Observation-Driven INAR(1) Models with Novel and Flexible Links

Observation-driven integer-valued autoregressive models are widely used for modeling count time series exhibiting dynamic dependence, yet their performance critically depends on the way that thinning probabilities are linked to past observations. Most existing specifications rely on the logit link and may respond excessively to large counts. In this paper, we introduce a class of new observation-driven integer-valued autoregressive models using logarithmic and soft-clipping links that attenuate the influence of large observations. The proposed framework allows for stochastic covariates. Estimation is carried out using conditional maximum likelihood and conditional least squares methods. Simulation studies and two real data applications are used to illustrate the proposed models.