Quantile and expectile copula-based hidden Markov regression models for the analysis of the cryptocurrency market

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 this phenomenon and develop statistical methods able to capture their interrelationships, the links with other global systems and, at the same time, the serial heterogeneity. Here we introduce 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.