The role of cryptocurrencies within the financial systems has been expanding rapidly in recent years among investors and institutions. It is therefore crucial to investigate the phenomena and develop statistical methods able to capture their interrelationships, the links with other global systems, and, at the same time, the serial heterogeneity. For these reasons, this paper introduces hidden Markov regression models for jointly estimating quantiles and expectiles of cryptocurrency returns using regime-switching copulas. The proposed approach allows us to focus on extreme returns and describe their temporal evolution by introducing time-dependent coefficients evolving according to a latent Markov chain. Moreover to model their time-varying dependence structure, we consider elliptical copula functions defined by state-specific parameters. Maximum likelihood estimates are obtained via an Expectation-Maximization algorithm. The empirical analysis investigates the relationship between daily returns of five cryptocurrencies and major world market indices.

翻译：近年来，加密货币在投资者和金融机构中的金融系统角色迅速扩展。因此，研究其现象并开发能够捕捉加密货币间相互关系、与其他全球系统的联系以及序列异质性的统计方法至关重要。基于此，本文引入隐马尔可夫回归模型，利用状态切换copula联合估计加密货币收益的分位数和期望分位数。所提出的方法使我们能够聚焦极端收益，并通过引入随潜在马尔可夫链演化的时变系数来描述其时间演变。此外，为建模其动态相依结构，我们考虑了由状态特定参数定义的椭圆copula函数。通过期望最大化算法获得最大似然估计。实证分析研究了五种加密货币日收益率与主要全球市场指数之间的关系。