Soft-clipping INGARCH Models for Time Series of Bounded Counts

The soft-clipping binomial INGARCH (scBINGARCH) models are proposed as nearly linear time series models for bounded counts with possibly negative autocorrelations. 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 normality of maximum likelihood estimators are established, and finite-sample properties are studied with simulations. The practical relevance of the scBINGARCH’s ability to allow for negative parameter and ACF values is demonstrated by some real-data examples.