We developed a class of bivariate integer-valued time series models using copula theory. Each count time series is modeled as a Markov chain, with serial dependence characterized through copula-based transition probabilities for Poisson and Negative Binomial marginals. Cross-sectional dependence is modeled via a bivariate Gaussian copula, allowing for both positive and negative correlations and providing a flexible dependence structure. Model parameters are estimated using likelihood-based inference, where the bivariate Gaussian copula integral is evaluated through standard randomized Monte Carlo methods. The proposed approach is illustrated through an application to offense data from New South Wales, Australia, demonstrating its effectiveness in capturing complex dependence patterns.

We developed a class of multivariate integer-valued time series models using copula theory. Each count time series is modeled as a Markov chain, with serial dependence characterized through copula-based transition probabilities for Poisson and negative binomial marginals. Cross-sectional dependence is modeled via a trivariate Gaussian or a “t-copula”, allowing for both positive and negative correlations and providing a flexible dependence structure. Model parameters are estimated using likelihood-based inference, where the trivariate Gaussian or t-copula integrals are evaluated through standard randomized Monte Carlo methods. Simulation results, along with an analysis of annual counts of major hurricanes (Category 3+) across the North Atlantic, Eastern North Pacific, and Western North Pacific basins, demonstrate the effectiveness of the proposed model.