Time series of multivariate zero-inflated Poisson counts

This paper proposes a state space model to describe multivariate autocorrelated zero-inflated count series. The model extends the classical zero-inflated Poisson distribution into multivariate cases but is able to impose different zero inflations on different dimensions. Combing the zero inflation with the log-normal mixture of independent Poisson distribution, this model allows for flexible cross-correlations of multiple counts. Furthermore, By considering the zero-inflation parameters as well as the Poisson mean parameters as latent variables evolving according to state space models, the model can capture the autocorrelations of count data. Monte Carlo EM algorithm together with particle filtering method provides a satisfactory estimation for the model parameters and the latent process.