A zero-modified geometric INAR(1) model for analyzing count time series with multiple features

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.