Bitcoin has received a lot of attention from both investors and analysts, as it forms the highest market capitalization in the cryptocurrency market. This paper evaluates the volatility of Bitcoin returns using three GARCH models (sGARCH, iGARCH, and tGARCH). The new development allows for the modeling of volatility clustering effects, the leptokurtic and the skewed distribution in the return series of Bitcoin. Comparative to the Students’t-distribution and the Generalized error distribution, the Normal Inverse Gaussian (NIG) distribution captured adequately the leptokurtic and skewness in all the GARCH 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.

中文翻译：

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使用GARCH模型对比特币收益的波动性进行建模

比特币受到投资者和分析师的广泛关注，因为它构成了加密货币市场上最高的市值。本文使用三种GARCH模型（sGARCH，iGARCH和tGARCH）评估了比特币收益的波动性。新开发允许对波动性聚类效应，leptokurtic和比特币收益系列中的偏斜分布进行建模。与学生的t分布和广义误差分布相比，正态逆高斯（NIG）分布在所有GARCH模型中都充分捕获了轻快度和偏度。tGARCH模型是最好的模型，因为它描述了比特币市场中冲击的不对称发生。也就是说，投资者对相同数量的好消息和坏消息的反应是截然不同的。从实证结果来看，可以得出结论，tGARCH-NIG是评估比特币收益系列波动性的最佳模型。通常，最好在GARCH类型的模型中使用NIG分布，因为大多数加密货币的时间序列是瘦质的。