Copula Modelling of Serially Correlated Multivariate Data with Hidden Structures

TL;DR

This paper introduces a copula-based extension of hidden Markov models for multivariate data, enabling decoding of hidden states with complex dependence structures, and addresses computational challenges with a specialized EM algorithm.

Contribution

It develops a novel copula-based HMM framework for multivariate observations, incorporating dependence modeling and a tailored EM algorithm for inference.

Findings

Effective decoding of hidden states in multivariate data.

Successful application to house occupancy data.

Demonstrated computational feasibility of the method.

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 house occupancy.