Akademik Veri Yönetim Sistemi
Journal of Applied Statistics, 2026 (SCI-Expanded, Scopus)
In this study, the classical INAR(1) models are extended to the model integer-valued data exhibiting linear and exponential growth trends. Two different models are introduced, assuming the Poisson distribution related to innovation terms varying their means with linear and exponential trend functions over time. The basic statistical properties of the proposed INAR(1) models are presented; in addition, closed-form expressions for the multi-step ahead conditional mean and variance, and the probability generating function are derived and discussed. Conditional least squares and conditional maximum likelihood methods were used for parameter estimation. In the application section, population data from Türkiye and Malta are considered and it is observed that the Turkish population exhibits a linear growth trend, while the Maltese population exhibits an exponential growth pattern. The proposed models are applied separately to the data from both countries and the estimated parameters and model fit are evaluated. The results demonstrate that the proposed trend-based INAR(1) models successfully capture the population data exhibiting different growth dynamics.