Stylized Facts of High-Frequency Bitcoin Time Series

Yaoyue Tang; Karina Arias-Calluari; Morteza Nattagh Najafi; Michael S. Harré; Fernando Alonso-Marroquin

doi:10.3390/fractalfract9100635

Stylized Facts of High-Frequency Bitcoin Time Series

Yaoyue Tang
, Karina Arias-Calluari
, Morteza Nattagh Najafi
, Michael S. Harré
, Fernando Alonso-Marroquin^*

^*Corresponding author for this work

Center for Integrative Petroleum Research

Research output: Contribution to journal › Article › peer-review

Abstract

This paper analyzes high-frequency intraday Bitcoin data from 2019 to 2022. The Bitcoin market index exhibits two distinct periods, characterized by abrupt volatility shifts. Bitcoin returns can be described by anomalous diffusion processes, transitioning from subdiffusion for short intervals to weak superdiffusion at longer intervals. Heavy tails are captured well by q-Gaussian distributions, and the autocorrelation of absolute returns shows power law behavior. Both periods display multifractality, with Hurst exponents shifting toward 0.5 over time, indicating increased market efficiency. The time evolution of the empirical PDF of price return allows us to connect these stylized facts to the mathematical framework of multifractals and locally fractional porous medium equations.

Original language	English
Article number	635
Journal	Fractal and Fractional
Volume	9
Issue number	10
DOIs	https://doi.org/10.3390/fractalfract9100635
State	Published - Oct 2025

Bibliographical note

Publisher Copyright:
© 2025 by the authors.

Keywords

anomalous diffusion
bitcoin
fractional porous media
Hurst exponent
q-Gaussian
stylized facts

ASJC Scopus subject areas

Analysis
Statistical and Nonlinear Physics
Statistics and Probability

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10.3390/fractalfract9100635

Cite this

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title = "Stylized Facts of High-Frequency Bitcoin Time Series",

abstract = "This paper analyzes high-frequency intraday Bitcoin data from 2019 to 2022. The Bitcoin market index exhibits two distinct periods, characterized by abrupt volatility shifts. Bitcoin returns can be described by anomalous diffusion processes, transitioning from subdiffusion for short intervals to weak superdiffusion at longer intervals. Heavy tails are captured well by q-Gaussian distributions, and the autocorrelation of absolute returns shows power law behavior. Both periods display multifractality, with Hurst exponents shifting toward 0.5 over time, indicating increased market efficiency. The time evolution of the empirical PDF of price return allows us to connect these stylized facts to the mathematical framework of multifractals and locally fractional porous medium equations.",

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author = "Yaoyue Tang and Karina Arias-Calluari and Najafi, \{Morteza Nattagh\} and Harr{\'e}, \{Michael S.\} and Fernando Alonso-Marroquin",

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journal = "Fractal and Fractional",

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AU - Arias-Calluari, Karina

AU - Najafi, Morteza Nattagh

AU - Harré, Michael S.

AU - Alonso-Marroquin, Fernando

PY - 2025/10

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N2 - This paper analyzes high-frequency intraday Bitcoin data from 2019 to 2022. The Bitcoin market index exhibits two distinct periods, characterized by abrupt volatility shifts. Bitcoin returns can be described by anomalous diffusion processes, transitioning from subdiffusion for short intervals to weak superdiffusion at longer intervals. Heavy tails are captured well by q-Gaussian distributions, and the autocorrelation of absolute returns shows power law behavior. Both periods display multifractality, with Hurst exponents shifting toward 0.5 over time, indicating increased market efficiency. The time evolution of the empirical PDF of price return allows us to connect these stylized facts to the mathematical framework of multifractals and locally fractional porous medium equations.

AB - This paper analyzes high-frequency intraday Bitcoin data from 2019 to 2022. The Bitcoin market index exhibits two distinct periods, characterized by abrupt volatility shifts. Bitcoin returns can be described by anomalous diffusion processes, transitioning from subdiffusion for short intervals to weak superdiffusion at longer intervals. Heavy tails are captured well by q-Gaussian distributions, and the autocorrelation of absolute returns shows power law behavior. Both periods display multifractality, with Hurst exponents shifting toward 0.5 over time, indicating increased market efficiency. The time evolution of the empirical PDF of price return allows us to connect these stylized facts to the mathematical framework of multifractals and locally fractional porous medium equations.

KW - anomalous diffusion

KW - bitcoin

KW - fractional porous media

KW - Hurst exponent

KW - q-Gaussian

KW - stylized facts

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ER -

Stylized Facts of High-Frequency Bitcoin Time Series

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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