INAR(1) process with Poisson-transmuted record type exponential innovations

Abstract

In their article, Erbayram and Akdoğan (Ricerche di Matematica, 2023) introduced the Poisson-transmuted record type exponential distribution by combining the Poisson and transmuted record type exponential distributions. This article presents a novel approach to modeling time series data using integer-valued time series with binomial thinning framework and the Poisson-transmuted record type exponential distribution as the innovation distribution. This model demonstrates remarkable proficiency in accurately representing over-dispersed integer-valued time series. Under this configuration, which is a flexible and highly dependable choice, the model accurately captures the underlying patterns present in the time series data. A comprehensive analysis of the statistical characteristics of the process is given. The conditional maximum likelihood and conditional least squares methods are employed to estimate the process parameters. The performance of the estimates is meticulously evaluated through extensive simulation studies. Finally, the proposed model is validated using real-time series data and compared against existing models to demonstrate its practical effectiveness.