2022/08/03 by Wagner Barreto‐Souza, Luiza S. C. Piancastelli, Barreto-Souza, Wagner +5
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2208.02024
openalex publication_date 2022/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a general class of INteger-valued Generalized AutoRegressive Conditionally Heteroscedastic (INGARCH) processes by allowing time-varying mean and dispersion parameters, which we call time-varying dispersion INGARCH (tv-DINGARCH) models. More specifically, we consider mixed Poisson INGARCH models and allow for dynamic modeling of the dispersion parameter (as well as the mean), similar to the spirit of the ordinary GARCH models. We derive conditions to obtain first and second-order stationarity, and ergodicity as well. Estimation of the parameters is addressed and their associated asymptotic properties are established as well. A restricted bootstrap procedure is proposed for testing constant dispersion against time-varying dispersion. Monte Carlo simulation studies are presented for checking point estimation, standard errors, and the performance of the restricted bootstrap approach. We apply the tv-DINGARCH process to model the weekly number of reported measles infections in North Rhine-Westphalia, Germany, from January 2001 to May 2013, and compare its performance to the ordinary INGARCH approach.