  This paper considers a general class of parameter-driven models for time
series of counts. A comprehensive simulation study is conducted to evaluate the
accuracy and efficiency of three estimators: the maximum likelihood estimators
of the generalized linear model, 2-state finite mixture model, and 2-state
hidden Markov model. Standard errors for these estimators are derived. Our
results show that except in extreme cases, the maximum likelihood estimator of
the generalized linear model is an efficient, consistent and robust estimator
with a well-behaved estimated standard error. The maximum likelihood estimator
of the 2-state hidden Markov model is appropriate only when the true model is
extreme relative to the generalized linear model. Our results are applied to
problems concerning polio incidence and daily numbers of epileptic seizures.
