Measuring Crypto Market Irreversibility with Trend Pattern Statistics

Summary

This paper proposes a statistical measure of time irreversibility based on contrasting rising and falling trend subsequences in a return series. It defines an irreversibility index as the Kullback–Leibler divergence between the distributions of upward-trend patterns and their downward-trend counterparts. The index is applied over time to log returns for Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash.

The analysis reports strong evidence of irreversibility across all five cryptocurrencies, with the measured characteristic changing over time. The paper also evaluates market efficiency using a recently proposed information-theoretic measure, then compares inefficiency with irreversibility. It finds that the relationship between the two features is not straightforward. These results describe statistical properties rather than a trading strategy or a demonstrated source of returns. The document does not specify the sampling period, pattern construction details, or predictive tests, so the reported irreversibility should not be interpreted by itself as proof of exploitable inefficiency.

Key ideas

• The proposed irreversibility index compares distributions of rising and falling trend subsequences using Kullback–Leibler divergence.
• The measure is applied over time to log returns for five named cryptocurrencies.
• The analysis reports strong irreversibility across the studied assets, with changes over time.
• The paper compares irreversibility with market inefficiency measured using an information-theoretic approach.
• Irreversibility and inefficiency have a non-trivial relationship and do not alone establish a trading opportunity.

Tags

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


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









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.

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