A0826
Title: Learning dynamic conditional dependence via hidden Markov quantile regression
Authors: Beatrice Foroni - Sapienza University (Italy) [presenting]
Luca Merlo - Link Campus University (Italy)
Lea Petrella - Sapienza University of Rome (Italy)
Nicola Salvati - University of Pisa (Italy)
Abstract: A hidden Markov quantile graphical model is proposed to study multivariate time series with evolving conditional dependencies. The model combines quantile regression with hidden Markov dynamics to estimate state-specific networks that characterize the dependence structure among variables across unobserved regimes. Within each latent state, conditional independence is recovered through sparsity in the quantile regression coefficients. The estimation procedure relies on a penalized expectation-maximization algorithm that maximizes a pseudo-likelihood function and introduces $\ell_1$-regularization to identify interpretable networks. Simulation studies under various scenarios of regime persistence, transition probabilities, and dependency strength show that the method accurately recovers the underlying structure and outperforms standard benchmarks. An empirical application investigates PM$_{2.5}$ concentration levels in 14 major cities in northern Italy between 2019 and 2022. The model uncovers temporal shifts in inter-city dependence, identifies periods with higher systemic pollution risk, and reveals heterogeneous network connectivity patterns likely associated with policy interventions, lockdown effects, and seasonal phenomena. The framework offers a flexible tool for studying dynamic systems in environmental, financial, and biomedical domains.
