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. © 2023 Informa UK Limited, trading as Taylor & Francis Group.
ABSTRACT
This paper introduces a flexible discrete transmuted record type discrete Burr-Hatke (TRT-DBH) model that seems suitable for handling over-dispersion and equi-dispersion in count data analysis. Further to the elegant properties of the TRT-DBH, we propose, in the time series context, a first-order integer-valued autoregressive process with TRT-DBH distributed innovations [TRBH-INAR(1)]. The moment properties and inferential procedures of this new INAR(1) process are studied. Some Monte Carlo simulation experiments are executed to assess the consistency of the parameters of the TRBH-INAR(1) model. To further motivate its purpose, the TRBH-INAR(1) is applied to analyze the series of the COVID-19 deaths in Netherlands and the series of infected cases due to the Tularaemia disease in Bavaria. The proposed TRBH-INAR(1) model yields superior fitting criteria than other established competitive INAR(1) models in the literature. Further diagnostics related to the residual analysis and forecasting based on the TRBH-INAR(1) model are also discussed. Based on modified Sieve bootstrap predictors, we provide integer forecasts of future death of COVID-19 and infected of Tularemia.