Robust closed-form estimators for the integer-valued GARCH (1,1) model

A closed-form estimator and its several robust versions for the integer-valued GARCH(1, 1) model are proposed. These estimators are easy to implement and do not require the use of any numerical optimization procedure. Consistency and asymptotic normality for the non-robust closed-form estimator is established. The robustification of the closed-form estimator is done by replacing the sample mean and autocorrelations by robust estimators of them, respectively. The performances of these closed-form estimators are investigated and compared via simulations. New estimators are applied to 5 stock-market data sets with different periods and time intervals, and their prediction performances are assessed by in-sample prediction, out-of-sample prediction and scoring rules. Other possible proposals related to the closed-form estimators are also discussed.