We present a novel first-order nonnegative integer-valued autoregressive
model for stationary count data processes with Bernoulli-geometric marginals based
on a new type of generalized thinning operator. It can be used for modeling time
series of counts with equidispersion, underdispersion and overdispersion. The main
properties of the model are derived, such as probability generating function, moments,
transition probabilities and zero probability. The maximum likelihood method is used
for estimating the model parameters. The proposed model is fitted to time series of
counts of iceberg orders and of cases of family violence illustrating its capabilities in
challenging cases of overdispersed and equidispersed count data.

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• An INAR(1) process for modeling count time series with equidispersion, underdispersion and overdispersion