A First Order Stationary Branching Negative Binomial Autoregressive Model with Application
- 1 Department of Mathematics, Pan African University, Institute of Basic Science, Technology and Innovation (PAUSTI), Nairobi, Kenya
- 2 Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya
- 3 Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya
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.
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