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Abstract
Count time series are frequently encountered in biomedical, epidemiological and public health applications. In principle, such series may exhibit three distinctive features: overdispersion, zero-inflation and temporal correlation. Developing a modelling framework that is sufficiently general to accommodate all three of these characteristics poses a challenge. To address this challenge, we propose a flexible class of dynamic models in the state-space framework. Certain models that have been previously introduced in the literature may be viewed as special cases of this model class. For parameter estimation, we devise a Monte Carlo Expectation-Maximization (MCEM) algorithm, where particle filtering and particle smoothing methods are employed to approximate the high-dimensional integrals in the E-step of the algorithm. To illustrate the proposed methodology, we consider an application based on the evaluation of a participatory ergonomics intervention, which is designed to reduce the incidence of workplace injuries among a group of hospital cleaners. The data consists of aggregated monthly counts of work-related injuries that were reported before and after the intervention.
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