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.

翻译：本文提出一类具有时变均值与离散度参数的广义整数值自回归条件异方差过程，称为时变离散度INGARCH模型。具体而言，我们考虑混合泊松INGARCH模型，并借鉴经典GARCH模型的思想，允许离散度参数与均值参数进行动态建模。我们推导了该模型获得一阶与二阶平稳性及遍历性的条件，同时讨论了参数估计问题并建立了相应的渐近性质。为检验离散度时变特性，我们提出一种受限自助法。通过蒙特卡洛模拟研究评估了点估计、标准误及受限自助法的性能。我们将tv-DINGARCH模型应用于2001年1月至2013年5月德国北莱茵-威斯特法伦州每周麻疹感染报告病例数的建模，并与经典INGARCH方法进行了性能比较。