  In this paper, we introduce a new first-order mixture integer-valued
threshold autoregressive process, based on the binomial and negative binomial
thinning operators. Basic probabilistic and statistical properties of this
model are discussed. Conditional least squares (CLS) and conditional maximum
likelihood (CML) estimators are derived and the asymptotic properties of the
estimators are established. The inference for the threshold parameter is
obtained based on the CLS and CML score functions. Moreover, the Wald test is
applied to detect the existence of the piecewise structure. Simulation studies
are considered, along with an application: the number of criminal mischief
incidents in the Pittsburgh dataset.
