Hierarchical Markov-switching models for multivariate integer-valued time-series

We propose a new flexible dynamic model for multivariate nonnegative integer-valued time-series. Observations are assumed to depend on the realization of two unobserved integer-valued stochastic variables which control for the time- and cross-dependence of the data. We provide conditional and unconditional (cross)-moments implied by the model, as well as the limiting distribution of the series. An Expectation–Maximization algorithm for maximum likelihood estimation of the model parameters is derived, and an extensive Monte Carlo experiment investigates the finite sample properties of the resulting maximum likelihood estimator. Constrained specifications of the model are also formulated by modifying the assumptions about the dependence structure of the latent variables, and model identification is discussed accordingly. An application by means of a crime data set from the New South Wales (NSW) Bureau Of Crime Statistics And Research with observations spanning beyond 20 years is reported to illustrate the methodology. Results indicate that the proposed approach provides a good description of the conditional distribution of crime records, outperforming the standard hidden Markov model.