Stylized Facts of High-Frequency Bitcoin Time Series

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.