Bayesian forecasting of zero-inflated time-series of counts

In this paper, we extend the current literature on Poisson dynamic time series models to account for excess zeros, motivated by uncertainty quantification in consumer goods demand patterns. In doing so, we implement an updating scheme that is analytically tractable under certain conditions. We refer to the model as the Zero-Inflated Poisson-Gamma State Space (ZIP-GSS) model and introduce its multivariate extension. We develop efficient Markov chain Monte Carlo methods, coupled with data augmentation strategies, to enable model learning, updating, monitoring, and forecasting in a sequential analysis framework. Finally, we demonstrate the implementation of the proposed models using both simulated and real consumer goods demand datasets, and we compare their forecasting performance against benchmark models.