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比特币收益、波动不对称性与多重分形特征

文章 arXiv papers · 作者: Tetsuya Takaishi
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总结

本研究分析比特币一分钟收益，描述其分布、不同采样间隔下的表现、波动不对称性和多重分形特征。研究报告称，收益呈现厚尾，峰度远离高斯基准；随着采样期延长，峰度向该基准靠近的速度较慢。短于一天的间隔内收益偏度为负，超过约一周后则与零一致。

针对日度波动不对称性，作者使用 GARCH、GJR 和 RGARCH 模型，未发现相关效应的证据。作者使用多重分形去趋势波动分析识别多重分形特征，继而考察其来源，并认为时间相关性和厚尾都有贡献。研究还比较了英国脱欧公投前后比特币与 GBP–USD 的多重分形特征：汇率受到影响，而据报告，比特币表现稳健。这些是针对所研究序列和事件的统计发现；它们并未确立交易策略，也不能说明观察到的模式会持续存在。

核心观点

  • 一分钟比特币收益呈现厚尾；采样间隔变长时，峰度向高斯基准收敛的速度较慢。
  • 比特币收益偏度在短时间尺度上为负，在长得多的时间尺度上与零一致。
  • 在所分析的比特币数据中，GARCH 系列模型未发现日度波动不对称性的证据。
  • 多重分形去趋势波动分析识别出多重分形特征，这与时间相关性和厚尾收益均有关。
  • 英国脱欧公投前后，GBP–USD 呈现多重分形响应，而据报告，比特币表现稳健。

标签

加密资产统计学波动率外汇
全文
# Statistical properties and multifractality of Bitcoin


# Statistical properties and multifractality of Bitcoin









Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian expectation. Although for large sampling periods, kurtosis is anticipated to approach the Gaussian expectation, we find that convergence to that is very slow. Skewness is found to be negative at time scales shorter than one day and becomes consistent with zero at time scales longer than about one week. We also investigate daily volatility-asymmetry by using GARCH, GJR, and RGARCH models, and find no evidence of it. On exploring multifractality using multifractal detrended fluctuation analysis, we find that the Bitcoin time series exhibits multifractality. The sources of multifractality are investigated, confirming that both temporal correlation and the fat-tailed distribution contribute to it. The influence of "Brexit" on June 23, 2016 to GBP--USD exchange rate and Bitcoin is examined in multifractal properties. We find that, while Brexit influenced the GBP--USD exchange rate, Bitcoin was robust to Brexit.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。