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In this paper, we introduce a new first-order mixture integer-valuedthreshold autoregressive process, based on the binomial and negative binomialthinning operators. Basic probabilistic and statistical properties of thismodel are discussed. Conditional least squares (CLS) and conditional maximumlikelihood (CML) estimators are derived and the asymptotic properties of theestimators are established. The inference for the threshold parameter isobtained based on the CLS and CML score functions. Moreover, the Wald test isapplied to detect the existence of the piecewise structure. Simulation studiesare considered, along with an application: the number of criminal mischiefincidents in the Pittsburgh dataset.

A new First-Order mixture integer-valued threshold autoregressive process based on binomial thinning and negative binomial thinning