TITLE:
Nonstationary Autoregressive Modeling of Time Series Count Data with Covariates: Addressing Seasonality in Branching Negative Binomial Models
AUTHORS:
Bakary Traore, Ibrahima Sory Mamikouny Camara, Alpha Oumar Baldé
KEYWORDS:
Non-Stationary Time Series, Covariates, Branching Process, Time Series of Count Data, Overdispersion
JOURNAL NAME:
Open Journal of Statistics,
Vol.16 No.2,
April
10,
2026
ABSTRACT: Various models for time series of count data account for discreteness, overdispersion and serial dependence. In addition to these, accounting for covariates incorparation pattern are the complexities that arise while dealing with data which involve seasonality aspects. Specifying a model that can handle such kind of time series of count data is very important in several real-life application. However in this paper, we present a non-stationary autoregressive model where covariates information are incorporated in the Branching Negative Binomial (bNB) autoregressive model in order to assess the seasonality in the process of time series event. A simulation study is done to evaluate how well the proposed strategy performs, and inference is based on maximum likelihood estimate. The model is used to analyse a real-world dataset, which is an infectious disease with covariates information, including temperature and rainfall.