Time‐Varying Dispersion Integer‐Valued GARCH Models
提出一类允许均值和离散参数同时随时间变化的整数广义自回归条件异方差模型，推导了随机稳定性条件，给出了极大似然估计的渐近分布，并通过德国麻疹病例数据展示了其优于传统模型。
ABSTRACT We introduce a general class of INteger‐valued Generalized AutoRegressive Conditionally Heteroscedastic (INGARCH) processes by allowing simultaneously time‐varying mean and dispersion parameters. We call such models time‐varying dispersion INGARCH (tv‐DINGARCH) models. More specifically, we consider mixed Poisson INGARCH models and allow for dynamic modeling of both mean and dispersion parameters. We derive conditions to obtain stochastic stability of tv‐DINGARCH processes. Additionally, we study maximum likelihood estimation in detail including its asymptotic distribution. 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.