Poisson count time series

This article reviews and compares popular methods, some old and some recent, that produce time series having Poisson marginal distributions. The article begins by narrating ways where time series with Poisson marginal distributions can be produced. Modeling nonstationary series with covariates motivates consideration of methods where the Poisson parameter depends on time. Here, estimation methods are developed for some of the more flexible methods. The results are used in the analysis of (1) a count sequence of tropical cyclones occurring in the North Atlantic Basin since 1970, and (2) the number of no-hitter games pitched in Major League Baseball since 1893. Tests for whether the Poisson marginal distribution is appropriate are included.