In this paper we develop a linear expectile hidden Markov model for the analysis of cryptocurrency time series in a risk management framework. The methodology proposed allows to focus on extreme returns and describe their temporal evolution by introducing in the model time-dependent coefficients evolving according to a latent discrete homogeneous Markov chain. As it is often used in the expectile literature, estimation of the model parameters is based on the asymmetric normal distribution. Maximum likelihood estimates are obtained via an Expectation-Maximization algorithm using efficient M-step update formulas for all parameters. We evaluate the introduced method with both artificial data under several experimental settings and real data investigating the relationship between daily Bitcoin returns and major world market indices.

翻译：本文在风险管理框架下，针对加密货币时间序列分析提出一种线性分位数隐马尔可夫模型。所提方法通过引入服从潜在离散齐次马尔可夫链的时变系数，能够聚焦极端收益并描述其时间演化特征。遵循分位数回归文献中的常用做法，模型参数估计基于非对称正态分布。采用期望最大化算法实现极大似然估计，并通过参数的高效M步更新公式进行计算。我们在多组实验设置下使用人工数据验证该方法的有效性，并利用实际数据探究比特币日收益与全球主要市场指数之间的关系。