TITLE:
A First Order Stationary Branching Negative Binomial Autoregressive Model with Application
AUTHORS:
Bakary Traore, Bonface Miya Malenje, Herbert Imboga
KEYWORDS:
Branching Process, Negative Binomial, Time Series of Count Data, Serial Dependence, Overdispersion
JOURNAL NAME:
Open Journal of Statistics,
Vol.12 No.6,
December
30,
2022
ABSTRACT: 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.