A Copula-Based Framework for Multivariate Count Time Series with Mixed Marginal Distributions

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.