally, hybrid residual multifractal diagnostics indicate that the framework effectively captures deep long-range correlations, reducing the Hurst exponent of the prediction residuals from ~0.83 to approximately 0.50, a level consistent with the absence of significant long-range dependence. Full article
(This article belongs to the Special Issue Fractal Approaches and Machine Learning in Financial Markets)
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20 pages, 2033 KB  
Article
On the Predictability of Green Finance Markets: An Assessment Based on Fractal and Shannon Entropy
by Sonia Benghiat and Salim Lahmiri
Fractal Fract. 2026, 10(3), 205; https://doi.org/10.3390/fractalfract10030205 - 22 Mar 2026
Cited by 1 | Viewed by 470
Abstract
Econophysics is an interdisciplinary field that applies physics concepts to economic and financial systems. By utilizing tools such as statistical physics, including fractal analysis and entropy measures, econophysics helps model the complex and non-linear dynamics of equity markets. This paper examines the intrinsic [...] Read more.
Econophysics is an interdisciplinary field that applies physics concepts to economic and financial systems. By utilizing tools such as statistical physics, including fractal analysis and entropy measures, econophysics helps model the complex and non-linear dynamics of equity markets. This paper examines the intrinsic dynamics and regularity in information content in green finance markets (carbon, clean energy, and sustainability markets) by means of range scale analysis (R/S), detrended fluctuation analysis (DFA), fractionally integrated generalized auto-regressive conditionally heteroskedastic (FIGARCH) process, and Shannon entropy (SE). The empirical results can be summarized as follows. First, prices in all markets are persistent; however, returns are likely random as estimated Hurst exponents are close to 0.5. Second, the FIGARCH process shows that volatility series in carbon and sustainability markets are persistent, whilst volatility in clean energy is anti-persistent. Third, in carbon and sustainability markets, entropy is high in prices compared to returns and volatility series. On the contrary, the clean energy market shows lower entropy for prices than for returns and volatility. In sum, it is concluded that price and volatility series are predictable, whilst return series are not. Finally, based on a rolling window framework, it is concluded that the COVID-19 pandemic and the Russia–Ukraine war have altered long memory and randomness in all three green finance markets. Full article
(This article belongs to the Special Issue Fractal Approaches and Machine Learning in Financial Markets)
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