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We propose a generalized INGARCH model with structural changes including exogenous covariates (hereafter referred to as GCP-INGARCHX), which belongs to the observation-driven type models where the regime-switching is driven by certain failure points occurring in the time. Necessary and sufficient conditions for the second-order stationarity, both in the mean and in the second-order moment, are established. The explicit formula of the mean and the second-order moment are then given under these second-order stationarity conditions. The autocovariance structure is studied while providing the closed-form of the piecewise autocorrelation function. The conditional least squares (CLS) and the conditional maximum likelihood (CML) estimators of the underlying parameters are obtained for both the cases that the breakpoints are known or not. A simulation study and an application on real data set are provided to assess the performance of the model.
