  This paper proposes a method for analyzing count time series with inflation
or deflation of zeros. In particular, zero-modified Poisson and zero-modified
negative binomial series with intensities generated by non-negative Markov
sequences are studied in detail. Parameters of the model are estimated by the
method of estimating equations which is facilitated by expressing the model in
a generalized state space form. The latent intensities required for estimation
are extracted using generalized Kalman filter. The applications of proposed
model and its estimation methods are illustrated using simulated and real data
sets.
