Diagnostic analytics for the mixed Poisson INGARCH model with applications

In statistical diagnosis and sensitivity analysis, the local influence method plays a crucial role and is sometimes more advantageous than other methods. The mixed Poisson integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) model is built on a flexible family of mixed Poisson distributions. It not only encompasses the negative binomial INGARCH model but also allows for the introduction of the Poisson-inverse Gaussian INGARCH model and the Poisson generalized hyperbolic secant INGARCH model. This paper applies the local influence analysis method to count time series data within the framework of the mixed Poisson INGARCH model. For parameter estimation, the Expectation-Maximization algorithm is utilized. In the context of local influence analysis, two global influence methods (generalized Cook distance and Q-distance) and four perturbations–case weights perturbation, data perturbation, additive perturbation, and scale perturbation–are considered to identify influential points. Finally, the feasibility and effectiveness of the proposed methods are demonstrated through simulations and analysis of a real data set.