In the
area of time series modelling, several applications are encountered in
real-life that involve analysis of count time series data. The distribution
characteristics and dependence structure are the major issues that arise while
specifying a modelling strategy to handle the analysis of those kinds of data.
Owing to the numerous applications there is a need to develop models that can
capture these features. However, accounting for both aspects simultaneously
presents complexities while specifying a modeling strategy. In this paper, an
alternative statistical model able to deal with issues of discreteness,
overdispersion, serial correlation over time is proposed. In particular, we
adopt a branching mechanism to develop a first-order stationary negative
binomial autoregressive model. Inference is based on maximum likelihood
estimation and a simulation study is conducted to evaluate the performance of
the proposed approach. As an illustration, the model is applied to a real-life
dataset in crime analysis.
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