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Description:
In this paper we introduce a binary autoregressive model. In contrast to the typical autoregression framework, we allow the conditional distribution of the observed process to depend on past values of the time series and some exogenous variables. Such processes have potential applications in econometrics, medicine and environmental sciences. In this paper, we establish stationarity and geometric ergodicity of these processes under suitable conditions on the parameters of the model. Such properties are important for understanding the stability properties of the model as well as for deriving the asymptotic behavior of the parameter estimators.