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Unravelling the volume-volatility nexus in cryptos under structural breaks using fat-tailed distributions: mixture of distribution hypothesis and implications for market efficiency

Journal: European Journal of Finance

Date: 2025

Author: Saswat Patra; Neha Gupta

Abstract:
The study examines the relationship between volume and volatility in leading cryptocurrencies i.e. Bitcoin and Ethereum, within the framework of Mixture of Distribution Hypothesis (MDH). It accommodates structural shifts in the cryptocurrency prices and uses fat-tailed distributions. The results show that the MDH is rejected for both cryptocurrencies, and volume alone cannot explain the heteroskedasticity of returns; however, it acts as a significant predictor for volatility, especially when incorporating structural breaks in the model. Further, the forecasting performance improves when fat-tailed distributions, such as the skewed student’s t and Johnson’s Su distribution are used to model the innovations. Thus, volume holds important information in the crypto markets and can affect returns, thereby, raising concerns about market efficiency. Our results are robust across different periods, modelling approaches and forecasting horizons, and hold substantial implications for traders, market participants, regulators, and governments in designing effective policies.

Link: Google Scholar

Background and Context

Research Focus

This study examines whether trading volume can predict volatility in Bitcoin and Ethereum markets using the Mixture of Distribution Hypothesis framework.

Methodology

The researchers used EGARCH models with fat-tailed distributions and incorporated structural breaks identified through the Bai-Perron test on daily cryptocurrency prices.

Data Analyzed

The study analyzed 3,350 daily Bitcoin observations (May 2013-Jan 2023) and 2,762 Ethereum observations (Aug 2015-Jan 2023) from coinmarketcap.com.

Cryptocurrency Returns Exhibit Non-Normal Fat-Tailed Distributions

  • Normal distributions have excess kurtosis of zero; values above indicate heavy tails with extreme price movements.
  • Ethereum shows extraordinarily high kurtosis (69.7) in the full sample, indicating more extreme volatility events than Bitcoin.
  • This fat-tailed behavior necessitates specialized distributions like Skewed Student's t for accurate volatility modeling.

Volume Coefficient is Positive and Significant for Ethereum Volatility

  • The volume coefficient (δ) measures how strongly trading volume influences cryptocurrency price volatility predictions.
  • Positive coefficients confirm volume acts as a significant predictor of volatility in cryptocurrency markets.
  • This finding has implications for traders who can use volume data to anticipate market volatility changes.

Volatility Persistence Remains High Even After Including Volume

Bitcoin β Values Model 1 (No Volume): 0.981 Model 3 (With Volume): 0.979 Drop: Only 0.2% Ethereum β Values Model 1 (No Volume): 0.936 Model 3 (With Volume): 0.936 Drop: Only 0.06% MDH Rejected: Volume Does Not Explain Persistence
  • The Mixture of Distribution Hypothesis predicts that including volume should dramatically reduce volatility persistence (β).
  • Bitcoin's persistence dropped only 0.2% and Ethereum's only 0.06% when volume was added to models.
  • This rejection of MDH suggests volume provides information quality rather than being a pure information proxy.

Skewed Student's t Distribution Dominates Model Confidence Sets

  • The Model Confidence Set test identifies which models have statistically equivalent best forecasting performance.
  • Skewed Student's t distribution was included in the MCS 100% of the time across all loss functions.
  • Using appropriate fat-tailed distributions is critical for accurate cryptocurrency volatility forecasting and risk management.

Structural Breaks Significantly Improve Volatility Model Performance

Bitcoin: 3 Structural Breaks Aug 2017 Crypto Boom Jun 2019 Crypto Winter Dec 2020 COVID Rally Ethereum: 4 Structural Breaks Jun 2017 NFT Launch Aug 2018 Market Dip Dec 2019 Pre-COVID Feb 2021 Bull Run Breaks are Statistically Significant (p<0.05)
  • The Bai-Perron test identified multiple structural breaks corresponding to major cryptocurrency market events.
  • Dummy variables for structural breaks were statistically significant, improving volatility model accuracy substantially.
  • Ignoring structural breaks leads to overestimated volatility persistence and poor forecasting during regime changes.

Contribution and Implications

  • First study to test Mixture of Distribution Hypothesis on cryptocurrencies while accounting for structural breaks.
  • Volume acts as a significant volatility predictor, enabling traders to anticipate market volatility using volume data.
  • Rejection of MDH suggests volume represents information quality and dispersion rather than information flow itself.
  • Skewed Student's t distribution is recommended for modeling cryptocurrency innovations in risk management applications.
  • Results support cryptocurrencies exhibiting inverse leverage effects, confirming potential safe-haven properties against traditional assets.
  • Regulators can use volume-based monitoring to design policies that help stabilize cryptocurrency market volatility.

Data Sources

  • Chart 1 (Kurtosis): Data extracted from Table 2 showing summary statistics for full sample and subsamples.
  • Chart 2 (Volume Coefficients): Data extracted from Table 3 parameter estimates showing δ values across distributions.
  • Chart 3 (Persistence): SVG based on Table 3 β coefficients comparing Model 1 vs Model 3 under SST distribution.
  • Chart 4 (MCS Results): Data extracted from Table 6 showing Model Confidence Set inclusion at 90% level.
  • Chart 5 (Structural Breaks): SVG based on Table 1 and Figure 1 showing breakpoint dates for both cryptocurrencies.