[Paper Review] Analysis of inter-transaction time fluctuations in the cryptocurrency market

Jarosław Kwapień, Marcin Wątorek+4 more|arXiv (Cornell University)|Jun 15, 2022

Complex Systems and Time Series Analysis62 references25 citations

TL;DR

This study analyzes high-frequency tick-by-tick data from six major cryptocurrency exchanges to investigate inter-transaction times (ITTs), transaction counts, traded volume, and volatility. Using detrended fluctuation analysis and multifractal spectrum analysis, it finds that ITTs exhibit long-range power-law autocorrelations and right-skewed singularity spectra, indicating richer multifractality during high market activity. The stretched exponential model fails to universally describe ITT and volume distributions, while power-law fits are inconsistent across platforms, revealing significant cross-platform statistical disparities—especially on HitBTC—suggesting potential market microstructure or data quality differences.

ABSTRACT

We analyse tick-by-tick data representing major cryptocurrencies traded on some different cryptocurrency trading platforms. We focus on such quantities like the inter-transaction times, the number of transactions in time unit, the traded volume, and volatility. We show that the inter-transaction times show long-range power-law autocorrelations. These lead to multifractality expressed by the right-side asymmetry of the singularity spectra $f(\alpha)$ indicating that the periods of increased market activity are characterised by richer multifractality compared to the periods of quiet market. We also show that neither the stretched exponential distribution nor the power-law-tail distribution are able to model universally the cumulative distribution functions of the quantities considered in this work. For each quantity, some data sets can be modeled by the former, some data sets by the latter, while both fail in other cases. An interesting, yet difficult to account for, observation is that parallel data sets from different trading platforms can show disparate statistical properties.

Motivation & Objective

• To investigate the statistical properties of inter-transaction times (ITTs) in the cryptocurrency market using high-frequency tick data.
• To assess whether stretched exponential or power-law distributions universally model ITT, transaction count, volume, and volatility distributions.
• To examine long-range autocorrelations and multifractal structures in ITT time series.
• To identify discrepancies in statistical behavior across parallel data streams from different cryptocurrency trading platforms.
• To explore implications of observed inconsistencies for market microstructure and data integrity, particularly regarding platforms like HitBTC.

Proposed method

• Applied detrended fluctuation analysis (DFA) to detect long-range power-law autocorrelations in ITT time series.
• Used multifractal detrended fluctuation analysis (MF-DFA) to compute singularity spectra f(α), revealing asymmetry indicating stronger multifractality during high-activity periods.
• Evaluated cumulative distribution functions (CDFs) of ITTs, transaction counts, volume, and volatility against stretched exponential (SE) and power-law models.
• Compared model fits across six major exchanges (Binance, Bitfinex, Bitstamp, Coinbase, HitBTC, Kraken) for BTC, ETH, XRP, and LTC.
• Employed double logarithmic plots to assess power-law scaling in CDF tails and used SE parameters α and power-law exponents β for model comparison.
• Conducted detrended cross-correlation analysis (DCCA) to quantify cross-correlations between transaction count, volume, and volatility.

Experimental results

Research questions

• RQ1 Do inter-transaction times in the cryptocurrency market exhibit long-range power-law autocorrelations, and what are their implications for market efficiency and clustering?
• RQ2 To what extent can stretched exponential or power-law distributions universally model the statistical behavior of ITTs, transaction counts, and traded volume across different cryptocurrencies and exchanges?
• RQ3 How does the multifractal structure of ITT time series vary across market activity levels, and what does this reveal about market dynamics?
• RQ4 Why do parallel data streams from different exchanges—such as those for the same cryptocurrency—show divergent statistical properties, especially in distribution fits?
• RQ5 What do discrepancies in statistical behavior, particularly on platforms like HitBTC, suggest about market microstructure, data quality, or potential manipulative practices?

Key findings

• ITT time series across all major cryptocurrencies and exchanges exhibit long-range power-law autocorrelations with Hurst exponents H ≈ 0.64–0.94, indicating persistent clustering of transactions.
• Singularity spectra f(α) show right-side asymmetry, confirming that multifractality is primarily driven by small ITTs (high market activity), with richer multifractal structure during active trading periods.
• The stretched exponential model fails to universally describe ITT and volume CDFs; some platforms (e.g., HitBTC) show better agreement with power-law fits, while others (e.g., Coinbase for XRP) favor power-law scaling.
• Cross-platform comparisons reveal inconsistent statistical behavior: for example, the same cryptocurrency (e.g., ETH) may follow SE on Bitfinex but power-law on HitBTC, indicating platform-specific microstructure effects.
• Volume CDFs show poor agreement with power-law models in most cases, with only a few platforms (e.g., BTC on Kraken and Coinbase) showing traceable scaling in tails.
• HitBTC data consistently deviate from both SE and power-law models, especially in volume and ITT distributions, suggesting unique data characteristics or potential market practices.