Multiple values-inflated bivariate INAR time series of counts: featuring zero–one inflated Poisson-Lindly case

This study considers multiple values-inflated bivariate integer-valued autoregressive (MV-inflated BINAR) models. It develops the inferential procedures for parameter estimation on this model, which apply to constructing a change point test and outlier detection rule. We first introduce the MV-inflated BINAR model with one parameter exponential family and Poisson-Lindley innovations. Then, we propose a quasi-maximum likelihood estimator (QMLE) and divergence-based estimator featuring minimum density power divergence estimator (MDPDE) for robust estimation. To evaluate the performance of these estimators, we conduct Monte Carlo simulations and demonstrate the adequacy of MDPDE in zero–one inflated models. Real data analysis is also carried out using the number of monthly earthquake cases in the United States.