Trend patterns statistics for assessing irreversibility in cryptocurrencies: time-asymmetry versus inefficiency

ArXiv ID: 2307.08612 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we present a measure of time irreversibility using trend pattern statistics. We define the irreversibility index as the Kullback-Leibler divergence between the distribution of uptrends subsequences (increasing trends) and the corresponding downtrends subsequences distribution (decreasing trends) in a time series. We use this index to analyze the degree of irreversibility in log return series over time, specifically focusing on five cryptocurrencies: Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash. Our analysis reveals a strong indication of irreversibility in all these cryptocurrencies and the characteristic evolves over time. We additionally evaluate the market efficiency for these cryptocurrencies based on a recently proposed information-theoretic measure. By comparing inefficiency and irreversibility, we explore the relationship between these statistical features. This comparison provides insight into the non-trivial relationship between inefficiency and irreversibility.

Keywords: Time Irreversibility, Kullback-Leibler Divergence, Market Efficiency, Cryptocurrency, Trend Analysis

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail
  • Why: The paper introduces a formal irreversibility index based on Kullback-Leibler divergence, showing mathematical density with stochastic process theory and derivations. It applies the method to real cryptocurrency data with statistical tests, providing backtest-ready analysis but lacks code or implementation details.
  flowchart TD
    A["Research Goal:<br>Assess Irreversibility in Cryptocurrencies"] --> B["Data Inputs:<br>Log Return Series of 5 Cryptocurrencies"]
    B --> C["Key Methodology:<br>Trend Pattern Statistics"]
    C --> D["Computational Process:<br>Calculate Irreversibility Index<br>(Kullback-Leibler Divergence)"]
    D --> E["Comparative Analysis:<br>Irreversibility vs. Market Inefficiency"]
    E --> F["Key Finding 1:<br>Strong Irreversibility in all Cryptocurrencies"]
    E --> G["Key Finding 2:<br>Non-trivial Relationship between<br>Irreversibility and Inefficiency"]
    F --> H["Outcome:<br>Dynamic Evolution of Irreversibility over Time"]
    G --> H