Cryptocurrency Time Series on the Binary Complexity-Entropy Plane: Ranking Efficiency from the Perspective of Complex Systems

ArXiv ID: 2504.01974 “View on arXiv”

Authors: Unknown

Abstract

We report the first application of a tailored Complexity-Entropy Plane designed for binary sequences and structures. We do so by considering the daily up/down price fluctuations of the largest cryptocurrencies in terms of capitalization (stable-coins excluded) that are worth $circa ,, 90 %$ of the total crypto market capitalization. With that, we focus on the basic elements of price motion that compare with the random walk backbone features associated with mathematical properties of the Efficient Market Hypothesis. From the location of each crypto on the Binary Complexity-Plane (BiCEP) we define an inefficiency score, $\mathcal I$, and rank them accordingly. The results based on the BiCEP analysis, which we substantiate with statistical testing, indicate that only Shiba Inu (SHIB) is significantly inefficient, whereas the largest stake of crypto trading is reckoned to operate in close-to-efficient conditions. Generically, our $\mathcal I$-based ranking hints the design and consensus architecture of a crypto is at least as relevant to efficiency as the features that are usually taken into account in the appraisal of the efficiency of financial instruments, namely canonical fiat money. Lastly, this set of results supports the validity of the binary complexity analysis.

Keywords: Efficient Market Hypothesis (EMH), Binary Complexity-Plane (BiCEP), Cryptocurrency, Inefficiency score, Price fluctuations, Cryptocurrency

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced mathematical concepts like block entropy, complexity-entropy planes, and statistical testing for efficiency rankings, indicating high math complexity. It demonstrates high empirical rigor by analyzing 47 cryptocurrencies with real daily data, using specific metrics (BiCEP, I score), and performing statistical validation, making it data and implementation-heavy.
  flowchart TD
    A["Research Goal:<br>Determine efficiency ranking of cryptocurrencies<br>using the Binary Complexity-Entropy Plane"] --> B["Input Data:<br>Daily up/down price fluctuations<br>of top cryptocurrencies (90% market cap)"]
    B --> C["Methodology:<br>Apply Binary Complexity-Entropy Plane<br>BiCEP analysis"]
    C --> D["Compute Inefficiency Score (I):<br>Quantify deviation from random walk<br>backbone features"]
    D --> E["Statistical Testing:<br>Validate BiCEP results"]
    E --> F["Key Findings:<br>1. Shiba Inu (SHIB) significantly inefficient<br>2. Most cryptos operate in close-to-efficient conditions<br>3. Design/consensus architecture impacts efficiency<br>4. Binary complexity analysis validated"]