A non-linear random environment INAR(1) model

In this paper we introduce a new integer valued autoregressive model of order one. The specificity of this model is based on its non-linear structure. The autoregressive component is defined through the binomial thinning operator. Also, an additional process is introduced into the autoregressive component. This random process controls how the previous value influences the next value of the observed series. For such a model, the main properties are derived and the unknown parameters of the model are estimated using the conditional maximum likelihood method. The practical aspect of the model is discussed on real data sets. (C) 2021 Elsevier B.V. All rights reserved.