%0 Journal Article
%T A First Order Stationary Branching Negative Binomial Autoregressive Model with Application
%A Bakary Traore
%A Bonface Miya Malenje
%A Herbert Imboga
%J Open Journal of Statistics
%P 810-826
%@ 2161-7198
%D 2022
%I Scientific Research Publishing
%R 10.4236/ojs.2022.126046
%X 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.
%K Branching Process
%K Negative Binomial
%K Time Series of Count Data
%K Serial Dependence
%K Overdispersion
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=122186