Discovering AI tokens in the Fractal Markets Hypothesis and their time-frequency co-movements with the leading high-carbon cryptocurrency

Po-Sheng Ko; Kuo-Shing Chen; Po-Sheng Ko; Kuo-Shing Chen

doi:10.3934/DSFE.2025013

Data Science in Finance and Economics

2025, Volume 5, Issue 3: 293-319. doi: 10.3934/DSFE.2025013

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Research article

Discovering AI tokens in the Fractal Markets Hypothesis and their time-frequency co-movements with the leading high-carbon cryptocurrency

Po-Sheng Ko ¹,
Kuo-Shing Chen ^{1,2
,
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1.
Department of Public Finance and Taxation, National Kaohsiung University of Science and Technology, Kaohsiung 807618, Taiwan
2.
Department of Accounting, Ming Chuan University, 250 Zhong Shan N. Rd., Sec. 5, Taipei 111, Taiwan

Received: 19 February 2025 Revised: 10 June 2025 Accepted: 25 June 2025 Published: 15 July 2025
JEL Codes: G11, G14, G15, G21, O33

In the AI era, we contribute to the literature by uncovering that the price dynamics of most AI tokens could be fully characterized by the processes driven by fractal Brownian motion, which robustly supports the principles of the fractal markets hypothesis. Using rescaled range (R/S, i.e., Fractal) analysis and the wavelet coherence technique, we analyzed daily log-returns from seven major AI tokens and Bitcoin over the period 2020–2024. Our empirical results rejected the weak form of the Efficient Market Hypothesis (EMH), supporting the Fractal Market Hypothesis (FMH) as a better explanation for the dynamics of AI crypto tokens. More importantly, the log-returns of all analyzed AI tokens, each exhibiting a Hurst exponent exceeding 0.58, provided evidence of persistent behavior and an inherent tendency toward positive price trajectories. These results implied that Fractal analysis can enhance investors' ability to model return dynamics and identify potential appreciation in AI tokens, particularly as short-term trading activity intensifies during episodes of elevated market turbulence. Finally, this work reveals that AI tokens exhibit strong coherence patterns with Bitcoin, varying across time and frequency domains, suggesting Bitcoin's limited role as a hedge against AI tokens. Crucially, this study highlights the significant role of AI tokens as potential safe-haven assets during market turmoil, offering valuable insights for portfolio diversification for crypto investors with intuitive and plausible results that carry strong policy implications.
- AI-related tokens,
- fractal market hypothesis,
- rescaled range analysis (Hurst exponent),
- efficient market hypothesis
Citation: Po-Sheng Ko, Kuo-Shing Chen. Discovering AI tokens in the Fractal Markets Hypothesis and their time-frequency co-movements with the leading high-carbon cryptocurrency[J]. Data Science in Finance and Economics, 2025, 5(3): 293-319. doi: 10.3934/DSFE.2025013

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Abstract

In the AI era, we contribute to the literature by uncovering that the price dynamics of most AI tokens could be fully characterized by the processes driven by fractal Brownian motion, which robustly supports the principles of the fractal markets hypothesis. Using rescaled range (R/S, i.e., Fractal) analysis and the wavelet coherence technique, we analyzed daily log-returns from seven major AI tokens and Bitcoin over the period 2020–2024. Our empirical results rejected the weak form of the Efficient Market Hypothesis (EMH), supporting the Fractal Market Hypothesis (FMH) as a better explanation for the dynamics of AI crypto tokens. More importantly, the log-returns of all analyzed AI tokens, each exhibiting a Hurst exponent exceeding 0.58, provided evidence of persistent behavior and an inherent tendency toward positive price trajectories. These results implied that Fractal analysis can enhance investors' ability to model return dynamics and identify potential appreciation in AI tokens, particularly as short-term trading activity intensifies during episodes of elevated market turbulence. Finally, this work reveals that AI tokens exhibit strong coherence patterns with Bitcoin, varying across time and frequency domains, suggesting Bitcoin's limited role as a hedge against AI tokens. Crucially, this study highlights the significant role of AI tokens as potential safe-haven assets during market turmoil, offering valuable insights for portfolio diversification for crypto investors with intuitive and plausible results that carry strong policy implications.

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