Robust estimation for general integer-valued autoregressive models based on the exponential-polynomial divergence

In this study, we develop a robust estimator for integer-valued one-parameter exponential family autoregressive models, named general integer-valued autoregressive models. This model accommodates a broad class of integer-valued time series models. In particular, we propose a robust estimation method that minimizes the exponential-polynomial divergence (EPD) belonging to the Brègman divergence family. EPD subsumes the density power divergence (DPD), which has been extensively studied by many authors for the past decades. Under regularity conditions, the minimum EPD estimator (MEPDE) is shown to be consistent and asymptotically normal. Comparing the performance of MEPDE with the minimum DPD estimator, we substantiate the validity of MEPDE through a simulation study and real data analysis.