Alternative estimation and forecasting procedures for the integer-valued autoregressive process with dependent geometric counting series are investigated. Some nonparametric estimation methods are applied to estimate the parameters of the model. The performance of the estimators is assessed via simulation study. We investigate an application of the process using COVID-19 data set and illustrate the best performance of the proposed model among some competitive INAR(1) models via the residual analysis and model adequacy. Consequently, the selected model is applied to predict the number of cases of COVID-19 based on the classic and Bayesian approaches.
