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

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.