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Talk · International Conference on Electronics, Computer and Computation · April 10, 2026

Beyond the Random Walk: Hierarchical Structures in Cryptocurrency and Traditional Markets

Nargiza Zhumalieva, Burul Shambetova, Ruslan Isaev

Ruslan Isaev
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Abstract

Financial markets are usually modeled as random walks, but real-world data often reveals hierarchical structures beneath the noise. A multi-resolution investigation of fractal organization and nonlinear dynamics in Bitcoin, the S&P 500, and Gold is presented. Utilizing Detrended Fluctuation Analysis and the Brock-Dechert-Scheinkman test integrated with GARCH-filtering, a multifractal hierarchy is identified in Bitcoin, where trend persistence strengthens systematically from daily to monthly horizons. Short-term complexity mainly comes from volatility clustering. However, when we segment waves across multiple resolutions, a hierarchical price geometry emerges that holds across three orders of magnitude. All analyzed assets exhibit robust positive amplitude-duration scaling, with structural consistency optimized within a 3-7 week characteristic scale. These findings demonstrate that while mature markets approximate informational efficiency at high frequencies, an endogenous behavioral skeleton remains visible through multiscale aggregation. Objective statistical evidence is provided for the existence of recursive market cycles. These results are consistent with the hierarchical premises of behavioral frameworks such as Elliott Wave Theory, though they operate at the threshold of detectable structure and do not provide a direct validation of specific wave-counting rules.

Complex Systems and Time Series AnalysisFinancial Markets and Investment StrategiesStock Market Forecasting MethodsBitcoinS&P 500gold prices

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