  Count data appears in various disciplines. In this work, a new method to
analyze time series count data has been proposed. The method assumes
exponentially decaying covariance structure, a special class of the Mat\'ern
covariance function, for the latent variable in a Poisson regression model. It
is implemented in a Bayesian framework, with the help of Gibbs sampling and
ARMS sampling techniques. The proposed approach provides reliable estimates for
the covariate effects and estimates the extent of variability explained by the
temporally dependent process and the white noise process. The method is
flexible, allows irregular spaced data, and can be extended naturally to bigger
datasets. The Bayesian implementation helps us to compute the posterior
predictive distribution and hence is more appropriate and attractive for count
data forecasting problems. Two real life applications of different flavors are
included in the paper. These two examples and a short simulation study
establish that the proposed approach has good inferential and predictive
abilities and performs better than the other competing models.
