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A new class of integer-valued autoregressive models with dynamic survivalprobability is proposed. The peculiarity of this class of models lies on thespecification of the survival probability through a stochastic recurrenceequation. The estimation of the model can be performed by maximum likelihoodand the consistency of the estimator is proved in a misspecified model setting.The flexibility of the proposed specification is illustrated in a simulationstudy. An application to a time series of crime reports is presented. Theresults show how the dynamic survival probability can enhance both in-sampleand out-of-sample performances of integer-valued autoregressive models.

Integer-valued autoregressive models with survival probability driven by a stochastic recurrence equation