Robust Bayesian Inference of Dynamic Intervention Two-Pieces Normal Autoregressive Process with Local Influence Analysis

This study’s objective is to introduce a flexible interventional autoregressive process modified based on the random autoregressive coefficient and asymmetric innovations. The transfer function of the proposed process is designed to follow the dynamic step change structure. In interventional analysis, outliers or influential observations have a considerable influence on statistical inference. Hence, we discuss the Bayesian local influence analysis to evaluate the impact of perturbations in response variables, priors, and simultaneous perturbations regarding the Bayes factor assessor. Considering the Markov Chain Monte Carlo samples, the proposed local influences and diagnostic measures can be easily obtained. The real data of the weekly new cases of COVID-19 within the period 2020-03-01 to 2023-12-17 in Greece verifies the effectiveness of the presented methodologies.