Hidden Markov Quantile Graphical Models

This paper introduces a novel hidden Markov quantile graphical model for capturing time-varying conditional dependence structures in multivariate time series. The proposed method allows the identification of state-specific graphs and the dynamic relationships between variables across hidden regimes via joint mixtures of hidden Markov quantile regressions. We leverage the sparsity pattern of the quantile regression coefficients to recover conditional independence networks within each latent state. Estimation of model parameters is achieved through pseudo maximum likelihood using a penalized Expectation-Maximization algorithm to induce sparsity in the quantile regression coefficients. The performance of the method is validated through simulations and compared with existing approaches. The proposed model is applied to air pollution data in Northern Italy, analyzing the interdependence of PM2.5 concentration levels across 14 major cities from 2019 to 2022.