论文标题
比特币价格回报的最新缩放属性
Recent scaling properties of Bitcoin price returns
论文作者
论文摘要
尽管对比特币市场观察到相关的风格化事实，但我们发现了累积回报分布的缩放行为的独特属性。对于各种资产，累积回报分布的尾部指数$μ$显示出$μ\ 3 $，称为“逆立方法”。另一方面，比特币申报表的回报率为$μ\约2 $，称为“反平方法”。我们使用最近的比特币数据研究了缩放属性，发现尾部指数变为$μ\ 3 $，这与逆立方定律一致。这表明比特币市场的某些特性可能会随着时间而变化。我们还研究了绝对回报的自相关，发现它是由具有两个缩放指数的幂律描述的。通过分析通过实现波动率标准化的绝对回报，我们验证了比特币返回时间序列与正常的随机变量一致，随着时间变化的波动。
While relevant stylized facts are observed for Bitcoin markets, we find a distinct property for the scaling behavior of the cumulative return distribution. For various assets, the tail index $μ$ of the cumulative return distribution exhibits $μ\approx 3$, which is referred to as "the inverse cubic law." On the other hand, that of the Bitcoin return is claimed to be $μ\approx 2$, which is known as "the inverse square law." We investigate the scaling properties using recent Bitcoin data and find that the tail index changes to $μ\approx 3$, which is consistent with the inverse cubic law. This suggests that some properties of the Bitcoin market could vary over time. We also investigate the autocorrelation of absolute returns and find that it is described by a power-law with two scaling exponents. By analyzing the absolute returns standardized by the realized volatility, we verify that the Bitcoin return time series is consistent with normal random variables with time-varying volatility.
