Parameter estimation using Bayesian techniques for INAR(1) model with censored observations: a case of generalized poisson

{Approximate Bayesian Computation (ABC) under two loss function and Conditional Least Squares (CLS) with data augmentation are applied to address parameter estimation challenges in censored count time series, demonstrating significant improvement in estimation accuracy and robustness for Generalized Poisson-based INAR(1) models.} In this paper, we investigate the challenges of parameter estimation in censored count time series data using the Generalized Poisson-based INAR(1) model. This model accounts for dispersion and integrates censoring mechanisms that commonly arise in real-world data collection. Two approaches are used for the parameter estimation: Conditional Least Squares (CLS) with data augmentation and Approximate Bayesian Computation (ABC) under two distinct loss function. Simulation studies demonstrate that both methods improve the accuracy of estimation, with ABC showing superior performance under higher censoring levels. The study emphasizes how ignoring censoring leads to bias in parameters, especially the dispersion term, and proposes efficient estimation frameworks under such complexities.