High-Frequency Bitcoin Returns: Volatility, Diffusion, and Multifractality

Summary

The paper analyzes high-frequency intraday Bitcoin data from 2019 to 2022, separating the sample into two periods with an abrupt change in volatility. It characterizes returns as anomalous diffusion: subdiffusive over short intervals and weakly superdiffusive over longer ones. The study examines heavy tails using a q-Gaussian distribution and investigates dependence through return autocorrelations.

Absolute-return autocorrelation initially follows a power-law pattern in both periods, while ordinary return autocorrelation decays rapidly; the second period has a slightly higher fitted decay rate. Detrending analysis finds multifractality and self-similarity in both periods. The short-interval Hurst estimate rises from about 0.42 to about 0.49, which the authors interpret as movement toward greater market efficiency. These findings describe the sampled periods and depend on the chosen statistical analyses; they do not establish that the patterns persist in other periods or markets.

Key ideas

• Bitcoin volatility differed abruptly between the two analyzed periods.
• Returns show short-interval subdiffusion and weak long-interval superdiffusion.
• Heavy tails are described with a q-Gaussian distribution.
• Absolute-return autocorrelation follows an initial power-law pattern, while return autocorrelation decays rapidly.
• Both periods show multifractality, and the short-interval Hurst estimate moves closer to one half.

Tags

# Stylized Facts of High-Frequency Bitcoin Time Series


# Stylized Facts of High-Frequency Bitcoin Time Series









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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.