Nonparanormal Hidden Semi-Markov Graphical Models for Analyzing Financial Markets Interconnectivity

Understanding how relationships among global financial markets change over time is crucial for effective risk management, portfolio diversification, and risk assessment. Motivated by the recent episodes of market turmoil, in this paper we analyse daily returns for 21 major indices covering cryptocurrencies, equities, energy commodities, and exchange rates from 2017 to 2025 by developing a novel time-varying graphical model for detecting the evolution of conditional dependency structures in financial markets. To identify temporal shifts in market regimes and account for the characteristics of returns, we exploit nonparanormal distributions with state-dependent parameters that evolve according to a latent finite-state semi-Markov chain. Our methodology results in regime-specific graphs that capture dynamic network connectivity while preserving the tractability of Gaussian methods for identifying conditional dependencies. Model estimation is carried out with a penalized Expectation-Maximization algorithm to induce sparsity in the state-specific precision matrices, without parametric assumptions about the states' sojourn distributions.