Robust estimation for the one-parameter exponential family integer-valued GARCH(1,1) models based on a modified Tukey's biweight function

In this paper, we study a robust estimation method for observation-driven integer-valued time series models whose conditional distribution belongs to the one-parameter exponential family. Maximum likelihood estimator (MLE) is commonly used to estimate parameters, but it is highly affected by outliers. We resort to the Mallows' quasi-likelihood estimator based on a modified Tukey's biweight function as a robust estimator and establish its existence, uniqueness, consistency and asymptotic normality under some regularity conditions. Compared with MLE, simulation results illustrate the better performance of the new estimator. An application is performed on data for two real data sets, and a comparison with other existing robust estimators is also given.