Year: 2026
Type: preprint
Abstract: A unit root makes linear count time series models such as the Poisson INGARCH(1,1) nonstationary. We show that a softplus link changes this. Weiß, Zhu and Hoshiyar (2022) introduced softplus INGARCH models and gave a sufficient condition for stationarity. For Poisson, negative binomial, gamma and related versions of these models, we obtain the necessary and sufficient condition, which allows a unit root. At a stationary unit root, the conditional mean has a power-law tail, and the observations can have infinite variance or long memory. To our knowledge, this is the first stationary unit root established for an INGARCH-type count model. For a fixed softplus scale, the Poisson quasi-maximum likelihood estimator is asymptotically normal both below and at the unit root, including cases with infinite variance. Two applications show that unit-root conclusions can depend on the softplus scale.
Source: arXiv (Cornell University)
Authors: Lu, Yang, Zhu, Fukang
Institutions: Concordia University, Jilin University
Language: English
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G3215492904, G6956711515
OpenAlex ID: W7221945840