Inference for multiple change points in integer-valued GARCH model via likelihood ratio scan method

Integer-valued time series are widely used in many fields. The integer-valued generalized autoregressive conditional heteroskedasticity (INGARCH) model can be used to fit integer-valued time series. In this paper, we study the change point detection in Poisson INGARCH and log-linear Poisson INGARCH models. Based on the likelihood ratio scanning method (LRSM), the numbers and locations of the change points in the piecewise stationary Poisson INGARCH process and loglinear Poisson INGARCH process are discussed. The minimum description length (MDL) functions of Poisson INGARCH and log-linear Poisson INGARCH models are given. Finally, simulation experiments and real data analysis are conducted to illustrate the feasibility of the LRSM.