On Bivariate Self-Exciting Hysteretic Integer-Valued Autoregressive Processes

This paper introduces a bivariate hysteretic integer-valued autoregressive (INAR) process driven by a bivariate Poisson innovation. It deals well with the buffered or hysteretic characteristics of the data. Model properties such as sationarity and ergodicity are studied in detail. Parameter estimation problem is also well address via methods of two-step conditional least squares (CLS) and conditional maximum likelihood (CML). The boundary parameters are estimated via triangular grid searching algorithm. The estimation effect is verified through simulations based on three scenarios. Finally, the new model is applied to the offence counts in New South Wales (NSW), Australia.