Zero-modified count time series modeling with an application to influenza cases

The past few decades have seen considerable interest in modeling time series of counts, with applications in many domains. Classical and Bayesian modeling have primarily focused on conditional Poisson sampling distributions at each time. There is very little research on modeling time series involving Zero-Modified (i.e., Zero Deflated or Inflated) distributions. This paper aims to fill this gap and develop models for count time series involving Zero-Modified distributions, which belong to the Power Series family and are suitable for time series exhibiting both zero-inflation and zero-deflation. A full Bayesian approach via the Hamiltonian Monte Carlo (HMC) technique enables accurate modeling and inference. The paper illustrates our approach using time series on the number of deaths from the influenza virus in the city of São Paulo, Brazil.