On the novel geometric and negative binomial INAR(1) processes
Abstract
Guerrero et al. GBSO propose a novel approach to building first-order integer-valued autoregressive (∈ar1) models based on the concept of thinning. The standard approach requires that the thinning operator be defined first and ∈ar1 models with either a specified marginal (the forward approach) or a specified innovation (the backward approach) are developed. In contrast, the approach in GBSO is to start out by specifying both the marginal distribution of the process and that of its innovation sequence, and then proceed to identify the thinning operator by solving a functional equation. In this article we discuss the connection between the thinning operators the authors obtained for their novel geometric and negative binomial ∈ar1 models and the thinning operator introduced in AB1 and AB2. More specifically, we show that the existence of the two models has been established in AB1 using the forward approach and a different parameterization. In the process, we strenghthen some of the authors' results obtained for the novel geometric ∈ar1 process and we extend their results to the novel negative binomial ∈ar1 process.
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