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

TL;DR

This paper introduces a new measure of time irreversibility in cryptocurrency returns using trend pattern statistics and explores its relationship with market inefficiency, revealing strong irreversibility and evolving characteristics over time.

Contribution

It proposes a novel irreversibility index based on Kullback-Leibler divergence and analyzes its application to multiple cryptocurrencies, linking irreversibility with market inefficiency.

Findings

Strong irreversibility detected in all studied cryptocurrencies

Irreversibility characteristics evolve over time

Relationship between inefficiency and irreversibility is complex

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.