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

TL;DR

This paper develops a novel regime-switching copula-based hidden Markov regression model to analyze the joint behavior and extreme returns of cryptocurrencies and global market indices, capturing temporal dependence and heterogeneity.

Contribution

It introduces a new model combining hidden Markov processes, copulas, and quantile/expectile regression for cryptocurrency return analysis, addressing regime changes and dependence structures.

Findings

Model effectively captures regime shifts in cryptocurrency returns.

Reveals dynamic dependence between cryptocurrencies and global markets.

Highlights importance of extreme value analysis in financial risk assessment.

Abstract

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.