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The role of cryptocurrencies within the financial systems has been expandingrapidly in recent years among investors and institutions. It is thereforecrucial to investigate the phenomena and develop statistical methods able tocapture their interrelationships, the links with other global systems, and, atthe same time, the serial heterogeneity. For these reasons, this paperintroduces hidden Markov regression models for jointly estimating quantiles andexpectiles of cryptocurrency returns using regime-switching copulas. Theproposed approach allows us to focus on extreme returns and describe theirtemporal evolution by introducing time-dependent coefficients evolvingaccording to a latent Markov chain. Moreover to model their time-varyingdependence structure, we consider elliptical copula functions defined bystate-specific parameters. Maximum likelihood estimates are obtained via anExpectation-Maximization algorithm. The empirical analysis investigates therelationship between daily returns of five cryptocurrencies and major worldmarket indices.

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