**State-Space Models for Binomial Time Series with Excess Zeros** State-Space Models for Binomial Time Series with

DOI: 10.5772/intechopen.71336

Fan Tang and Joseph E. Cavanaugh

Additional information is available at the end of the chapter Fan Tang and Joseph E. Cavanaugh

http://dx.doi.org/10.5772/intechopen.71336 Additional information is available at the end of the chapter

### Abstract

Excess Zeros

Count time series with excess zeros are frequently encountered in practice. In characterizing a time series of counts with excess zeros, two types of models are commonplace: models that assume a Poisson mixture distribution, and models that assume a binomial mixture distribution. Extensive work has been published dealing with modeling frameworks based on Poisson-type approaches, yet little has concentrated on binomial-type methods. To handle such data, we propose two general classes of time series models: a class of observation-driven ZIB (ODZIB) models, and a class of parameter-driven ZIB (PDZIB) models. The ODZIB model is formulated in the partial likelihood framework, which facilitates model fitting using standard statistical software for ZIB regression models. The PDZIB model is conveniently formulated in the state-space framework. For parameter estimation, we devise a Monte Carlo Expectation Maximization (MCEM) algorithm, with particle filtering and particle smoothing methods employed to approximate the intractable conditional expectations in the E-step of the algorithm. We investigate the efficacy of the proposed methodology in a simulation study, which compares the performance of the proposed ZIB models to their counterpart zero-inflated Poisson (ZIP) models in characterizing zero-inflated count time series. We also present a practical application pertaining to disease coding.

Keywords: autocorrelation, count time series, observation-driven models, parameter-driven-models, particle methods, zero-inflation
