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使用 GARCH 模型与 NIG 误差估算比特币波动率

文章 arXiv papers · 作者: Samuel Asante Gyamerah
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总结

论文比较了 sGARCH、iGARCH 和 tGARCH 模型在估算比特币收益率波动率方面的表现。每种模型都与 Student t、广义误差和正态逆高斯（NIG）分布相结合，以刻画波动聚集、厚尾和偏度等特征。比较重点在于这些模型与分布的组合对收益率序列特征的拟合程度。

报告结果显示，NIG 在刻画肥尾和偏度方面表现较好，并指出在所考察的规格中，tGARCH 与 NIG 的组合表现最佳。作者认为，tGARCH 的优势在于能够表示对正面和负面消息的不同波动率响应。他们认为，NIG 也可能适用于其他加密货币，因为其收益率通常呈尖峰厚尾分布。文档没有提供样本期、评估指标、预测表现或交易结果的详情，因此结论仅限于所报告的模型比较，未必适用于其他资产或时期。

核心观点

  • GARCH 系列模型能够刻画比特币收益率中的波动聚集。
  • 研究比较了 Student t、广义误差和正态逆高斯收益率分布。
  • 据报告，正态逆高斯分布能够较好地刻画偏度和厚尾。
  • tGARCH 允许对正向和负向冲击产生不同的波动率响应。
  • 报告中表现较好的规格是 tGARCH 与正态逆高斯误差的组合。

标签

加密资产波动率统计学
全文
# Estimating the volatility of Bitcoin using GARCH models


# Estimating the volatility of Bitcoin using GARCH models









In this paper, an application of three GARCH-type models (sGARCH, iGARCH, and tGARCH) with Student t-distribution, Generalized Error distribution (GED), and Normal Inverse Gaussian (NIG) distribution are examined. The new development allows for the modeling of volatility clustering effects, the leptokurtic and the skewed distributions in the return series of Bitcoin. Comparative to the two distributions, the normal inverse Gaussian distribution captured adequately the fat tails and skewness in all the GARCH type models. The tGARCH model was the best model as it described the asymmetric occurrence of shocks in the Bitcoin market. That is, the response of investors to the same amount of good and bad news are distinct. From the empirical results, it can be concluded that tGARCH-NIG was the best model to estimate the volatility in the return series of Bitcoin. Generally, it would be optimal to use the NIG distribution in GARCH type models since time series of most cryptocurrency are leptokurtic.

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。