Negative Binomial INAR(1) Process with Poisson-transmuted Record Type Exponential Innovations

The integration of an integer-valued time series model with a negative binomial thinning operator is essential for effective modeling, addressing overdispersion, and accommodating intricate dependence structures. This article introduces a novel approach to modeling integer-valued time series data through the negative binomial first-order integer-valued autoregressive process with Poisson-transmuted record-type exponential innovations. The extension of the traditional first-order integer-valued autoregressive model incorporates a flexible negative binomial thinning operator to address overdispersion. The study derives the statistical properties of the process and estimates its parameters using conditional maximum likelihood and conditional least squares methods. The performance of the estimators is evaluated through simulation studies. Finally, we demonstrate the usefulness of the proposed model by analyzing some count time series data and comparing it with competing models.