Abstract: Aiming at the modeling problem of overdispersed, zero-and-one inflated integer-valued time series data with interdependent structures between individuals, we proposed a first-order generalized integer-valued autoregressive model with zero-and-one inflated Poisson-Lindley innovation. Firstly, we gave some statistical properties of the model, including expectation, variance, autocovariance, and transition probability. Secondly, the conditional maximum likelihood estimation method was used to estimate the unknown parameters of the model. Finally, the model was applied to a set of real data for fitting, and some evaluation criteria were used to verify the model. The case analysis results show that the model has a good fitting effect.

Key words: integer-valued time series, generalized binomial thinning operator, zero-and-one inflated Poisson-Lindley, conditional maximum likelihood estimation