Minimum Density Power Divergence Estimator for Negative Binomial Integer-Valued GARCH Models

In this paper, we study a robust estimation method for the observation-driven integer-valued time-series models in which the conditional probability mass of current observations is assumed to follow a negative binomial distribution. Maximum likelihood estimator is highly affected by the outliers. We resort to the minimum density power divergence estimator as a robust estimator and show that it is strongly consistent and asymptotically normal under some regularity conditions. Simulation results are provided to illustrate the performance of the estimator. An application is performed on data for campylobacteriosis infections.