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 characterized by abrupt changes 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 dependency in both periods initially. The ensemble autocorrelation of returns decays rapidly and exhibits periodicity. We fitted the autocorrelation with a power law and a cosine function to capture both the decay and the fluctuation and found that the two periods have distinctive periodicity. 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 be closer to 0.5 in Period 2 ($\sim$ 0.49), indicating the market is more efficient at short time scales.

翻译：本文分析了2019年至2022年期间的高频日内比特币数据集。在此时间范围内，比特币市场指数呈现出两个以波动率突变区分的显著时期。两个时期的比特币价格收益率均可由异常扩散过程描述，其表现为从短时间间隔的次扩散向较长时间间隔的弱超扩散的过渡。本文研究的与这种异常行为相关的特征包括重尾现象（可用$q$-高斯分布描述）以及相关性。当我们对绝对收益率的自相关进行采样时，观察到幂律关系，表明两个时期初期均存在时间依赖性。收益率的集合自相关迅速衰减并呈现周期性。我们通过幂律函数和余弦函数拟合自相关，以同时捕捉衰减和波动，发现两个时期具有不同的周期性。进一步研究涉及通过去趋势分析检验比特币时间序列的内生效应。我们发现两个时期均具有多重分形特征，且去趋势概率密度函数（PDF）呈现出自相似性。短时间间隔的赫斯特指数从时期1的小于0.5（约0.42）转变为时期2的更接近0.5（约0.49），表明市场在短时间尺度上更为有效。