Zero inflation, zero deflation, overdispersion, and underdispersion are commonly encountered in count time series. To better describe these characteristics of counts, this article introduces a zero-modified geometric first-order integer-valued autoregressive (INAR(1)) model based on the generalized negative binomial thinning operator, which contains dependent zero-inflated geometric counting series. The new model contains the NGINAR(1) model, ZMGINAR(1) model, and GNBINAR(1) model with geometric marginals as special cases. Some statistical properties are studied, and estimates of the model parameters are derived by the Yule–Walker, conditional least squares, and maximum likelihood methods. Asymptotic properties and numerical results of the estimators are also studied. In addition, some test and forecasting problems are addressed. Three real-data examples are given to show the flexibility and practicability of the new model.

中文翻译：

---

用于分析具有多个特征的计数时间序列的零修改几何 INAR(1) 模型

零通货膨胀、零通货紧缩、过度离散和欠离散在计数时间序列中很常见。为了更好地描述计数的这些特征，本文引入了一种基于广义负二项式细化算子的零修正几何一阶整数值自回归（INAR（1））模型，该模型包含相关的零膨胀几何计数序列。新模型包含 NGINAR(1) 模型、ZMGINAR(1) 模型和以几何边缘作为特例的 GNBINAR(1) 模型。研究了一些统计特性，并通过 Yule–Walker、条件最小二乘法和最大似然法推导了模型参数的估计值。还研究了估计量的渐近性质和数值结果。此外，还解决了一些测试和预测问题。