Abstract A Gegenbauer long memory stochastic volatility model with leverage and a bivariate Student’s t-error distribution to model the innovations of the observation and latent volatility jointly for cryptocurrency time series is presented. This is inspired by the deep rooted characteristics found in cryptocurrencies. Until recently their econometric properties have not been thoroughly investigated. Thus, a rigorous in-sample simulation is conducted to assess the performance of the model with its nested alternatives and study the behavior of many cryptocurrencies and in particular Bitcoin. The data analysis is initiated with a broad scope of 114 cryptocurrencies, then a more detailed understanding of five of the most popular cryptocurrencies and followed up with forecasts focused specifically on Bitcoin (while other forecasts are available as supplementary material). The model parameters are estimated with Bayesian approach using Markov Chain Monte Carlo sampling. In order to implement model selection, the Deviance Information Criterion (DIC) is used. Proposed models are compared with many popular models including those commonly used in industry. The models are applied in a Value-at-Risk (VaR) context and several measures are used to assess model performance.

中文翻译：

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关于具有杠杆作用的广义双变量Student-t Gegenbauer长记忆随机波动率模型：贝叶斯对加密货币的预测，重点是比特币

摘要提出了一种具有杠杆作用和双变量学生t误差分布的Gegenbauer长记忆随机波动率模型，以共同模拟加密货币时间序列的观测值和潜在波动率。这是受到加密货币中根深蒂固的特征的启发。直到最近，它们的计量经济性质还没有被彻底研究过。因此，进行了严格的样本内仿真，以评估模型及其嵌套替代方案的性能，并研究许多加密货币（尤其是比特币）的行为。数据分析从114种加密货币的广泛范围开始，然后更详细地了解了五种最受欢迎​​的加密货币，并随后进行了专门针对比特币的预测（其他预测可作为补充材料）。使用贝氏方法，使用马尔可夫链蒙特卡洛采样法估计模型参数。为了实现模型选择，使用了偏差信息准则（DIC）。将提议的模型与许多流行的模型进行了比较，其中包括工业上常用的模型。将模型应用于风险价值（VaR）上下文中，并使用多种度量来评估模型性能。将提议的模型与许多流行的模型进行了比较，其中包括工业上常用的模型。将模型应用于风险价值（VaR）上下文中，并使用多种度量来评估模型性能。将提议的模型与许多流行的模型进行了比较，其中包括工业上常用的模型。将模型应用于风险价值（VaR）上下文中，并使用多种度量来评估模型性能。