Copula Modeling of Serially Correlated Multivariate Data with Hidden Structures

Robert Zimmerman, Radu V. Craiu and Vianey Leos-Barajas

Journal of the American Statistical Association, 2024, vol. 119, issue 548, 2598-2609

Abstract: We propose a copula-based extension of the hidden Markov model (HMM) which applies when the observations recorded at each time in the sample are multivariate. The joint model produced by the copula extension allows decoding of the hidden states based on information from multiple observations. However, unlike the case of independent marginals, the copula dependence structure embedded into the likelihood poses additional computational challenges. We tackle the latter using a theoretically-justified variation of the EM algorithm developed within the framework of inference functions for margins. We illustrate the method using numerical experiments and an analysis of room occupancy. Supplementary materials for this article are available online.

Date: 2024
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DOI: 10.1080/01621459.2023.2263202

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