Self-exciting threshold -valued autoregressive processes for non-stationary time series of counts

To handle non-stationary integer-valued time series of counts with piecewise characteristics and linear trends, this paper introduced a class of self-exciting threshold Z-valued autoregressive processes. The process is defined with a free type distribution for the innovation, which enhances the flexibility of the model. The basic probabilistic and statistical properties of the proposed model are discussed. Conditional least squares (CLS) estimator and modified quasi-likelihood (MQL) estimator, as well as their asymptotic properties are obtained. A searching algorithm for estimating the threshold parameter is also provided. Some simulation studies are conducted to show the performances of the proposed methods. Finally, an application to a real data example is provided.