Heavy-tailed matrix-variate hidden Markov models

The matrix-variate framework for hidden Markov models (HMMs) is expanded with two families of models using matrix-variate 𝑡 and contaminated normal distributions. These models improve the handling of tail behavior, clustering, and address challenges in identifying outlying matrices in matrix-variate data. Two Expectation-Conditional Maximization (ECM) algorithms are implemented in the R package MatrixHMM for parameter estimation. Simulations assess parameter recovery, robustness, anomaly detection, and show the advantages over alternative approaches. The models are applied to real-world data to analyze labor market dynamics across Italian provinces.