Time-Varying Zero-Adjusted Poisson Distribution for Modeling Count Time Series

Many studies have used extensions of ARMA models for the analysis of non-Gaussian time series. One of them is the Generalized Autoregressive Moving Average, GARMA, enabling the modeling of count time series with distributions such as Poisson. The GARMA class is being expanded to accommodate other distributions, aiming to capture the typical characteristics of count data, including under or overdispersion and excess zeros. This study aims to propose an approach based on the GARMA class in order to analyze count time series with excess zeros, assuming a time-varying zero-adjusted Poisson distribution. This approach allows for capturing serial correlation, forecasting the future values, and estimating the future probability of zeros. For inference, a Bayesian analysis was adopted using the Hamiltonian Monte Carlo (HMC) algorithm for sampling from the joint posterior distribution. We conducted a simulation study and presented an application to influenza mortality reported in Brazil. Our findings demonstrated the usefulness of the model in estimating the probability of non-occurrence and the number of counts in future periods.