One- and two-sided monitoring schemes for BINARCH(1) processes

In this article we propose and study one- and two-sided control charts for monitoring a first order binomial integer-valued ARCH process. This model can be used for modeling integer-valued time series of counts with a finite support, which also exhibit overdispersion. We consider Shewhart as well as exponentially weighted moving average control charts. The performance of both schemes is investigated for various shifts in process parameters, which result in an upward or a downward shift in process mean level. Practical guidelines concerning the statistical design of the proposed charts are given as well. The case of two-sided control charts is also considered. Finally, we describe the implementation of the proposed schemes by using a real dataset about the monthly inflation of the Eurozone members.