Abstract
In the present paper, we concentrate on an INAR(1) model with flexible binomial-discrete Poisson Lindley innovations (BDPLINAR(1)), which describes several attractive properties. The applicability of the proposed process is evaluated by the daily counts of the COVID-19 data sets that indicate the superiority of the BDPLINAR(1) model among some competitor models. The model adequacy checking using Pearson residuals indicates that the BDPLINAR(1) model is appropriate for modeling the COVID-19 data. Several forecasting approaches, such as the classic, mode, probability function, and modified Sieve Bootstrap methods, are considered for the COVID-19 data under the BDPLINAR(1) model.