We often encounter time series in which the observations represent count data. One such example is…

A model for time series of counts

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We often encounter time series in which the observations represent count data. One such example is the monthly number of newly recorded cases of poliomyelitis in the U.S. for the years 1970–1983 plotted in Figure 8.6. Unless the actual counts are large and can be approximated by continuous variables, Gaussian and linear time series models are generally inappropriate for analyzing such data. The parameter-driven specification provides a flexible class of models for modeling count data. We now discuss a specific model based on a Poisson observation density.  This model is similar to the one presented by Zeger (1988) for analyzing the polio data. The observation

density is assumed to be Poisson with mean exp{xt }, i.e.,

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