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

Paper: arXiv 2307.06400

Authors: Beatrice Foroni, Luca Merlo, Lea Petrella

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a sophisticated statistical methodology combining regime-switching copulas, hidden Markov models, and quantile/expectile regressions to evaluate cryptocurrency dependencies. It features strong mathematical rigor and applied empirical analysis on daily cryptocurrency and global index returns, though code availability for exact replication is limited.

Research Flowchart

  flowchart TD
    A[Research Goal: Model cryptocurrency extreme returns & time-varying market dependencies] --> B[Data Inputs: Daily returns of 5 Cryptocurrencies & Major World Market Indices]
    B --> C[Methodology: Copula-based Hidden Markov Regression Models for Quantiles & Expectiles]
    C --> D[Model Specs: Latent Markov Chain for regime switching + Elliptical Copulas for dependence]
    D --> E[Computation: Expectation-Maximization EM Algorithm for Maximum Likelihood Estimation]
    E --> F[Outcomes: Successfully captured serial heterogeneity, extreme risk links, and time-dependent market regimes]