Threshold integer-valued autoregressive model with serially dependent innovation

Nonlinearity in count time series is commonly encountered in practice. To better explain the nonlinear phenomena in count time series, this article introduces a new threshold INAR(1) model using the idea of serially dependent innovation. The proposed model contains some existing INAR(1) models as special cases and establishes a connection between the threshold INAR(1) model and the threshold INARCH(1) model. The basic probabilistic and statistical properties of the new model are investigated. Model parameters, including the threshold variable, are estimated by the conditional least squares, modified quasi-likelihood and conditional maximum likelihood methods. Asymptotic properties and numerical results of the estimates are also studied. An application to the monthly trading volume of stock B in Shanghai Stock Exchange is conducted to show the practicability of the proposed model.