Paper: arXiv 2307.08612

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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