Stylized Facts of High-Frequency Bitcoin Time Series

ArXiv ID: 2402.11930 “View on arXiv”

Authors: Unknown

Abstract

This paper analyses the high-frequency intraday Bitcoin dataset from 2019 to 2022. During this time frame, the Bitcoin market index exhibited two distinct periods, 2019-20 and 2021-22, characterized by an abrupt change in volatility. The Bitcoin price returns for both periods can be described by an anomalous diffusion process, transitioning from subdiffusion for short intervals to weak superdiffusion over longer time intervals. The characteristic features related to this anomalous behavior studied in the present paper include heavy tails, which can be described using a $q$-Gaussian distribution and correlations. When we sample the autocorrelation of absolute returns, we observe a power-law relationship, indicating time dependence in both periods initially. The ensemble autocorrelation of the returns decays rapidly. We fitted the autocorrelation with a power law to capture the decay and found that the second period experienced a slightly higher decay rate. The further study involves the analysis of endogenous effects within the Bitcoin time series, which are examined through detrending analysis. We found that both periods are multifractal and present self-similarity in the detrended probability density function (PDF). The Hurst exponent over short time intervals shifts from less than 0.5 ($\sim$ 0.42) in Period 1 to closer to 0.5 in Period 2 ($\sim$ 0.49), indicating that the market has gained efficiency over time.

Keywords: Bitcoin, Anomalous Diffusion, Hurst Exponent, Detrended Fluctuation Analysis, Market Efficiency, Cryptocurrencies

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical frameworks like anomalous diffusion, q-Gaussians, multifractal detrended fluctuation analysis (MF-DFA), and power-law fitting, indicating high math density. It demonstrates strong empirical rigor through the use of high-frequency tick data (2019-2022), explicit statistical analysis (autocorrelation, Hurst exponent), and comparative period assessment, making it highly data and implementation-focused.

  flowchart TD
    A["Research Goal<br>Analyze stylized facts of<br>high-frequency Bitcoin data"] --> B["Data Collection<br>Intraday Bitcoin dataset<br>2019-2022"]
    
    B --> C["Market Segmentation<br>Identify two distinct periods<br>2019-20 and 2021-22"]
    
    C --> D["Anomaly & Distribution Analysis<br>Test for anomalous diffusion<br>Fit q-Gaussian for heavy tails"]
    
    D --> E["Correlation Analysis<br>Calculate autocorrelation of returns<br>Analyze power-law decay"]
    
    E --> F["Detrended Analysis<br>DFA for multifractality<br>Study self-similarity in PDF"]
    
    F --> G["Key Findings/Outcomes"]
    
    G --> H1["Anomalous Diffusion<br>Subdiffusion → Superdiffusion<br>based on time scale"]
    
    G --> H2["Market Efficiency<br>Hurst exponent ~0.42 (2019-20)<br>~0.49 (2021-22)<br>indicating increased efficiency"]
    
    G --> H3["Correlation Structure<br>Power-law decay in autocorrelation<br>Higher decay rate in Period 2"]
    
    G --> H4["Multifractality<br>Both periods show<br>self-similar multifractal behavior"]