Chance or Chaos? Fractal geometry aimed to inspect the nature of Bitcoin

ArXiv ID: 2309.00390 “View on arXiv”

Authors: Unknown

Abstract

The aim of this paper is to analyse the Bitcoin in order to shed some light on its nature and behaviour. We select 9 cryptocurrencies that account for almost 75% of total market capitalisation and compare their evolution with that of a wide variety of traditional assets: commodities with spot and futures contracts, treasury bonds, stock indices, growth and value stocks. Fractal geometry will be applied to carry out a careful statistical analysis of the performance of the Bitcoin returns. As a main conclusion, we have detected a high degree of persistence in its prices, which decreases the efficiency but increases its predictability. Moreover, we observe that the underlying technology influences price dynamics, with fully decentralised cryptocurrencies being the only ones to exhibit self-similarity features at any time scale.

Keywords: Bitcoin, cryptocurrencies, fractal geometry, market efficiency, predictability, Cryptocurrency

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats
  • Why: The paper employs advanced fractal geometry and the R/S method with statistical inference tests, representing substantial mathematical density. However, its empirical rigor is moderate, relying on historical price data and statistical analysis rather than backtesting a specific trading strategy or implementing complex data pipelines.
  flowchart TD
    A["Research Goal<br/>Analyze nature of Bitcoin &amp; cryptocurrencies"] --> B["Data Selection<br/>9 top cryptocurrencies<br/>+ Traditional assets"]
    B --> C["Methodology<br/>Fractal Geometry &amp; Statistical Analysis"]
    C --> D{"Computational Process<br/>Analyze price returns<br/>at multiple time scales"}
    D --> E["Persistence detected<br/>High degree in prices"]
    D --> F["Efficiency vs. Predictability<br/>Persistence decreases efficiency<br/>Increases predictability"]
    D --> G["Technology Influence<br/>Fully decentralized coins show<br/>self-similarity at all scales"]
    E --> H["Key Outcomes<br/>Bitcoin nature: Chaotic but predictable<br/>Tech dictates fractal behavior"]
    F --> H
    G --> H