Local influence analysis in the softplus INGARCH model

In statistical diagnostics, detecting influential observations is pivotal for assessing model fitting. To address parameter restrictions while maintaining necessary properties, the softplus INGARCH model has emerged as an alternative to the INGARCH model and its variants. This paper delves into statistical diagnostics within the softplus INGARCH model using local influence analysis, establishing a framework encompassing first-order diagnostics, second-order diagnostics and stepwise diagnostics. Additionally, we focus on perturbation schemes, refining conventional approaches and offering modifications. To demonstrate the effectiveness and suitability of our proposed methodology, particularly with the inclusion of stepwise diagnostics, we analyze two simulated datasets and two real-world examples. Compared to traditional methods, our approach adeptly handles potential issues such as the “masking effect” and “smearing effect” without necessitating complex calculations.