Count time series prediction using particle filters

Non-Gaussian dynamic models are proposed to analyse time series of counts. Three models are proposed for responses generated by a Poisson, a negative binomial and a mixture of Poisson distributions. The parameters of these distributions are allowed to vary dynamically according to state space models. Particle filters or sequential Monte Carlo methods are used for inference and forecasting purposes. The performance of the proposed methodology is evaluated by two simulation studies for the Poisson and the negative binomial models. The methodology is illustrated by considering data consisting of medical contacts of schoolchildren suffering from asthma in England.