In this paper, we revisit the stylized facts of bitcoin markets and propose various approaches for modeling the dynamics governing the mean and variance processes. We first provide the statistical properties of our proposed models and study in detail their forecasting performance and adequacy by means of point and density forecasts. We adopt two loss functions and the model confidence set test to evaluate the predictive ability of the models and the likelihood ratio test to assess their adequacy. Our results confirm that bitcoin markets are characterized by regime shifting , long memory and multifractality . We find that the Markov switching multifractal and FIGARCH models outperform other GARCH-type models in forecasting bitcoin returns volatility. Furthermore, combined forecasts improve upon forecasts from individual models.

中文翻译：

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预测比特币市场的波动

在本文中，我们将回顾比特币市场的典型事实，并提出各种方法来模拟控制均值和方差过程的动力学。我们首先提供建议模型的统计特性，然后通过点和密度预测来详细研究其预测性能和适当性。我们采用两个损失函数和模型置信度检验来评估模型的预测能力，并采用似然比检验来评估模型的充分性。我们的结果证实，比特币市场的特征在于政权转移，长期记忆和多重分形。我们发现，在预测比特币收益波动率方面，马尔可夫切换多重分形模型和FIGARCH模型优于其他GARCH类型模型。此外，合并的预测会改进各个模型的预测。