Soft-clipping INGARCH models for time series of bounded counts

The soft-clipping binomial INGARCH (scBINGARCH) models are proposed as time series models for bounded counts, which have a nearly linear structure and also allow for negative autocor-relations. Conditions that guarantee the existence and certain mixing properties of the scBINGARCH process are derived, and further stochastic properties are discussed. The consistency and asymptotic nor-mality of maximum likelihood estimators are established, and finite-sample properties are studied with simulations. The practical relevance of the scBINGARCH model’s ability to allow for negative parameter and ACF values is demonstrated by some real-data examples.